%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV418-1.100 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:25 AM UTC 2025
% Result : Unsatisfiable 48.92s 49.09s
% Output : Proof 50.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV418-1.100 : TPTP v9.0.0. Released v3.5.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:47:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 48.92/49.09 % SZS status Unsatisfiable
% 48.92/49.09 % SZS output start Proof
% 48.92/49.09 tff(trans_type, type, (
% 48.92/49.09 trans: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s42_type, type, (
% 48.92/49.09 s42: $i)).
% 48.92/49.09 tff(s99_type, type, (
% 48.92/49.09 s99: $i)).
% 48.92/49.09 tff(always5_type, type, (
% 48.92/49.09 always5: $i > $o)).
% 48.92/49.09 tff(s43_type, type, (
% 48.92/49.09 s43: $i)).
% 48.92/49.09 tff(s44_type, type, (
% 48.92/49.09 s44: $i)).
% 48.92/49.09 tff(s45_type, type, (
% 48.92/49.09 s45: $i)).
% 48.92/49.09 tff(s46_type, type, (
% 48.92/49.09 s46: $i)).
% 48.92/49.09 tff(s47_type, type, (
% 48.92/49.09 s47: $i)).
% 48.92/49.09 tff(s48_type, type, (
% 48.92/49.09 s48: $i)).
% 48.92/49.09 tff(s49_type, type, (
% 48.92/49.09 s49: $i)).
% 48.92/49.09 tff(s50_type, type, (
% 48.92/49.09 s50: $i)).
% 48.92/49.09 tff(s51_type, type, (
% 48.92/49.09 s51: $i)).
% 48.92/49.09 tff(s52_type, type, (
% 48.92/49.09 s52: $i)).
% 48.92/49.09 tff(s53_type, type, (
% 48.92/49.09 s53: $i)).
% 48.92/49.09 tff(s54_type, type, (
% 48.92/49.09 s54: $i)).
% 48.92/49.09 tff(s55_type, type, (
% 48.92/49.09 s55: $i)).
% 48.92/49.09 tff(s56_type, type, (
% 48.92/49.09 s56: $i)).
% 48.92/49.09 tff(s57_type, type, (
% 48.92/49.09 s57: $i)).
% 48.92/49.09 tff(s58_type, type, (
% 48.92/49.09 s58: $i)).
% 48.92/49.09 tff(s59_type, type, (
% 48.92/49.09 s59: $i)).
% 48.92/49.09 tff(s60_type, type, (
% 48.92/49.09 s60: $i)).
% 48.92/49.09 tff(s61_type, type, (
% 48.92/49.09 s61: $i)).
% 48.92/49.09 tff(s62_type, type, (
% 48.92/49.09 s62: $i)).
% 48.92/49.09 tff(s63_type, type, (
% 48.92/49.09 s63: $i)).
% 48.92/49.09 tff(s64_type, type, (
% 48.92/49.09 s64: $i)).
% 48.92/49.09 tff(s65_type, type, (
% 48.92/49.09 s65: $i)).
% 48.92/49.09 tff(s66_type, type, (
% 48.92/49.09 s66: $i)).
% 48.92/49.09 tff(s67_type, type, (
% 48.92/49.09 s67: $i)).
% 48.92/49.09 tff(s68_type, type, (
% 48.92/49.09 s68: $i)).
% 48.92/49.09 tff(s69_type, type, (
% 48.92/49.09 s69: $i)).
% 48.92/49.09 tff(s70_type, type, (
% 48.92/49.09 s70: $i)).
% 48.92/49.09 tff(s71_type, type, (
% 48.92/49.09 s71: $i)).
% 48.92/49.09 tff(s72_type, type, (
% 48.92/49.09 s72: $i)).
% 48.92/49.09 tff(s73_type, type, (
% 48.92/49.09 s73: $i)).
% 48.92/49.09 tff(s74_type, type, (
% 48.92/49.09 s74: $i)).
% 48.92/49.09 tff(s75_type, type, (
% 48.92/49.09 s75: $i)).
% 48.92/49.09 tff(s76_type, type, (
% 48.92/49.09 s76: $i)).
% 48.92/49.09 tff(s77_type, type, (
% 48.92/49.09 s77: $i)).
% 48.92/49.09 tff(s78_type, type, (
% 48.92/49.09 s78: $i)).
% 48.92/49.09 tff(s79_type, type, (
% 48.92/49.09 s79: $i)).
% 48.92/49.09 tff(s80_type, type, (
% 48.92/49.09 s80: $i)).
% 48.92/49.09 tff(s81_type, type, (
% 48.92/49.09 s81: $i)).
% 48.92/49.09 tff(s82_type, type, (
% 48.92/49.09 s82: $i)).
% 48.92/49.09 tff(s83_type, type, (
% 48.92/49.09 s83: $i)).
% 48.92/49.09 tff(s84_type, type, (
% 48.92/49.09 s84: $i)).
% 48.92/49.09 tff(s85_type, type, (
% 48.92/49.09 s85: $i)).
% 48.92/49.09 tff(s86_type, type, (
% 48.92/49.09 s86: $i)).
% 48.92/49.09 tff(s87_type, type, (
% 48.92/49.09 s87: $i)).
% 48.92/49.09 tff(s88_type, type, (
% 48.92/49.09 s88: $i)).
% 48.92/49.09 tff(s89_type, type, (
% 48.92/49.09 s89: $i)).
% 48.92/49.09 tff(s90_type, type, (
% 48.92/49.09 s90: $i)).
% 48.92/49.09 tff(s91_type, type, (
% 48.92/49.09 s91: $i)).
% 48.92/49.09 tff(s92_type, type, (
% 48.92/49.09 s92: $i)).
% 48.92/49.09 tff(s93_type, type, (
% 48.92/49.09 s93: $i)).
% 48.92/49.09 tff(s94_type, type, (
% 48.92/49.09 s94: $i)).
% 48.92/49.09 tff(s95_type, type, (
% 48.92/49.09 s95: $i)).
% 48.92/49.09 tff(m_counter_cell_v_value_type, type, (
% 48.92/49.09 m_counter_cell_v_value: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s98_type, type, (
% 48.92/49.09 s98: $i)).
% 48.92/49.09 tff(c_bit2_type, type, (
% 48.92/49.09 c_bit2: $i)).
% 48.92/49.09 tff(node1_type, type, (
% 48.92/49.09 node1: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s97_type, type, (
% 48.92/49.09 s97: $i)).
% 48.92/49.09 tff(m_counter_cell_v_carry_in_type, type, (
% 48.92/49.09 m_counter_cell_v_carry_in: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s96_type, type, (
% 48.92/49.09 s96: $i)).
% 48.92/49.09 tff(m_counter_cell_v_carry_out_type, type, (
% 48.92/49.09 m_counter_cell_v_carry_out: ( $i * $i ) > $o)).
% 48.92/49.09 tff(c_bit1_type, type, (
% 48.92/49.09 c_bit1: $i)).
% 48.92/49.09 tff(c_bit0_type, type, (
% 48.92/49.09 c_bit0: $i)).
% 48.92/49.09 tff(node4_type, type, (
% 48.92/49.09 node4: ( $i * $i ) > $o)).
% 48.92/49.09 tff(node2_type, type, (
% 48.92/49.09 node2: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s41_type, type, (
% 48.92/49.09 s41: $i)).
% 48.92/49.09 tff(s40_type, type, (
% 48.92/49.09 s40: $i)).
% 48.92/49.09 tff(s39_type, type, (
% 48.92/49.09 s39: $i)).
% 48.92/49.09 tff(s38_type, type, (
% 48.92/49.09 s38: $i)).
% 48.92/49.09 tff(s37_type, type, (
% 48.92/49.09 s37: $i)).
% 48.92/49.09 tff(s36_type, type, (
% 48.92/49.09 s36: $i)).
% 48.92/49.09 tff(s35_type, type, (
% 48.92/49.09 s35: $i)).
% 48.92/49.09 tff(s34_type, type, (
% 48.92/49.09 s34: $i)).
% 48.92/49.09 tff(s33_type, type, (
% 48.92/49.09 s33: $i)).
% 48.92/49.09 tff(s32_type, type, (
% 48.92/49.09 s32: $i)).
% 48.92/49.09 tff(s31_type, type, (
% 48.92/49.09 s31: $i)).
% 48.92/49.09 tff(s30_type, type, (
% 48.92/49.09 s30: $i)).
% 48.92/49.09 tff(s29_type, type, (
% 48.92/49.09 s29: $i)).
% 48.92/49.09 tff(s28_type, type, (
% 48.92/49.09 s28: $i)).
% 48.92/49.09 tff(s27_type, type, (
% 48.92/49.09 s27: $i)).
% 48.92/49.09 tff(s26_type, type, (
% 48.92/49.09 s26: $i)).
% 48.92/49.09 tff(s25_type, type, (
% 48.92/49.09 s25: $i)).
% 48.92/49.09 tff(s24_type, type, (
% 48.92/49.09 s24: $i)).
% 48.92/49.09 tff(s23_type, type, (
% 48.92/49.09 s23: $i)).
% 48.92/49.09 tff(s22_type, type, (
% 48.92/49.09 s22: $i)).
% 48.92/49.09 tff(s21_type, type, (
% 48.92/49.09 s21: $i)).
% 48.92/49.09 tff(s20_type, type, (
% 48.92/49.09 s20: $i)).
% 48.92/49.09 tff(s19_type, type, (
% 48.92/49.09 s19: $i)).
% 48.92/49.09 tff(s18_type, type, (
% 48.92/49.09 s18: $i)).
% 48.92/49.09 tff(s17_type, type, (
% 48.92/49.09 s17: $i)).
% 48.92/49.09 tff(s16_type, type, (
% 48.92/49.09 s16: $i)).
% 48.92/49.09 tff(s15_type, type, (
% 48.92/49.09 s15: $i)).
% 48.92/49.09 tff(s14_type, type, (
% 48.92/49.09 s14: $i)).
% 48.92/49.09 tff(s13_type, type, (
% 48.92/49.09 s13: $i)).
% 48.92/49.09 tff(s12_type, type, (
% 48.92/49.09 s12: $i)).
% 48.92/49.09 tff(s11_type, type, (
% 48.92/49.09 s11: $i)).
% 48.92/49.09 tff(s10_type, type, (
% 48.92/49.09 s10: $i)).
% 48.92/49.09 tff(s9_type, type, (
% 48.92/49.09 s9: $i)).
% 48.92/49.09 tff(s8_type, type, (
% 48.92/49.09 s8: $i)).
% 48.92/49.09 tff(s7_type, type, (
% 48.92/49.09 s7: $i)).
% 48.92/49.09 tff(node3_type, type, (
% 48.92/49.09 node3: ( $i * $i * $i ) > $o)).
% 48.92/49.09 tff(s6_type, type, (
% 48.92/49.09 s6: $i)).
% 48.92/49.09 tff(succ_type, type, (
% 48.92/49.09 succ: ( $i * $i ) > $o)).
% 48.92/49.09 tff(s5_type, type, (
% 48.92/49.09 s5: $i)).
% 48.92/49.09 tff(s4_type, type, (
% 48.92/49.09 s4: $i)).
% 48.92/49.09 tff(s3_type, type, (
% 48.92/49.09 s3: $i)).
% 48.92/49.09 tff(s2_type, type, (
% 48.92/49.09 s2: $i)).
% 48.92/49.09 tff(s1_type, type, (
% 48.92/49.09 s1: $i)).
% 48.92/49.09 tff(s0_type, type, (
% 48.92/49.09 s0: $i)).
% 48.92/49.09 tff(xuntil7_type, type, (
% 48.92/49.09 xuntil7: $i > $o)).
% 48.92/49.09 tff(until6_type, type, (
% 48.92/49.09 until6: $i > $o)).
% 48.92/49.09 tff(until2p8_type, type, (
% 48.92/49.09 until2p8: $i > $o)).
% 48.92/49.09 tff(xuntil2p9_type, type, (
% 48.92/49.09 xuntil2p9: $i > $o)).
% 48.92/49.09 tff(last_type, type, (
% 48.92/49.09 last: $i > $o)).
% 48.92/49.09 tff(loop_type, type, (
% 48.92/49.09 loop: $o)).
% 48.92/49.09 tff(1,plain,
% 48.92/49.09 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(2,plain,
% 48.92/49.09 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 48.92/49.09 inference(quant_intro,[status(thm)],[1])).
% 48.92/49.09 tff(3,plain,
% 48.92/49.09 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(4,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound101')).
% 48.92/49.09 tff(5,plain,
% 48.92/49.09 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[4, 3])).
% 48.92/49.09 tff(6,plain,(
% 48.92/49.09 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 48.92/49.09 inference(skolemize,[status(sab)],[5])).
% 48.92/49.09 tff(7,plain,
% 48.92/49.09 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[6, 2])).
% 48.92/49.09 tff(8,plain,
% 48.92/49.09 (succ(s6, s7) <=> succ(s6, s7)),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(9,axiom,(succ(s6, s7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound7')).
% 48.92/49.09 tff(10,plain,
% 48.92/49.09 (succ(s6, s7)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[9, 8])).
% 48.92/49.09 tff(11,plain,
% 48.92/49.09 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(12,plain,
% 48.92/49.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(13,plain,
% 48.92/49.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[12, 11])).
% 48.92/49.09 tff(14,plain,
% 48.92/49.09 (trans(s6, s7)),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 48.92/49.09 tff(15,plain,
% 48.92/49.09 (^[Y: $i, I0: $i, X: $i] : refl(((~trans(X, Y)) | node3(I0, X, Y)) <=> ((~trans(X, Y)) | node3(I0, X, Y)))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(16,plain,
% 48.92/49.09 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y)) <=> ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 48.92/49.09 inference(quant_intro,[status(thm)],[15])).
% 48.92/49.09 tff(17,plain,
% 48.92/49.09 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y)) <=> ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(18,axiom,(![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_8')).
% 48.92/49.09 tff(19,plain,
% 48.92/49.09 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[18, 17])).
% 48.92/49.09 tff(20,plain,(
% 48.92/49.09 ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 48.92/49.09 inference(skolemize,[status(sab)],[19])).
% 48.92/49.09 tff(21,plain,
% 48.92/49.09 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[20, 16])).
% 48.92/49.09 tff(22,plain,
% 48.92/49.09 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(23,plain,
% 48.92/49.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(24,plain,
% 48.92/49.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[23, 22])).
% 48.92/49.09 tff(25,plain,
% 48.92/49.09 (node3(c_bit0, s6, s7)),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 48.92/49.09 tff(26,assumption,(m_counter_cell_v_value(c_bit0, s0)), introduced(assumption)).
% 48.92/49.09 tff(27,plain,
% 48.92/49.09 (^[I0: $i] : refl((~m_counter_cell_v_value(I0, s0)) <=> (~m_counter_cell_v_value(I0, s0)))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(28,plain,
% 48.92/49.09 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 48.92/49.09 inference(quant_intro,[status(thm)],[27])).
% 48.92/49.09 tff(29,plain,
% 48.92/49.09 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(30,axiom,(![I0: $i] : (~m_counter_cell_v_value(I0, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_1')).
% 48.92/49.09 tff(31,plain,
% 48.92/49.09 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[30, 29])).
% 48.92/49.09 tff(32,plain,(
% 48.92/49.09 ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 48.92/49.09 inference(skolemize,[status(sab)],[31])).
% 48.92/49.09 tff(33,plain,
% 48.92/49.09 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[32, 28])).
% 48.92/49.09 tff(34,plain,
% 48.92/49.09 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit0, s0))),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(35,plain,
% 48.92/49.09 ($false),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 48.92/49.09 tff(36,plain,(~m_counter_cell_v_value(c_bit0, s0)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.09 tff(37,plain,
% 48.92/49.09 (^[X: $i] : refl(m_counter_cell_v_carry_in(c_bit0, X) <=> m_counter_cell_v_carry_in(c_bit0, X))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(38,plain,
% 48.92/49.09 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 48.92/49.09 inference(quant_intro,[status(thm)],[37])).
% 48.92/49.09 tff(39,plain,
% 48.92/49.09 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(40,axiom,(![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_1')).
% 48.92/49.09 tff(41,plain,
% 48.92/49.09 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[40, 39])).
% 48.92/49.09 tff(42,plain,(
% 48.92/49.09 ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 48.92/49.09 inference(skolemize,[status(sab)],[41])).
% 48.92/49.09 tff(43,plain,
% 48.92/49.09 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[42, 38])).
% 48.92/49.09 tff(44,plain,
% 48.92/49.09 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s0)),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(45,plain,
% 48.92/49.09 (m_counter_cell_v_carry_in(c_bit0, s0)),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[44, 43])).
% 48.92/49.09 tff(46,plain,
% 48.92/49.09 (^[I0: $i, X: $i] : refl(((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(47,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(quant_intro,[status(thm)],[46])).
% 48.92/49.09 tff(48,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(49,plain,
% 48.92/49.09 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> (((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) | (~node1(I0, X))))), rewrite((((~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X)) | (~node1(I0, X))) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))))),
% 48.92/49.09 inference(bind,[status(th)],[])).
% 48.92/49.09 tff(50,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(quant_intro,[status(thm)],[49])).
% 48.92/49.09 tff(51,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | (~m_counter_cell_v_carry_in(I0, X))) | (~node1(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_2')).
% 48.92/49.09 tff(52,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[51, 50])).
% 48.92/49.09 tff(53,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[52, 48])).
% 48.92/49.09 tff(54,plain,(
% 48.92/49.09 ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(skolemize,[status(sab)],[53])).
% 48.92/49.09 tff(55,plain,
% 48.92/49.09 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[54, 47])).
% 48.92/49.09 tff(56,plain,
% 48.92/49.09 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(57,plain,
% 48.92/49.09 (((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)) <=> (m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(58,plain,
% 48.92/49.09 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0))))),
% 48.92/49.09 inference(monotonicity,[status(thm)],[57])).
% 48.92/49.09 tff(59,plain,
% 48.92/49.09 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)))),
% 48.92/49.09 inference(transitivity,[status(thm)],[58, 56])).
% 48.92/49.09 tff(60,plain,
% 48.92/49.09 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(61,plain,
% 48.92/49.09 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0))),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[60, 59])).
% 48.92/49.09 tff(62,plain,
% 48.92/49.09 (m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0))),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[61, 55, 45])).
% 48.92/49.09 tff(63,plain,
% 48.92/49.09 (~node1(c_bit0, s0)),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[62, 36])).
% 48.92/49.09 tff(64,plain,
% 48.92/49.09 (succ(s0, s1) <=> succ(s0, s1)),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(65,axiom,(succ(s0, s1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound1')).
% 48.92/49.09 tff(66,plain,
% 48.92/49.09 (succ(s0, s1)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[65, 64])).
% 48.92/49.09 tff(67,plain,
% 48.92/49.09 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1))),
% 48.92/49.09 inference(rewrite,[status(thm)],[])).
% 48.92/49.09 tff(68,plain,
% 48.92/49.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 48.92/49.09 inference(quant_inst,[status(thm)],[])).
% 48.92/49.09 tff(69,plain,
% 48.92/49.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 48.92/49.09 inference(modus_ponens,[status(thm)],[68, 67])).
% 48.92/49.09 tff(70,plain,
% 48.92/49.09 (trans(s0, s1)),
% 48.92/49.09 inference(unit_resolution,[status(thm)],[69, 66, 7])).
% 48.92/49.10 tff(71,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(72,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(73,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[72, 71])).
% 48.92/49.10 tff(74,plain,
% 48.92/49.10 (node3(c_bit0, s0, s1)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[73, 21, 70])).
% 48.92/49.10 tff(75,plain,
% 48.92/49.10 (^[Y: $i, I0: $i, X: $i] : refl((node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(76,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[75])).
% 48.92/49.10 tff(77,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(78,plain,
% 48.92/49.10 (^[Y: $i, I0: $i, X: $i] : rewrite(((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y))) <=> (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(79,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : ((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[78])).
% 48.92/49.10 tff(80,axiom,(![Y: $i, I0: $i, X: $i] : ((m_counter_cell_v_value(I0, Y) | node1(I0, X)) | (~node3(I0, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_6')).
% 48.92/49.10 tff(81,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[80, 79])).
% 48.92/49.10 tff(82,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[81, 77])).
% 48.92/49.10 tff(83,plain,(
% 48.92/49.10 ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(skolemize,[status(sab)],[82])).
% 48.92/49.10 tff(84,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[83, 76])).
% 48.92/49.10 tff(85,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(86,plain,
% 48.92/49.10 ((node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1)) <=> (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(87,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[86])).
% 48.92/49.10 tff(88,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[87, 85])).
% 48.92/49.10 tff(89,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(90,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[89, 88])).
% 48.92/49.10 tff(91,plain,
% 48.92/49.10 (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[90, 84, 74])).
% 48.92/49.10 tff(92,plain,
% 48.92/49.10 (m_counter_cell_v_value(c_bit0, s1)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[91, 63])).
% 48.92/49.10 tff(93,plain,
% 48.92/49.10 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s1)),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(94,plain,
% 48.92/49.10 (m_counter_cell_v_carry_in(c_bit0, s1)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[93, 43])).
% 48.92/49.10 tff(95,plain,
% 48.92/49.10 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(96,plain,
% 48.92/49.10 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[95])).
% 48.92/49.10 tff(97,plain,
% 48.92/49.10 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(98,plain,
% 48.92/49.10 (^[I0: $i, X: $i] : trans(monotonicity(rewrite(((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)))), ((((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> (((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X))) | (~node2(I0, X))))), rewrite((((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X))) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))), ((((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(99,plain,
% 48.92/49.10 (![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[98])).
% 48.92/49.10 tff(100,axiom,(![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) | (~node2(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_5')).
% 48.92/49.10 tff(101,plain,
% 48.92/49.10 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[100, 99])).
% 48.92/49.10 tff(102,plain,
% 48.92/49.10 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[101, 97])).
% 48.92/49.10 tff(103,plain,(
% 48.92/49.10 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(skolemize,[status(sab)],[102])).
% 48.92/49.10 tff(104,plain,
% 48.92/49.10 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[103, 96])).
% 48.92/49.10 tff(105,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(106,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(107,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[106, 105])).
% 48.92/49.10 tff(108,plain,
% 48.92/49.10 ((~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[107, 104, 94])).
% 48.92/49.10 tff(109,plain,
% 48.92/49.10 (~node2(c_bit0, s1)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[108, 92])).
% 48.92/49.10 tff(110,plain,
% 48.92/49.10 (succ(s1, s2) <=> succ(s1, s2)),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(111,axiom,(succ(s1, s2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound2')).
% 48.92/49.10 tff(112,plain,
% 48.92/49.10 (succ(s1, s2)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[111, 110])).
% 48.92/49.10 tff(113,plain,
% 48.92/49.10 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(114,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(115,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[114, 113])).
% 48.92/49.10 tff(116,plain,
% 48.92/49.10 (trans(s1, s2)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[115, 112, 7])).
% 48.92/49.10 tff(117,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(118,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(119,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[118, 117])).
% 48.92/49.10 tff(120,plain,
% 48.92/49.10 (node3(c_bit0, s1, s2)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[119, 21, 116])).
% 48.92/49.10 tff(121,plain,
% 48.92/49.10 (^[Y: $i, I0: $i, X: $i] : refl((node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(122,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[121])).
% 48.92/49.10 tff(123,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(124,plain,
% 48.92/49.10 (^[Y: $i, I0: $i, X: $i] : rewrite((((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y))) <=> (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y))))),
% 48.92/49.10 inference(bind,[status(th)],[])).
% 48.92/49.10 tff(125,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y))) <=> ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(quant_intro,[status(thm)],[124])).
% 48.92/49.10 tff(126,axiom,(![Y: $i, I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, Y)) | node2(I0, X)) | (~node3(I0, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_7')).
% 48.92/49.10 tff(127,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[126, 125])).
% 48.92/49.10 tff(128,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[127, 123])).
% 48.92/49.10 tff(129,plain,(
% 48.92/49.10 ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(skolemize,[status(sab)],[128])).
% 48.92/49.10 tff(130,plain,
% 48.92/49.10 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[129, 122])).
% 48.92/49.10 tff(131,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(132,plain,
% 48.92/49.10 ((node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2))) <=> ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(133,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[132])).
% 48.92/49.10 tff(134,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[133, 131])).
% 48.92/49.10 tff(135,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s1) | (~node3(c_bit0, s1, s2)) | (~m_counter_cell_v_value(c_bit0, s2)))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(136,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[135, 134])).
% 48.92/49.10 tff(137,plain,
% 48.92/49.10 ((~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[136, 130, 120])).
% 48.92/49.10 tff(138,plain,
% 48.92/49.10 (~m_counter_cell_v_value(c_bit0, s2)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[137, 109])).
% 48.92/49.10 tff(139,plain,
% 48.92/49.10 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s2)),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(140,plain,
% 48.92/49.10 (m_counter_cell_v_carry_in(c_bit0, s2)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[139, 43])).
% 48.92/49.10 tff(141,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(142,plain,
% 48.92/49.10 (((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2)) <=> (m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(143,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[142])).
% 48.92/49.10 tff(144,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[143, 141])).
% 48.92/49.10 tff(145,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(146,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[145, 144])).
% 48.92/49.10 tff(147,plain,
% 48.92/49.10 (m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2))),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[146, 55, 140])).
% 48.92/49.10 tff(148,plain,
% 48.92/49.10 (~node1(c_bit0, s2)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[147, 138])).
% 48.92/49.10 tff(149,plain,
% 48.92/49.10 (succ(s2, s3) <=> succ(s2, s3)),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(150,axiom,(succ(s2, s3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound3')).
% 48.92/49.10 tff(151,plain,
% 48.92/49.10 (succ(s2, s3)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[150, 149])).
% 48.92/49.10 tff(152,plain,
% 48.92/49.10 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(153,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(154,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[153, 152])).
% 48.92/49.10 tff(155,plain,
% 48.92/49.10 (trans(s2, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[154, 151, 7])).
% 48.92/49.10 tff(156,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(157,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(158,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[157, 156])).
% 48.92/49.10 tff(159,plain,
% 48.92/49.10 (node3(c_bit0, s2, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[158, 21, 155])).
% 48.92/49.10 tff(160,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(161,plain,
% 48.92/49.10 ((node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3)) <=> (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(162,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[161])).
% 48.92/49.10 tff(163,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[162, 160])).
% 48.92/49.10 tff(164,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(165,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[164, 163])).
% 48.92/49.10 tff(166,plain,
% 48.92/49.10 (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[165, 84, 159])).
% 48.92/49.10 tff(167,plain,
% 48.92/49.10 (m_counter_cell_v_value(c_bit0, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[166, 148])).
% 48.92/49.10 tff(168,plain,
% 48.92/49.10 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s3)),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(169,plain,
% 48.92/49.10 (m_counter_cell_v_carry_in(c_bit0, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[168, 43])).
% 48.92/49.10 tff(170,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(171,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(172,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[171, 170])).
% 48.92/49.10 tff(173,plain,
% 48.92/49.10 ((~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[172, 104, 169])).
% 48.92/49.10 tff(174,plain,
% 48.92/49.10 (~node2(c_bit0, s3)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[173, 167])).
% 48.92/49.10 tff(175,plain,
% 48.92/49.10 (succ(s3, s4) <=> succ(s3, s4)),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(176,axiom,(succ(s3, s4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound4')).
% 48.92/49.10 tff(177,plain,
% 48.92/49.10 (succ(s3, s4)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[176, 175])).
% 48.92/49.10 tff(178,plain,
% 48.92/49.10 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(179,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(180,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[179, 178])).
% 48.92/49.10 tff(181,plain,
% 48.92/49.10 (trans(s3, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[180, 177, 7])).
% 48.92/49.10 tff(182,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(183,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(184,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[183, 182])).
% 48.92/49.10 tff(185,plain,
% 48.92/49.10 (node3(c_bit0, s3, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[184, 21, 181])).
% 48.92/49.10 tff(186,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(187,plain,
% 48.92/49.10 ((node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4))) <=> (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(188,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[187])).
% 48.92/49.10 tff(189,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[188, 186])).
% 48.92/49.10 tff(190,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4)))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(191,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4)) | (~node3(c_bit0, s3, s4))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[190, 189])).
% 48.92/49.10 tff(192,plain,
% 48.92/49.10 (node2(c_bit0, s3) | (~m_counter_cell_v_value(c_bit0, s4))),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[191, 130, 185])).
% 48.92/49.10 tff(193,plain,
% 48.92/49.10 (~m_counter_cell_v_value(c_bit0, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[192, 174])).
% 48.92/49.10 tff(194,plain,
% 48.92/49.10 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s4)),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(195,plain,
% 48.92/49.10 (m_counter_cell_v_carry_in(c_bit0, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[194, 43])).
% 48.92/49.10 tff(196,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(197,plain,
% 48.92/49.10 (((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4)) <=> ((~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(198,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4))))),
% 48.92/49.10 inference(monotonicity,[status(thm)],[197])).
% 48.92/49.10 tff(199,plain,
% 48.92/49.10 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4)))),
% 48.92/49.10 inference(transitivity,[status(thm)],[198, 196])).
% 48.92/49.10 tff(200,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(201,plain,
% 48.92/49.10 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4) | (~m_counter_cell_v_carry_in(c_bit0, s4))),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[200, 199])).
% 48.92/49.10 tff(202,plain,
% 48.92/49.10 ((~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[201, 55, 195])).
% 48.92/49.10 tff(203,plain,
% 48.92/49.10 (~node1(c_bit0, s4)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[202, 193])).
% 48.92/49.10 tff(204,plain,
% 48.92/49.10 (succ(s4, s5) <=> succ(s4, s5)),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(205,axiom,(succ(s4, s5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound5')).
% 48.92/49.10 tff(206,plain,
% 48.92/49.10 (succ(s4, s5)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[205, 204])).
% 48.92/49.10 tff(207,plain,
% 48.92/49.10 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(208,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 48.92/49.10 inference(quant_inst,[status(thm)],[])).
% 48.92/49.10 tff(209,plain,
% 48.92/49.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 48.92/49.10 inference(modus_ponens,[status(thm)],[208, 207])).
% 48.92/49.10 tff(210,plain,
% 48.92/49.10 (trans(s4, s5)),
% 48.92/49.10 inference(unit_resolution,[status(thm)],[209, 206, 7])).
% 48.92/49.10 tff(211,plain,
% 48.92/49.10 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 48.92/49.10 inference(rewrite,[status(thm)],[])).
% 48.92/49.10 tff(212,plain,
% 48.92/49.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(213,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[212, 211])).
% 48.92/49.11 tff(214,plain,
% 48.92/49.11 (node3(c_bit0, s4, s5)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[213, 21, 210])).
% 48.92/49.11 tff(215,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(216,plain,
% 48.92/49.11 ((node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5)) <=> (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(217,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[216])).
% 48.92/49.11 tff(218,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[217, 215])).
% 48.92/49.11 tff(219,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(220,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[219, 218])).
% 48.92/49.11 tff(221,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[220, 84, 214])).
% 48.92/49.11 tff(222,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s5)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[221, 203])).
% 48.92/49.11 tff(223,assumption,(~m_counter_cell_v_carry_in(c_bit0, s5)), introduced(assumption)).
% 48.92/49.11 tff(224,plain,
% 48.92/49.11 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s5)),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(225,plain,
% 48.92/49.11 ($false),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[224, 43, 223])).
% 48.92/49.11 tff(226,plain,(m_counter_cell_v_carry_in(c_bit0, s5)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.11 tff(227,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(228,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(229,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[228, 227])).
% 48.92/49.11 tff(230,plain,
% 48.92/49.11 ((~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[229, 104, 226])).
% 48.92/49.11 tff(231,plain,
% 48.92/49.11 (~node2(c_bit0, s5)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[230, 222])).
% 48.92/49.11 tff(232,plain,
% 48.92/49.11 (succ(s5, s6) <=> succ(s5, s6)),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(233,axiom,(succ(s5, s6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound6')).
% 48.92/49.11 tff(234,plain,
% 48.92/49.11 (succ(s5, s6)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[233, 232])).
% 48.92/49.11 tff(235,plain,
% 48.92/49.11 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(236,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(237,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[236, 235])).
% 48.92/49.11 tff(238,plain,
% 48.92/49.11 (trans(s5, s6)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[237, 234, 7])).
% 48.92/49.11 tff(239,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(240,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(241,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[240, 239])).
% 48.92/49.11 tff(242,plain,
% 48.92/49.11 (node3(c_bit0, s5, s6)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[241, 21, 238])).
% 48.92/49.11 tff(243,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(244,plain,
% 48.92/49.11 ((node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6))) <=> ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(245,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[244])).
% 48.92/49.11 tff(246,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[245, 243])).
% 48.92/49.11 tff(247,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6)))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(248,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[247, 246])).
% 48.92/49.11 tff(249,plain,
% 48.92/49.11 ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[248, 130, 242])).
% 48.92/49.11 tff(250,plain,
% 48.92/49.11 (~m_counter_cell_v_value(c_bit0, s6)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[249, 231])).
% 48.92/49.11 tff(251,assumption,(~m_counter_cell_v_carry_in(c_bit0, s6)), introduced(assumption)).
% 48.92/49.11 tff(252,plain,
% 48.92/49.11 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s6)),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(253,plain,
% 48.92/49.11 ($false),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[252, 43, 251])).
% 48.92/49.11 tff(254,plain,(m_counter_cell_v_carry_in(c_bit0, s6)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.11 tff(255,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(256,plain,
% 48.92/49.11 (((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(257,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[256])).
% 48.92/49.11 tff(258,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[257, 255])).
% 48.92/49.11 tff(259,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(260,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[259, 258])).
% 48.92/49.11 tff(261,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[260, 55, 254])).
% 48.92/49.11 tff(262,plain,
% 48.92/49.11 (~node1(c_bit0, s6)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[261, 250])).
% 48.92/49.11 tff(263,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(264,plain,
% 48.92/49.11 ((node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7)) <=> (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(265,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[264])).
% 48.92/49.11 tff(266,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[265, 263])).
% 48.92/49.11 tff(267,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(268,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[267, 266])).
% 48.92/49.11 tff(269,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s7)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[268, 84, 262, 25])).
% 48.92/49.11 tff(270,assumption,(~m_counter_cell_v_carry_in(c_bit0, s7)), introduced(assumption)).
% 48.92/49.11 tff(271,plain,
% 48.92/49.11 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s7)),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(272,plain,
% 48.92/49.11 ($false),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[271, 43, 270])).
% 48.92/49.11 tff(273,plain,(m_counter_cell_v_carry_in(c_bit0, s7)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.11 tff(274,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(275,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(276,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[275, 274])).
% 48.92/49.11 tff(277,plain,
% 48.92/49.11 ((~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[276, 104, 273])).
% 48.92/49.11 tff(278,plain,
% 48.92/49.11 (~node2(c_bit0, s7)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[277, 269])).
% 48.92/49.11 tff(279,plain,
% 48.92/49.11 (succ(s7, s8) <=> succ(s7, s8)),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(280,axiom,(succ(s7, s8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound8')).
% 48.92/49.11 tff(281,plain,
% 48.92/49.11 (succ(s7, s8)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[280, 279])).
% 48.92/49.11 tff(282,plain,
% 48.92/49.11 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(283,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(284,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[283, 282])).
% 48.92/49.11 tff(285,plain,
% 48.92/49.11 (trans(s7, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[284, 281, 7])).
% 48.92/49.11 tff(286,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(287,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(288,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[287, 286])).
% 48.92/49.11 tff(289,plain,
% 48.92/49.11 (node3(c_bit0, s7, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[288, 21, 285])).
% 48.92/49.11 tff(290,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(291,plain,
% 48.92/49.11 ((node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8))) <=> ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(292,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[291])).
% 48.92/49.11 tff(293,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[292, 290])).
% 48.92/49.11 tff(294,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s7) | (~node3(c_bit0, s7, s8)) | (~m_counter_cell_v_value(c_bit0, s8)))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(295,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[294, 293])).
% 48.92/49.11 tff(296,plain,
% 48.92/49.11 ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[295, 130, 289])).
% 48.92/49.11 tff(297,plain,
% 48.92/49.11 (~m_counter_cell_v_value(c_bit0, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[296, 278])).
% 48.92/49.11 tff(298,plain,
% 48.92/49.11 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s8)),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(299,plain,
% 48.92/49.11 (m_counter_cell_v_carry_in(c_bit0, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[298, 43])).
% 48.92/49.11 tff(300,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(301,plain,
% 48.92/49.11 (((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(302,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[301])).
% 48.92/49.11 tff(303,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[302, 300])).
% 48.92/49.11 tff(304,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(305,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[304, 303])).
% 48.92/49.11 tff(306,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[305, 55, 299])).
% 48.92/49.11 tff(307,plain,
% 48.92/49.11 (~node1(c_bit0, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[306, 297])).
% 48.92/49.11 tff(308,plain,
% 48.92/49.11 (succ(s8, s9) <=> succ(s8, s9)),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(309,axiom,(succ(s8, s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound9')).
% 48.92/49.11 tff(310,plain,
% 48.92/49.11 (succ(s8, s9)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[309, 308])).
% 48.92/49.11 tff(311,plain,
% 48.92/49.11 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(312,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(313,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[312, 311])).
% 48.92/49.11 tff(314,plain,
% 48.92/49.11 (trans(s8, s9)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[313, 310, 7])).
% 48.92/49.11 tff(315,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(316,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(317,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[316, 315])).
% 48.92/49.11 tff(318,plain,
% 48.92/49.11 (node3(c_bit0, s8, s9)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[317, 21, 314])).
% 48.92/49.11 tff(319,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(320,plain,
% 48.92/49.11 ((node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9)) <=> (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(321,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[320])).
% 48.92/49.11 tff(322,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[321, 319])).
% 48.92/49.11 tff(323,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s8) | (~node3(c_bit0, s8, s9)) | m_counter_cell_v_value(c_bit0, s9))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(324,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[323, 322])).
% 48.92/49.11 tff(325,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[324, 84, 318])).
% 48.92/49.11 tff(326,plain,
% 48.92/49.11 (m_counter_cell_v_value(c_bit0, s9)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[325, 307])).
% 48.92/49.11 tff(327,plain,
% 48.92/49.11 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s9)),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(328,plain,
% 48.92/49.11 (m_counter_cell_v_carry_in(c_bit0, s9)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[327, 43])).
% 48.92/49.11 tff(329,plain,
% 48.92/49.11 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(330,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(331,plain,
% 48.92/49.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[330, 329])).
% 48.92/49.11 tff(332,plain,
% 48.92/49.11 ((~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[331, 104, 328])).
% 48.92/49.11 tff(333,plain,
% 48.92/49.11 (~node2(c_bit0, s9)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[332, 326])).
% 48.92/49.11 tff(334,plain,
% 48.92/49.11 (succ(s9, s10) <=> succ(s9, s10)),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(335,axiom,(succ(s9, s10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound10')).
% 48.92/49.11 tff(336,plain,
% 48.92/49.11 (succ(s9, s10)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[335, 334])).
% 48.92/49.11 tff(337,plain,
% 48.92/49.11 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(338,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(339,plain,
% 48.92/49.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[338, 337])).
% 48.92/49.11 tff(340,plain,
% 48.92/49.11 (trans(s9, s10)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[339, 336, 7])).
% 48.92/49.11 tff(341,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(342,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 48.92/49.11 inference(quant_inst,[status(thm)],[])).
% 48.92/49.11 tff(343,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10)),
% 48.92/49.11 inference(modus_ponens,[status(thm)],[342, 341])).
% 48.92/49.11 tff(344,plain,
% 48.92/49.11 (node3(c_bit0, s9, s10)),
% 48.92/49.11 inference(unit_resolution,[status(thm)],[343, 21, 340])).
% 48.92/49.11 tff(345,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(346,plain,
% 48.92/49.11 ((node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10))) <=> ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 48.92/49.11 inference(rewrite,[status(thm)],[])).
% 48.92/49.11 tff(347,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10))))),
% 48.92/49.11 inference(monotonicity,[status(thm)],[346])).
% 48.92/49.11 tff(348,plain,
% 48.92/49.11 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)))),
% 48.92/49.11 inference(transitivity,[status(thm)],[347, 345])).
% 48.92/49.11 tff(349,plain,
% 48.92/49.11 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s9) | (~node3(c_bit0, s9, s10)) | (~m_counter_cell_v_value(c_bit0, s10)))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(350,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9) | (~node3(c_bit0, s9, s10))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[349, 348])).
% 48.92/49.12 tff(351,plain,
% 48.92/49.12 ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[350, 130, 344])).
% 48.92/49.12 tff(352,plain,
% 48.92/49.12 (~m_counter_cell_v_value(c_bit0, s10)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[351, 333])).
% 48.92/49.12 tff(353,assumption,(~m_counter_cell_v_carry_in(c_bit0, s10)), introduced(assumption)).
% 48.92/49.12 tff(354,plain,
% 48.92/49.12 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s10)),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(355,plain,
% 48.92/49.12 ($false),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[354, 43, 353])).
% 48.92/49.12 tff(356,plain,(m_counter_cell_v_carry_in(c_bit0, s10)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.12 tff(357,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(358,plain,
% 48.92/49.12 (((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(359,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[358])).
% 48.92/49.12 tff(360,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[359, 357])).
% 48.92/49.12 tff(361,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(362,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[361, 360])).
% 48.92/49.12 tff(363,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[362, 55, 356])).
% 48.92/49.12 tff(364,plain,
% 48.92/49.12 (~node1(c_bit0, s10)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[363, 352])).
% 48.92/49.12 tff(365,plain,
% 48.92/49.12 (succ(s10, s11) <=> succ(s10, s11)),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(366,axiom,(succ(s10, s11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound11')).
% 48.92/49.12 tff(367,plain,
% 48.92/49.12 (succ(s10, s11)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[366, 365])).
% 48.92/49.12 tff(368,plain,
% 48.92/49.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(369,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(370,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[369, 368])).
% 48.92/49.12 tff(371,plain,
% 48.92/49.12 (trans(s10, s11)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[370, 367, 7])).
% 48.92/49.12 tff(372,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(373,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(374,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[373, 372])).
% 48.92/49.12 tff(375,plain,
% 48.92/49.12 (node3(c_bit0, s10, s11)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[374, 21, 371])).
% 48.92/49.12 tff(376,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(377,plain,
% 48.92/49.12 ((node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11)) <=> (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(378,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[377])).
% 48.92/49.12 tff(379,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[378, 376])).
% 48.92/49.12 tff(380,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s10) | (~node3(c_bit0, s10, s11)) | m_counter_cell_v_value(c_bit0, s11))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(381,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[380, 379])).
% 48.92/49.12 tff(382,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[381, 84, 375])).
% 48.92/49.12 tff(383,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s11)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[382, 364])).
% 48.92/49.12 tff(384,assumption,(~m_counter_cell_v_carry_in(c_bit0, s11)), introduced(assumption)).
% 48.92/49.12 tff(385,plain,
% 48.92/49.12 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s11)),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(386,plain,
% 48.92/49.12 ($false),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[385, 43, 384])).
% 48.92/49.12 tff(387,plain,(m_counter_cell_v_carry_in(c_bit0, s11)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.12 tff(388,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(389,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(390,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[389, 388])).
% 48.92/49.12 tff(391,plain,
% 48.92/49.12 ((~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[390, 104, 387])).
% 48.92/49.12 tff(392,plain,
% 48.92/49.12 (~node2(c_bit0, s11)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[391, 383])).
% 48.92/49.12 tff(393,plain,
% 48.92/49.12 (succ(s11, s12) <=> succ(s11, s12)),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(394,axiom,(succ(s11, s12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound12')).
% 48.92/49.12 tff(395,plain,
% 48.92/49.12 (succ(s11, s12)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[394, 393])).
% 48.92/49.12 tff(396,plain,
% 48.92/49.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(397,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(398,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[397, 396])).
% 48.92/49.12 tff(399,plain,
% 48.92/49.12 (trans(s11, s12)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[398, 395, 7])).
% 48.92/49.12 tff(400,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(401,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(402,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[401, 400])).
% 48.92/49.12 tff(403,plain,
% 48.92/49.12 (node3(c_bit0, s11, s12)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[402, 21, 399])).
% 48.92/49.12 tff(404,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(405,plain,
% 48.92/49.12 ((node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12))) <=> ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(406,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[405])).
% 48.92/49.12 tff(407,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[406, 404])).
% 48.92/49.12 tff(408,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s11) | (~node3(c_bit0, s11, s12)) | (~m_counter_cell_v_value(c_bit0, s12)))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(409,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11) | (~node3(c_bit0, s11, s12))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[408, 407])).
% 48.92/49.12 tff(410,plain,
% 48.92/49.12 ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[409, 130, 403])).
% 48.92/49.12 tff(411,plain,
% 48.92/49.12 (~m_counter_cell_v_value(c_bit0, s12)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[410, 392])).
% 48.92/49.12 tff(412,assumption,(~m_counter_cell_v_carry_in(c_bit0, s12)), introduced(assumption)).
% 48.92/49.12 tff(413,plain,
% 48.92/49.12 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s12)),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(414,plain,
% 48.92/49.12 ($false),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[413, 43, 412])).
% 48.92/49.12 tff(415,plain,(m_counter_cell_v_carry_in(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.12 tff(416,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(417,plain,
% 48.92/49.12 (((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(418,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[417])).
% 48.92/49.12 tff(419,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[418, 416])).
% 48.92/49.12 tff(420,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(421,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[420, 419])).
% 48.92/49.12 tff(422,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[421, 55, 415])).
% 48.92/49.12 tff(423,plain,
% 48.92/49.12 (~node1(c_bit0, s12)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[422, 411])).
% 48.92/49.12 tff(424,plain,
% 48.92/49.12 (succ(s12, s13) <=> succ(s12, s13)),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(425,axiom,(succ(s12, s13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound13')).
% 48.92/49.12 tff(426,plain,
% 48.92/49.12 (succ(s12, s13)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[425, 424])).
% 48.92/49.12 tff(427,plain,
% 48.92/49.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(428,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(429,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[428, 427])).
% 48.92/49.12 tff(430,plain,
% 48.92/49.12 (trans(s12, s13)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[429, 426, 7])).
% 48.92/49.12 tff(431,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(432,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(433,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[432, 431])).
% 48.92/49.12 tff(434,plain,
% 48.92/49.12 (node3(c_bit0, s12, s13)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[433, 21, 430])).
% 48.92/49.12 tff(435,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(436,plain,
% 48.92/49.12 ((node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13)) <=> (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(437,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[436])).
% 48.92/49.12 tff(438,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[437, 435])).
% 48.92/49.12 tff(439,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s12) | (~node3(c_bit0, s12, s13)) | m_counter_cell_v_value(c_bit0, s13))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(440,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[439, 438])).
% 48.92/49.12 tff(441,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[440, 84, 434])).
% 48.92/49.12 tff(442,plain,
% 48.92/49.12 (m_counter_cell_v_value(c_bit0, s13)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[441, 423])).
% 48.92/49.12 tff(443,assumption,(~m_counter_cell_v_carry_in(c_bit0, s13)), introduced(assumption)).
% 48.92/49.12 tff(444,plain,
% 48.92/49.12 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s13)),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(445,plain,
% 48.92/49.12 ($false),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[444, 43, 443])).
% 48.92/49.12 tff(446,plain,(m_counter_cell_v_carry_in(c_bit0, s13)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.12 tff(447,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(448,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(449,plain,
% 48.92/49.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[448, 447])).
% 48.92/49.12 tff(450,plain,
% 48.92/49.12 ((~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[449, 104, 446])).
% 48.92/49.12 tff(451,plain,
% 48.92/49.12 (~node2(c_bit0, s13)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[450, 442])).
% 48.92/49.12 tff(452,plain,
% 48.92/49.12 (succ(s13, s14) <=> succ(s13, s14)),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(453,axiom,(succ(s13, s14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound14')).
% 48.92/49.12 tff(454,plain,
% 48.92/49.12 (succ(s13, s14)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[453, 452])).
% 48.92/49.12 tff(455,plain,
% 48.92/49.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(456,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(457,plain,
% 48.92/49.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[456, 455])).
% 48.92/49.12 tff(458,plain,
% 48.92/49.12 (trans(s13, s14)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[457, 454, 7])).
% 48.92/49.12 tff(459,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(460,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(461,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14)),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[460, 459])).
% 48.92/49.12 tff(462,plain,
% 48.92/49.12 (node3(c_bit0, s13, s14)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[461, 21, 458])).
% 48.92/49.12 tff(463,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(464,plain,
% 48.92/49.12 ((node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14))) <=> ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(465,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[464])).
% 48.92/49.12 tff(466,plain,
% 48.92/49.12 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)))),
% 48.92/49.12 inference(transitivity,[status(thm)],[465, 463])).
% 48.92/49.12 tff(467,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s13) | (~node3(c_bit0, s13, s14)) | (~m_counter_cell_v_value(c_bit0, s14)))),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(468,plain,
% 48.92/49.12 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14))),
% 48.92/49.12 inference(modus_ponens,[status(thm)],[467, 466])).
% 48.92/49.12 tff(469,plain,
% 48.92/49.12 ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[468, 130, 462])).
% 48.92/49.12 tff(470,plain,
% 48.92/49.12 (~m_counter_cell_v_value(c_bit0, s14)),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[469, 451])).
% 48.92/49.12 tff(471,assumption,(~m_counter_cell_v_carry_in(c_bit0, s14)), introduced(assumption)).
% 48.92/49.12 tff(472,plain,
% 48.92/49.12 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s14)),
% 48.92/49.12 inference(quant_inst,[status(thm)],[])).
% 48.92/49.12 tff(473,plain,
% 48.92/49.12 ($false),
% 48.92/49.12 inference(unit_resolution,[status(thm)],[472, 43, 471])).
% 48.92/49.12 tff(474,plain,(m_counter_cell_v_carry_in(c_bit0, s14)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.12 tff(475,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(476,plain,
% 48.92/49.12 (((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 48.92/49.12 inference(rewrite,[status(thm)],[])).
% 48.92/49.12 tff(477,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))))),
% 48.92/49.12 inference(monotonicity,[status(thm)],[476])).
% 48.92/49.12 tff(478,plain,
% 48.92/49.12 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[477, 475])).
% 48.92/49.13 tff(479,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(480,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[479, 478])).
% 48.92/49.13 tff(481,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[480, 55, 474])).
% 48.92/49.13 tff(482,plain,
% 48.92/49.13 (~node1(c_bit0, s14)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[481, 470])).
% 48.92/49.13 tff(483,plain,
% 48.92/49.13 (succ(s14, s15) <=> succ(s14, s15)),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(484,axiom,(succ(s14, s15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound15')).
% 48.92/49.13 tff(485,plain,
% 48.92/49.13 (succ(s14, s15)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[484, 483])).
% 48.92/49.13 tff(486,plain,
% 48.92/49.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(487,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(488,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[487, 486])).
% 48.92/49.13 tff(489,plain,
% 48.92/49.13 (trans(s14, s15)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[488, 485, 7])).
% 48.92/49.13 tff(490,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(491,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(492,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[491, 490])).
% 48.92/49.13 tff(493,plain,
% 48.92/49.13 (node3(c_bit0, s14, s15)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[492, 21, 489])).
% 48.92/49.13 tff(494,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(495,plain,
% 48.92/49.13 ((node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15)) <=> (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(496,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[495])).
% 48.92/49.13 tff(497,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[496, 494])).
% 48.92/49.13 tff(498,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(499,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[498, 497])).
% 48.92/49.13 tff(500,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[499, 84, 493])).
% 48.92/49.13 tff(501,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s15)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[500, 482])).
% 48.92/49.13 tff(502,assumption,(~m_counter_cell_v_carry_in(c_bit0, s15)), introduced(assumption)).
% 48.92/49.13 tff(503,plain,
% 48.92/49.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s15)),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(504,plain,
% 48.92/49.13 ($false),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[503, 43, 502])).
% 48.92/49.13 tff(505,plain,(m_counter_cell_v_carry_in(c_bit0, s15)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.13 tff(506,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(507,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(508,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[507, 506])).
% 48.92/49.13 tff(509,plain,
% 48.92/49.13 ((~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[508, 104, 505])).
% 48.92/49.13 tff(510,plain,
% 48.92/49.13 (~node2(c_bit0, s15)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[509, 501])).
% 48.92/49.13 tff(511,plain,
% 48.92/49.13 (succ(s15, s16) <=> succ(s15, s16)),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(512,axiom,(succ(s15, s16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound16')).
% 48.92/49.13 tff(513,plain,
% 48.92/49.13 (succ(s15, s16)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[512, 511])).
% 48.92/49.13 tff(514,plain,
% 48.92/49.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(515,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(516,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[515, 514])).
% 48.92/49.13 tff(517,plain,
% 48.92/49.13 (trans(s15, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[516, 513, 7])).
% 48.92/49.13 tff(518,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(519,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(520,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[519, 518])).
% 48.92/49.13 tff(521,plain,
% 48.92/49.13 (node3(c_bit0, s15, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[520, 21, 517])).
% 48.92/49.13 tff(522,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(523,plain,
% 48.92/49.13 ((node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16))) <=> ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(524,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[523])).
% 48.92/49.13 tff(525,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[524, 522])).
% 48.92/49.13 tff(526,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | (~m_counter_cell_v_value(c_bit0, s16)))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(527,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[526, 525])).
% 48.92/49.13 tff(528,plain,
% 48.92/49.13 ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[527, 130, 521])).
% 48.92/49.13 tff(529,plain,
% 48.92/49.13 (~m_counter_cell_v_value(c_bit0, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[528, 510])).
% 48.92/49.13 tff(530,plain,
% 48.92/49.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s16)),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(531,plain,
% 48.92/49.13 (m_counter_cell_v_carry_in(c_bit0, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[530, 43])).
% 48.92/49.13 tff(532,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(533,plain,
% 48.92/49.13 (((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(534,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[533])).
% 48.92/49.13 tff(535,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[534, 532])).
% 48.92/49.13 tff(536,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(537,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[536, 535])).
% 48.92/49.13 tff(538,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[537, 55, 531])).
% 48.92/49.13 tff(539,plain,
% 48.92/49.13 (~node1(c_bit0, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[538, 529])).
% 48.92/49.13 tff(540,plain,
% 48.92/49.13 (succ(s16, s17) <=> succ(s16, s17)),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(541,axiom,(succ(s16, s17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound17')).
% 48.92/49.13 tff(542,plain,
% 48.92/49.13 (succ(s16, s17)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[541, 540])).
% 48.92/49.13 tff(543,plain,
% 48.92/49.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(544,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(545,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[544, 543])).
% 48.92/49.13 tff(546,plain,
% 48.92/49.13 (trans(s16, s17)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[545, 542, 7])).
% 48.92/49.13 tff(547,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(548,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(549,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[548, 547])).
% 48.92/49.13 tff(550,plain,
% 48.92/49.13 (node3(c_bit0, s16, s17)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[549, 21, 546])).
% 48.92/49.13 tff(551,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(552,plain,
% 48.92/49.13 ((node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17)) <=> (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(553,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[552])).
% 48.92/49.13 tff(554,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[553, 551])).
% 48.92/49.13 tff(555,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | m_counter_cell_v_value(c_bit0, s17))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(556,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[555, 554])).
% 48.92/49.13 tff(557,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[556, 84, 550])).
% 48.92/49.13 tff(558,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s17)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[557, 539])).
% 48.92/49.13 tff(559,assumption,(~m_counter_cell_v_carry_in(c_bit0, s17)), introduced(assumption)).
% 48.92/49.13 tff(560,plain,
% 48.92/49.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s17)),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(561,plain,
% 48.92/49.13 ($false),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[560, 43, 559])).
% 48.92/49.13 tff(562,plain,(m_counter_cell_v_carry_in(c_bit0, s17)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.13 tff(563,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(564,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(565,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[564, 563])).
% 48.92/49.13 tff(566,plain,
% 48.92/49.13 ((~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[565, 104, 562])).
% 48.92/49.13 tff(567,plain,
% 48.92/49.13 (~node2(c_bit0, s17)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[566, 558])).
% 48.92/49.13 tff(568,plain,
% 48.92/49.13 (succ(s17, s18) <=> succ(s17, s18)),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(569,axiom,(succ(s17, s18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound18')).
% 48.92/49.13 tff(570,plain,
% 48.92/49.13 (succ(s17, s18)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[569, 568])).
% 48.92/49.13 tff(571,plain,
% 48.92/49.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(572,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(573,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[572, 571])).
% 48.92/49.13 tff(574,plain,
% 48.92/49.13 (trans(s17, s18)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[573, 570, 7])).
% 48.92/49.13 tff(575,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(576,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(577,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[576, 575])).
% 48.92/49.13 tff(578,plain,
% 48.92/49.13 (node3(c_bit0, s17, s18)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[577, 21, 574])).
% 48.92/49.13 tff(579,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(580,plain,
% 48.92/49.13 ((node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18))) <=> ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(581,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[580])).
% 48.92/49.13 tff(582,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[581, 579])).
% 48.92/49.13 tff(583,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s17) | (~node3(c_bit0, s17, s18)) | (~m_counter_cell_v_value(c_bit0, s18)))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(584,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[583, 582])).
% 48.92/49.13 tff(585,plain,
% 48.92/49.13 ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[584, 130, 578])).
% 48.92/49.13 tff(586,plain,
% 48.92/49.13 (~m_counter_cell_v_value(c_bit0, s18)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[585, 567])).
% 48.92/49.13 tff(587,assumption,(~m_counter_cell_v_carry_in(c_bit0, s18)), introduced(assumption)).
% 48.92/49.13 tff(588,plain,
% 48.92/49.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s18)),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(589,plain,
% 48.92/49.13 ($false),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[588, 43, 587])).
% 48.92/49.13 tff(590,plain,(m_counter_cell_v_carry_in(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.13 tff(591,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(592,plain,
% 48.92/49.13 (((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(593,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[592])).
% 48.92/49.13 tff(594,plain,
% 48.92/49.13 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[593, 591])).
% 48.92/49.13 tff(595,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(596,plain,
% 48.92/49.13 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[595, 594])).
% 48.92/49.13 tff(597,plain,
% 48.92/49.13 (m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[596, 55, 590])).
% 48.92/49.13 tff(598,plain,
% 48.92/49.13 (~node1(c_bit0, s18)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[597, 586])).
% 48.92/49.13 tff(599,plain,
% 48.92/49.13 (succ(s18, s19) <=> succ(s18, s19)),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(600,axiom,(succ(s18, s19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound19')).
% 48.92/49.13 tff(601,plain,
% 48.92/49.13 (succ(s18, s19)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[600, 599])).
% 48.92/49.13 tff(602,plain,
% 48.92/49.13 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(603,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(604,plain,
% 48.92/49.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[603, 602])).
% 48.92/49.13 tff(605,plain,
% 48.92/49.13 (trans(s18, s19)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[604, 601, 7])).
% 48.92/49.13 tff(606,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(607,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 48.92/49.13 inference(quant_inst,[status(thm)],[])).
% 48.92/49.13 tff(608,plain,
% 48.92/49.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19)),
% 48.92/49.13 inference(modus_ponens,[status(thm)],[607, 606])).
% 48.92/49.13 tff(609,plain,
% 48.92/49.13 (node3(c_bit0, s18, s19)),
% 48.92/49.13 inference(unit_resolution,[status(thm)],[608, 21, 605])).
% 48.92/49.13 tff(610,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(611,plain,
% 48.92/49.13 ((node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19)) <=> (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 48.92/49.13 inference(rewrite,[status(thm)],[])).
% 48.92/49.13 tff(612,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))))),
% 48.92/49.13 inference(monotonicity,[status(thm)],[611])).
% 48.92/49.13 tff(613,plain,
% 48.92/49.13 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)))),
% 48.92/49.13 inference(transitivity,[status(thm)],[612, 610])).
% 48.92/49.14 tff(614,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s18) | (~node3(c_bit0, s18, s19)) | m_counter_cell_v_value(c_bit0, s19))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(615,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[614, 613])).
% 48.92/49.14 tff(616,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[615, 84, 609])).
% 48.92/49.14 tff(617,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s19)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[616, 598])).
% 48.92/49.14 tff(618,assumption,(~m_counter_cell_v_carry_in(c_bit0, s19)), introduced(assumption)).
% 48.92/49.14 tff(619,plain,
% 48.92/49.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s19)),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(620,plain,
% 48.92/49.14 ($false),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[619, 43, 618])).
% 48.92/49.14 tff(621,plain,(m_counter_cell_v_carry_in(c_bit0, s19)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.14 tff(622,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(623,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(624,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[623, 622])).
% 48.92/49.14 tff(625,plain,
% 48.92/49.14 ((~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[624, 104, 621])).
% 48.92/49.14 tff(626,plain,
% 48.92/49.14 (~node2(c_bit0, s19)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[625, 617])).
% 48.92/49.14 tff(627,plain,
% 48.92/49.14 (succ(s19, s20) <=> succ(s19, s20)),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(628,axiom,(succ(s19, s20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound20')).
% 48.92/49.14 tff(629,plain,
% 48.92/49.14 (succ(s19, s20)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[628, 627])).
% 48.92/49.14 tff(630,plain,
% 48.92/49.14 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(631,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(632,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[631, 630])).
% 48.92/49.14 tff(633,plain,
% 48.92/49.14 (trans(s19, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[632, 629, 7])).
% 48.92/49.14 tff(634,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(635,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(636,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[635, 634])).
% 48.92/49.14 tff(637,plain,
% 48.92/49.14 (node3(c_bit0, s19, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[636, 21, 633])).
% 48.92/49.14 tff(638,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(639,plain,
% 48.92/49.14 ((node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20))) <=> ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(640,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[639])).
% 48.92/49.14 tff(641,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[640, 638])).
% 48.92/49.14 tff(642,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s19) | (~node3(c_bit0, s19, s20)) | (~m_counter_cell_v_value(c_bit0, s20)))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(643,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[642, 641])).
% 48.92/49.14 tff(644,plain,
% 48.92/49.14 ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[643, 130, 637])).
% 48.92/49.14 tff(645,plain,
% 48.92/49.14 (~m_counter_cell_v_value(c_bit0, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[644, 626])).
% 48.92/49.14 tff(646,plain,
% 48.92/49.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s20)),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(647,plain,
% 48.92/49.14 (m_counter_cell_v_carry_in(c_bit0, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[646, 43])).
% 48.92/49.14 tff(648,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(649,plain,
% 48.92/49.14 (((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(650,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[649])).
% 48.92/49.14 tff(651,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[650, 648])).
% 48.92/49.14 tff(652,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(653,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[652, 651])).
% 48.92/49.14 tff(654,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[653, 55, 647])).
% 48.92/49.14 tff(655,plain,
% 48.92/49.14 (~node1(c_bit0, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[654, 645])).
% 48.92/49.14 tff(656,plain,
% 48.92/49.14 (succ(s20, s21) <=> succ(s20, s21)),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(657,axiom,(succ(s20, s21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound21')).
% 48.92/49.14 tff(658,plain,
% 48.92/49.14 (succ(s20, s21)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[657, 656])).
% 48.92/49.14 tff(659,plain,
% 48.92/49.14 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(660,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(661,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[660, 659])).
% 48.92/49.14 tff(662,plain,
% 48.92/49.14 (trans(s20, s21)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[661, 658, 7])).
% 48.92/49.14 tff(663,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(664,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(665,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[664, 663])).
% 48.92/49.14 tff(666,plain,
% 48.92/49.14 (node3(c_bit0, s20, s21)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[665, 21, 662])).
% 48.92/49.14 tff(667,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(668,plain,
% 48.92/49.14 ((node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21)) <=> (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(669,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[668])).
% 48.92/49.14 tff(670,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[669, 667])).
% 48.92/49.14 tff(671,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s20) | (~node3(c_bit0, s20, s21)) | m_counter_cell_v_value(c_bit0, s21))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(672,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[671, 670])).
% 48.92/49.14 tff(673,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[672, 84, 666])).
% 48.92/49.14 tff(674,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s21)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[673, 655])).
% 48.92/49.14 tff(675,assumption,(~m_counter_cell_v_carry_in(c_bit0, s21)), introduced(assumption)).
% 48.92/49.14 tff(676,plain,
% 48.92/49.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s21)),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(677,plain,
% 48.92/49.14 ($false),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[676, 43, 675])).
% 48.92/49.14 tff(678,plain,(m_counter_cell_v_carry_in(c_bit0, s21)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.14 tff(679,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(680,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(681,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[680, 679])).
% 48.92/49.14 tff(682,plain,
% 48.92/49.14 ((~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[681, 104, 678])).
% 48.92/49.14 tff(683,plain,
% 48.92/49.14 (~node2(c_bit0, s21)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[682, 674])).
% 48.92/49.14 tff(684,plain,
% 48.92/49.14 (succ(s21, s22) <=> succ(s21, s22)),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(685,axiom,(succ(s21, s22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound22')).
% 48.92/49.14 tff(686,plain,
% 48.92/49.14 (succ(s21, s22)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[685, 684])).
% 48.92/49.14 tff(687,plain,
% 48.92/49.14 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(688,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(689,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[688, 687])).
% 48.92/49.14 tff(690,plain,
% 48.92/49.14 (trans(s21, s22)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[689, 686, 7])).
% 48.92/49.14 tff(691,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(692,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(693,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[692, 691])).
% 48.92/49.14 tff(694,plain,
% 48.92/49.14 (node3(c_bit0, s21, s22)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[693, 21, 690])).
% 48.92/49.14 tff(695,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(696,plain,
% 48.92/49.14 ((node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22))) <=> ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(697,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[696])).
% 48.92/49.14 tff(698,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[697, 695])).
% 48.92/49.14 tff(699,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s21) | (~node3(c_bit0, s21, s22)) | (~m_counter_cell_v_value(c_bit0, s22)))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(700,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[699, 698])).
% 48.92/49.14 tff(701,plain,
% 48.92/49.14 ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[700, 130, 694])).
% 48.92/49.14 tff(702,plain,
% 48.92/49.14 (~m_counter_cell_v_value(c_bit0, s22)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[701, 683])).
% 48.92/49.14 tff(703,assumption,(~m_counter_cell_v_carry_in(c_bit0, s22)), introduced(assumption)).
% 48.92/49.14 tff(704,plain,
% 48.92/49.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s22)),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(705,plain,
% 48.92/49.14 ($false),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[704, 43, 703])).
% 48.92/49.14 tff(706,plain,(m_counter_cell_v_carry_in(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 48.92/49.14 tff(707,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(708,plain,
% 48.92/49.14 (((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(709,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[708])).
% 48.92/49.14 tff(710,plain,
% 48.92/49.14 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[709, 707])).
% 48.92/49.14 tff(711,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(712,plain,
% 48.92/49.14 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[711, 710])).
% 48.92/49.14 tff(713,plain,
% 48.92/49.14 (m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[712, 55, 706])).
% 48.92/49.14 tff(714,plain,
% 48.92/49.14 (~node1(c_bit0, s22)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[713, 702])).
% 48.92/49.14 tff(715,plain,
% 48.92/49.14 (succ(s22, s23) <=> succ(s22, s23)),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(716,axiom,(succ(s22, s23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound23')).
% 48.92/49.14 tff(717,plain,
% 48.92/49.14 (succ(s22, s23)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[716, 715])).
% 48.92/49.14 tff(718,plain,
% 48.92/49.14 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(719,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(720,plain,
% 48.92/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[719, 718])).
% 48.92/49.14 tff(721,plain,
% 48.92/49.14 (trans(s22, s23)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[720, 717, 7])).
% 48.92/49.14 tff(722,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(723,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(724,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23)),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[723, 722])).
% 48.92/49.14 tff(725,plain,
% 48.92/49.14 (node3(c_bit0, s22, s23)),
% 48.92/49.14 inference(unit_resolution,[status(thm)],[724, 21, 721])).
% 48.92/49.14 tff(726,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(727,plain,
% 48.92/49.14 ((node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23)) <=> (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 48.92/49.14 inference(rewrite,[status(thm)],[])).
% 48.92/49.14 tff(728,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23))))),
% 48.92/49.14 inference(monotonicity,[status(thm)],[727])).
% 48.92/49.14 tff(729,plain,
% 48.92/49.14 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)))),
% 48.92/49.14 inference(transitivity,[status(thm)],[728, 726])).
% 48.92/49.14 tff(730,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s22) | (~node3(c_bit0, s22, s23)) | m_counter_cell_v_value(c_bit0, s23))),
% 48.92/49.14 inference(quant_inst,[status(thm)],[])).
% 48.92/49.14 tff(731,plain,
% 48.92/49.14 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23))),
% 48.92/49.14 inference(modus_ponens,[status(thm)],[730, 729])).
% 48.98/49.14 tff(732,plain,
% 48.98/49.14 (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22)),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[731, 84, 725])).
% 48.98/49.14 tff(733,plain,
% 48.98/49.14 (m_counter_cell_v_value(c_bit0, s23)),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[732, 714])).
% 48.98/49.14 tff(734,assumption,(~m_counter_cell_v_carry_in(c_bit0, s23)), introduced(assumption)).
% 48.98/49.14 tff(735,plain,
% 48.98/49.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s23)),
% 48.98/49.14 inference(quant_inst,[status(thm)],[])).
% 48.98/49.14 tff(736,plain,
% 48.98/49.14 ($false),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[735, 43, 734])).
% 48.98/49.14 tff(737,plain,(m_counter_cell_v_carry_in(c_bit0, s23)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.14 tff(738,plain,
% 48.98/49.14 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))),
% 48.98/49.14 inference(rewrite,[status(thm)],[])).
% 48.98/49.14 tff(739,plain,
% 48.98/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))),
% 48.98/49.14 inference(quant_inst,[status(thm)],[])).
% 48.98/49.14 tff(740,plain,
% 48.98/49.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 48.98/49.14 inference(modus_ponens,[status(thm)],[739, 738])).
% 48.98/49.14 tff(741,plain,
% 48.98/49.14 ((~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[740, 104, 737])).
% 48.98/49.14 tff(742,plain,
% 48.98/49.14 (~node2(c_bit0, s23)),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[741, 733])).
% 48.98/49.14 tff(743,plain,
% 48.98/49.14 (succ(s23, s24) <=> succ(s23, s24)),
% 48.98/49.14 inference(rewrite,[status(thm)],[])).
% 48.98/49.14 tff(744,axiom,(succ(s23, s24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound24')).
% 48.98/49.14 tff(745,plain,
% 48.98/49.14 (succ(s23, s24)),
% 48.98/49.14 inference(modus_ponens,[status(thm)],[744, 743])).
% 48.98/49.14 tff(746,plain,
% 48.98/49.14 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24))),
% 48.98/49.14 inference(rewrite,[status(thm)],[])).
% 48.98/49.14 tff(747,plain,
% 48.98/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 48.98/49.14 inference(quant_inst,[status(thm)],[])).
% 48.98/49.14 tff(748,plain,
% 48.98/49.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 48.98/49.14 inference(modus_ponens,[status(thm)],[747, 746])).
% 48.98/49.14 tff(749,plain,
% 48.98/49.14 (trans(s23, s24)),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[748, 745, 7])).
% 48.98/49.14 tff(750,plain,
% 48.98/49.14 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 48.98/49.14 inference(rewrite,[status(thm)],[])).
% 48.98/49.14 tff(751,plain,
% 48.98/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 48.98/49.14 inference(quant_inst,[status(thm)],[])).
% 48.98/49.14 tff(752,plain,
% 48.98/49.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24)),
% 48.98/49.14 inference(modus_ponens,[status(thm)],[751, 750])).
% 48.98/49.14 tff(753,plain,
% 48.98/49.14 (node3(c_bit0, s23, s24)),
% 48.98/49.14 inference(unit_resolution,[status(thm)],[752, 21, 749])).
% 48.98/49.14 tff(754,plain,
% 48.98/49.14 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(755,plain,
% 48.98/49.15 ((node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24))) <=> ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(756,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[755])).
% 48.98/49.15 tff(757,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[756, 754])).
% 48.98/49.15 tff(758,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(759,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[758, 757])).
% 48.98/49.15 tff(760,plain,
% 48.98/49.15 ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[759, 130, 753])).
% 48.98/49.15 tff(761,plain,
% 48.98/49.15 (~m_counter_cell_v_value(c_bit0, s24)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[760, 742])).
% 48.98/49.15 tff(762,assumption,(~m_counter_cell_v_carry_in(c_bit0, s24)), introduced(assumption)).
% 48.98/49.15 tff(763,plain,
% 48.98/49.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s24)),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(764,plain,
% 48.98/49.15 ($false),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[763, 43, 762])).
% 48.98/49.15 tff(765,plain,(m_counter_cell_v_carry_in(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.15 tff(766,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(767,plain,
% 48.98/49.15 (((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(768,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[767])).
% 48.98/49.15 tff(769,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[768, 766])).
% 48.98/49.15 tff(770,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(771,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[770, 769])).
% 48.98/49.15 tff(772,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[771, 55, 765])).
% 48.98/49.15 tff(773,plain,
% 48.98/49.15 (~node1(c_bit0, s24)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[772, 761])).
% 48.98/49.15 tff(774,plain,
% 48.98/49.15 (succ(s24, s25) <=> succ(s24, s25)),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(775,axiom,(succ(s24, s25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound25')).
% 48.98/49.15 tff(776,plain,
% 48.98/49.15 (succ(s24, s25)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[775, 774])).
% 48.98/49.15 tff(777,plain,
% 48.98/49.15 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(778,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(779,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[778, 777])).
% 48.98/49.15 tff(780,plain,
% 48.98/49.15 (trans(s24, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[779, 776, 7])).
% 48.98/49.15 tff(781,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(782,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(783,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[782, 781])).
% 48.98/49.15 tff(784,plain,
% 48.98/49.15 (node3(c_bit0, s24, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[783, 21, 780])).
% 48.98/49.15 tff(785,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(786,plain,
% 48.98/49.15 ((node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25)) <=> (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(787,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[786])).
% 48.98/49.15 tff(788,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[787, 785])).
% 48.98/49.15 tff(789,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s24) | (~node3(c_bit0, s24, s25)) | m_counter_cell_v_value(c_bit0, s25))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(790,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[789, 788])).
% 48.98/49.15 tff(791,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[790, 84, 784])).
% 48.98/49.15 tff(792,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[791, 773])).
% 48.98/49.15 tff(793,plain,
% 48.98/49.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s25)),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(794,plain,
% 48.98/49.15 (m_counter_cell_v_carry_in(c_bit0, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[793, 43])).
% 48.98/49.15 tff(795,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(796,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(797,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[796, 795])).
% 48.98/49.15 tff(798,plain,
% 48.98/49.15 ((~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[797, 104, 794])).
% 48.98/49.15 tff(799,plain,
% 48.98/49.15 (~node2(c_bit0, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[798, 792])).
% 48.98/49.15 tff(800,plain,
% 48.98/49.15 (succ(s25, s26) <=> succ(s25, s26)),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(801,axiom,(succ(s25, s26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound26')).
% 48.98/49.15 tff(802,plain,
% 48.98/49.15 (succ(s25, s26)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[801, 800])).
% 48.98/49.15 tff(803,plain,
% 48.98/49.15 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(804,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(805,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[804, 803])).
% 48.98/49.15 tff(806,plain,
% 48.98/49.15 (trans(s25, s26)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[805, 802, 7])).
% 48.98/49.15 tff(807,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(808,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(809,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[808, 807])).
% 48.98/49.15 tff(810,plain,
% 48.98/49.15 (node3(c_bit0, s25, s26)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[809, 21, 806])).
% 48.98/49.15 tff(811,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(812,plain,
% 48.98/49.15 ((node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26))) <=> ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(813,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[812])).
% 48.98/49.15 tff(814,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[813, 811])).
% 48.98/49.15 tff(815,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | (~m_counter_cell_v_value(c_bit0, s26)))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(816,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[815, 814])).
% 48.98/49.15 tff(817,plain,
% 48.98/49.15 ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[816, 130, 810])).
% 48.98/49.15 tff(818,plain,
% 48.98/49.15 (~m_counter_cell_v_value(c_bit0, s26)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[817, 799])).
% 48.98/49.15 tff(819,assumption,(~m_counter_cell_v_carry_in(c_bit0, s26)), introduced(assumption)).
% 48.98/49.15 tff(820,plain,
% 48.98/49.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s26)),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(821,plain,
% 48.98/49.15 ($false),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[820, 43, 819])).
% 48.98/49.15 tff(822,plain,(m_counter_cell_v_carry_in(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.15 tff(823,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(824,plain,
% 48.98/49.15 (((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(825,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[824])).
% 48.98/49.15 tff(826,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[825, 823])).
% 48.98/49.15 tff(827,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(828,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[827, 826])).
% 48.98/49.15 tff(829,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[828, 55, 822])).
% 48.98/49.15 tff(830,plain,
% 48.98/49.15 (~node1(c_bit0, s26)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[829, 818])).
% 48.98/49.15 tff(831,plain,
% 48.98/49.15 (succ(s26, s27) <=> succ(s26, s27)),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(832,axiom,(succ(s26, s27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound27')).
% 48.98/49.15 tff(833,plain,
% 48.98/49.15 (succ(s26, s27)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[832, 831])).
% 48.98/49.15 tff(834,plain,
% 48.98/49.15 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(835,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(836,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[835, 834])).
% 48.98/49.15 tff(837,plain,
% 48.98/49.15 (trans(s26, s27)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[836, 833, 7])).
% 48.98/49.15 tff(838,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(839,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(840,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[839, 838])).
% 48.98/49.15 tff(841,plain,
% 48.98/49.15 (node3(c_bit0, s26, s27)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[840, 21, 837])).
% 48.98/49.15 tff(842,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(843,plain,
% 48.98/49.15 ((node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27)) <=> (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(844,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[843])).
% 48.98/49.15 tff(845,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[844, 842])).
% 48.98/49.15 tff(846,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s26) | (~node3(c_bit0, s26, s27)) | m_counter_cell_v_value(c_bit0, s27))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(847,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[846, 845])).
% 48.98/49.15 tff(848,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[847, 84, 841])).
% 48.98/49.15 tff(849,plain,
% 48.98/49.15 (m_counter_cell_v_value(c_bit0, s27)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[848, 830])).
% 48.98/49.15 tff(850,assumption,(~m_counter_cell_v_carry_in(c_bit0, s27)), introduced(assumption)).
% 48.98/49.15 tff(851,plain,
% 48.98/49.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s27)),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(852,plain,
% 48.98/49.15 ($false),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[851, 43, 850])).
% 48.98/49.15 tff(853,plain,(m_counter_cell_v_carry_in(c_bit0, s27)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.15 tff(854,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(855,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(856,plain,
% 48.98/49.15 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[855, 854])).
% 48.98/49.15 tff(857,plain,
% 48.98/49.15 ((~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[856, 104, 853])).
% 48.98/49.15 tff(858,plain,
% 48.98/49.15 (~node2(c_bit0, s27)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[857, 849])).
% 48.98/49.15 tff(859,plain,
% 48.98/49.15 (succ(s27, s28) <=> succ(s27, s28)),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(860,axiom,(succ(s27, s28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound28')).
% 48.98/49.15 tff(861,plain,
% 48.98/49.15 (succ(s27, s28)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[860, 859])).
% 48.98/49.15 tff(862,plain,
% 48.98/49.15 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(863,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(864,plain,
% 48.98/49.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[863, 862])).
% 48.98/49.15 tff(865,plain,
% 48.98/49.15 (trans(s27, s28)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[864, 861, 7])).
% 48.98/49.15 tff(866,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(867,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(868,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28)),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[867, 866])).
% 48.98/49.15 tff(869,plain,
% 48.98/49.15 (node3(c_bit0, s27, s28)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[868, 21, 865])).
% 48.98/49.15 tff(870,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(871,plain,
% 48.98/49.15 ((node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28))) <=> ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 48.98/49.15 inference(rewrite,[status(thm)],[])).
% 48.98/49.15 tff(872,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))))),
% 48.98/49.15 inference(monotonicity,[status(thm)],[871])).
% 48.98/49.15 tff(873,plain,
% 48.98/49.15 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 48.98/49.15 inference(transitivity,[status(thm)],[872, 870])).
% 48.98/49.15 tff(874,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(875,plain,
% 48.98/49.15 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))),
% 48.98/49.15 inference(modus_ponens,[status(thm)],[874, 873])).
% 48.98/49.15 tff(876,plain,
% 48.98/49.15 ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[875, 130, 869])).
% 48.98/49.15 tff(877,plain,
% 48.98/49.15 (~m_counter_cell_v_value(c_bit0, s28)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[876, 858])).
% 48.98/49.15 tff(878,plain,
% 48.98/49.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s28)),
% 48.98/49.15 inference(quant_inst,[status(thm)],[])).
% 48.98/49.15 tff(879,plain,
% 48.98/49.15 (m_counter_cell_v_carry_in(c_bit0, s28)),
% 48.98/49.15 inference(unit_resolution,[status(thm)],[878, 43])).
% 48.98/49.15 tff(880,plain,
% 48.98/49.15 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(881,plain,
% 48.98/49.16 (((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(882,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))))),
% 48.98/49.16 inference(monotonicity,[status(thm)],[881])).
% 48.98/49.16 tff(883,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28)))),
% 48.98/49.16 inference(transitivity,[status(thm)],[882, 880])).
% 48.98/49.16 tff(884,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(885,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[884, 883])).
% 48.98/49.16 tff(886,plain,
% 48.98/49.16 (m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[885, 55, 879])).
% 48.98/49.16 tff(887,plain,
% 48.98/49.16 (~node1(c_bit0, s28)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[886, 877])).
% 48.98/49.16 tff(888,plain,
% 48.98/49.16 (succ(s28, s29) <=> succ(s28, s29)),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(889,axiom,(succ(s28, s29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound29')).
% 48.98/49.16 tff(890,plain,
% 48.98/49.16 (succ(s28, s29)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[889, 888])).
% 48.98/49.16 tff(891,plain,
% 48.98/49.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(892,plain,
% 48.98/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(893,plain,
% 48.98/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[892, 891])).
% 48.98/49.16 tff(894,plain,
% 48.98/49.16 (trans(s28, s29)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[893, 890, 7])).
% 48.98/49.16 tff(895,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(896,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(897,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[896, 895])).
% 48.98/49.16 tff(898,plain,
% 48.98/49.16 (node3(c_bit0, s28, s29)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[897, 21, 894])).
% 48.98/49.16 tff(899,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(900,plain,
% 48.98/49.16 ((node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29)) <=> (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(901,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29))))),
% 48.98/49.16 inference(monotonicity,[status(thm)],[900])).
% 48.98/49.16 tff(902,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)))),
% 48.98/49.16 inference(transitivity,[status(thm)],[901, 899])).
% 48.98/49.16 tff(903,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s28) | (~node3(c_bit0, s28, s29)) | m_counter_cell_v_value(c_bit0, s29))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(904,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29))),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[903, 902])).
% 48.98/49.16 tff(905,plain,
% 48.98/49.16 (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[904, 84, 898])).
% 48.98/49.16 tff(906,plain,
% 48.98/49.16 (m_counter_cell_v_value(c_bit0, s29)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[905, 887])).
% 48.98/49.16 tff(907,assumption,(~m_counter_cell_v_carry_in(c_bit0, s29)), introduced(assumption)).
% 48.98/49.16 tff(908,plain,
% 48.98/49.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s29)),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(909,plain,
% 48.98/49.16 ($false),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[908, 43, 907])).
% 48.98/49.16 tff(910,plain,(m_counter_cell_v_carry_in(c_bit0, s29)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.16 tff(911,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(912,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(913,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[912, 911])).
% 48.98/49.16 tff(914,plain,
% 48.98/49.16 ((~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[913, 104, 910])).
% 48.98/49.16 tff(915,plain,
% 48.98/49.16 (~node2(c_bit0, s29)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[914, 906])).
% 48.98/49.16 tff(916,plain,
% 48.98/49.16 (succ(s29, s30) <=> succ(s29, s30)),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(917,axiom,(succ(s29, s30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound30')).
% 48.98/49.16 tff(918,plain,
% 48.98/49.16 (succ(s29, s30)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[917, 916])).
% 48.98/49.16 tff(919,plain,
% 48.98/49.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(920,plain,
% 48.98/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(921,plain,
% 48.98/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[920, 919])).
% 48.98/49.16 tff(922,plain,
% 48.98/49.16 (trans(s29, s30)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[921, 918, 7])).
% 48.98/49.16 tff(923,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(924,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(925,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[924, 923])).
% 48.98/49.16 tff(926,plain,
% 48.98/49.16 (node3(c_bit0, s29, s30)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[925, 21, 922])).
% 48.98/49.16 tff(927,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(928,plain,
% 48.98/49.16 ((node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30))) <=> ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(929,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30))))),
% 48.98/49.16 inference(monotonicity,[status(thm)],[928])).
% 48.98/49.16 tff(930,plain,
% 48.98/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)))),
% 48.98/49.16 inference(transitivity,[status(thm)],[929, 927])).
% 48.98/49.16 tff(931,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s29) | (~node3(c_bit0, s29, s30)) | (~m_counter_cell_v_value(c_bit0, s30)))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(932,plain,
% 48.98/49.16 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30))),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[931, 930])).
% 48.98/49.16 tff(933,plain,
% 48.98/49.16 ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[932, 130, 926])).
% 48.98/49.16 tff(934,plain,
% 48.98/49.16 (~m_counter_cell_v_value(c_bit0, s30)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[933, 915])).
% 48.98/49.16 tff(935,assumption,(~m_counter_cell_v_carry_in(c_bit0, s30)), introduced(assumption)).
% 48.98/49.16 tff(936,plain,
% 48.98/49.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s30)),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(937,plain,
% 48.98/49.16 ($false),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[936, 43, 935])).
% 48.98/49.16 tff(938,plain,(m_counter_cell_v_carry_in(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 48.98/49.16 tff(939,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(940,plain,
% 48.98/49.16 (((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(941,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))))),
% 48.98/49.16 inference(monotonicity,[status(thm)],[940])).
% 48.98/49.16 tff(942,plain,
% 48.98/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30)))),
% 48.98/49.16 inference(transitivity,[status(thm)],[941, 939])).
% 48.98/49.16 tff(943,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 48.98/49.16 tff(944,plain,
% 48.98/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[943, 942])).
% 48.98/49.16 tff(945,plain,
% 48.98/49.16 (m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[944, 55, 938])).
% 48.98/49.16 tff(946,plain,
% 48.98/49.16 (~node1(c_bit0, s30)),
% 48.98/49.16 inference(unit_resolution,[status(thm)],[945, 934])).
% 48.98/49.16 tff(947,plain,
% 48.98/49.16 (succ(s30, s31) <=> succ(s30, s31)),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(948,axiom,(succ(s30, s31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound31')).
% 48.98/49.16 tff(949,plain,
% 48.98/49.16 (succ(s30, s31)),
% 48.98/49.16 inference(modus_ponens,[status(thm)],[948, 947])).
% 48.98/49.16 tff(950,plain,
% 48.98/49.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31))),
% 48.98/49.16 inference(rewrite,[status(thm)],[])).
% 48.98/49.16 tff(951,plain,
% 48.98/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 48.98/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(952,plain,
% 49.00/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[951, 950])).
% 49.00/49.16 tff(953,plain,
% 49.00/49.16 (trans(s30, s31)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[952, 949, 7])).
% 49.00/49.16 tff(954,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(955,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(956,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31)),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[955, 954])).
% 49.00/49.16 tff(957,plain,
% 49.00/49.16 (node3(c_bit0, s30, s31)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[956, 21, 953])).
% 49.00/49.16 tff(958,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(959,plain,
% 49.00/49.16 ((node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31)) <=> (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(960,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31))))),
% 49.00/49.16 inference(monotonicity,[status(thm)],[959])).
% 49.00/49.16 tff(961,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)))),
% 49.00/49.16 inference(transitivity,[status(thm)],[960, 958])).
% 49.00/49.16 tff(962,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s30) | (~node3(c_bit0, s30, s31)) | m_counter_cell_v_value(c_bit0, s31))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(963,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31))),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[962, 961])).
% 49.00/49.16 tff(964,plain,
% 49.00/49.16 (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[963, 84, 957])).
% 49.00/49.16 tff(965,plain,
% 49.00/49.16 (m_counter_cell_v_value(c_bit0, s31)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[964, 946])).
% 49.00/49.16 tff(966,assumption,(~m_counter_cell_v_carry_in(c_bit0, s31)), introduced(assumption)).
% 49.00/49.16 tff(967,plain,
% 49.00/49.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s31)),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(968,plain,
% 49.00/49.16 ($false),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[967, 43, 966])).
% 49.00/49.16 tff(969,plain,(m_counter_cell_v_carry_in(c_bit0, s31)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.16 tff(970,plain,
% 49.00/49.16 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(971,plain,
% 49.00/49.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(972,plain,
% 49.00/49.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[971, 970])).
% 49.00/49.16 tff(973,plain,
% 49.00/49.16 ((~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[972, 104, 969])).
% 49.00/49.16 tff(974,plain,
% 49.00/49.16 (~node2(c_bit0, s31)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[973, 965])).
% 49.00/49.16 tff(975,plain,
% 49.00/49.16 (succ(s31, s32) <=> succ(s31, s32)),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(976,axiom,(succ(s31, s32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound32')).
% 49.00/49.16 tff(977,plain,
% 49.00/49.16 (succ(s31, s32)),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[976, 975])).
% 49.00/49.16 tff(978,plain,
% 49.00/49.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(979,plain,
% 49.00/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(980,plain,
% 49.00/49.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[979, 978])).
% 49.00/49.16 tff(981,plain,
% 49.00/49.16 (trans(s31, s32)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[980, 977, 7])).
% 49.00/49.16 tff(982,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(983,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(984,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32)),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[983, 982])).
% 49.00/49.16 tff(985,plain,
% 49.00/49.16 (node3(c_bit0, s31, s32)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[984, 21, 981])).
% 49.00/49.16 tff(986,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(987,plain,
% 49.00/49.16 ((node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32))) <=> ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(988,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32))))),
% 49.00/49.16 inference(monotonicity,[status(thm)],[987])).
% 49.00/49.16 tff(989,plain,
% 49.00/49.16 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)))),
% 49.00/49.16 inference(transitivity,[status(thm)],[988, 986])).
% 49.00/49.16 tff(990,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s31) | (~node3(c_bit0, s31, s32)) | (~m_counter_cell_v_value(c_bit0, s32)))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(991,plain,
% 49.00/49.16 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32))),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[990, 989])).
% 49.00/49.16 tff(992,plain,
% 49.00/49.16 ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[991, 130, 985])).
% 49.00/49.16 tff(993,plain,
% 49.00/49.16 (~m_counter_cell_v_value(c_bit0, s32)),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[992, 974])).
% 49.00/49.16 tff(994,assumption,(~m_counter_cell_v_carry_in(c_bit0, s32)), introduced(assumption)).
% 49.00/49.16 tff(995,plain,
% 49.00/49.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s32)),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(996,plain,
% 49.00/49.16 ($false),
% 49.00/49.16 inference(unit_resolution,[status(thm)],[995, 43, 994])).
% 49.00/49.16 tff(997,plain,(m_counter_cell_v_carry_in(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.16 tff(998,plain,
% 49.00/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(999,plain,
% 49.00/49.16 (((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 49.00/49.16 inference(rewrite,[status(thm)],[])).
% 49.00/49.16 tff(1000,plain,
% 49.00/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))))),
% 49.00/49.16 inference(monotonicity,[status(thm)],[999])).
% 49.00/49.16 tff(1001,plain,
% 49.00/49.16 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32)))),
% 49.00/49.16 inference(transitivity,[status(thm)],[1000, 998])).
% 49.00/49.16 tff(1002,plain,
% 49.00/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))),
% 49.00/49.16 inference(quant_inst,[status(thm)],[])).
% 49.00/49.16 tff(1003,plain,
% 49.00/49.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 49.00/49.16 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 49.00/49.16 tff(1004,plain,
% 49.00/49.16 (m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1003, 55, 997])).
% 49.00/49.17 tff(1005,plain,
% 49.00/49.17 (~node1(c_bit0, s32)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1004, 993])).
% 49.00/49.17 tff(1006,plain,
% 49.00/49.17 (succ(s32, s33) <=> succ(s32, s33)),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1007,axiom,(succ(s32, s33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound33')).
% 49.00/49.17 tff(1008,plain,
% 49.00/49.17 (succ(s32, s33)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 49.00/49.17 tff(1009,plain,
% 49.00/49.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1010,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1011,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 49.00/49.17 tff(1012,plain,
% 49.00/49.17 (trans(s32, s33)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1011, 1008, 7])).
% 49.00/49.17 tff(1013,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1014,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1015,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 49.00/49.17 tff(1016,plain,
% 49.00/49.17 (node3(c_bit0, s32, s33)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1015, 21, 1012])).
% 49.00/49.17 tff(1017,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1018,plain,
% 49.00/49.17 ((node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33)) <=> (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1019,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1018])).
% 49.00/49.17 tff(1020,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1019, 1017])).
% 49.00/49.17 tff(1021,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s32) | (~node3(c_bit0, s32, s33)) | m_counter_cell_v_value(c_bit0, s33))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1022,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 49.00/49.17 tff(1023,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1022, 84, 1016])).
% 49.00/49.17 tff(1024,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s33)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1023, 1005])).
% 49.00/49.17 tff(1025,assumption,(~m_counter_cell_v_carry_in(c_bit0, s33)), introduced(assumption)).
% 49.00/49.17 tff(1026,plain,
% 49.00/49.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s33)),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1027,plain,
% 49.00/49.17 ($false),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1026, 43, 1025])).
% 49.00/49.17 tff(1028,plain,(m_counter_cell_v_carry_in(c_bit0, s33)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.17 tff(1029,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1030,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1031,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 49.00/49.17 tff(1032,plain,
% 49.00/49.17 ((~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1031, 104, 1028])).
% 49.00/49.17 tff(1033,plain,
% 49.00/49.17 (~node2(c_bit0, s33)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1032, 1024])).
% 49.00/49.17 tff(1034,plain,
% 49.00/49.17 (succ(s33, s34) <=> succ(s33, s34)),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1035,axiom,(succ(s33, s34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound34')).
% 49.00/49.17 tff(1036,plain,
% 49.00/49.17 (succ(s33, s34)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 49.00/49.17 tff(1037,plain,
% 49.00/49.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1038,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1039,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 49.00/49.17 tff(1040,plain,
% 49.00/49.17 (trans(s33, s34)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1039, 1036, 7])).
% 49.00/49.17 tff(1041,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1042,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1043,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 49.00/49.17 tff(1044,plain,
% 49.00/49.17 (node3(c_bit0, s33, s34)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1043, 21, 1040])).
% 49.00/49.17 tff(1045,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1046,plain,
% 49.00/49.17 ((node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34))) <=> ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1047,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1046])).
% 49.00/49.17 tff(1048,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1047, 1045])).
% 49.00/49.17 tff(1049,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | (~m_counter_cell_v_value(c_bit0, s34)))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1050,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 49.00/49.17 tff(1051,plain,
% 49.00/49.17 ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1050, 130, 1044])).
% 49.00/49.17 tff(1052,plain,
% 49.00/49.17 (~m_counter_cell_v_value(c_bit0, s34)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1051, 1033])).
% 49.00/49.17 tff(1053,assumption,(~m_counter_cell_v_carry_in(c_bit0, s34)), introduced(assumption)).
% 49.00/49.17 tff(1054,plain,
% 49.00/49.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s34)),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1055,plain,
% 49.00/49.17 ($false),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1054, 43, 1053])).
% 49.00/49.17 tff(1056,plain,(m_counter_cell_v_carry_in(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.17 tff(1057,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1058,plain,
% 49.00/49.17 (((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1059,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1058])).
% 49.00/49.17 tff(1060,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1059, 1057])).
% 49.00/49.17 tff(1061,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1062,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 49.00/49.17 tff(1063,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1062, 55, 1056])).
% 49.00/49.17 tff(1064,plain,
% 49.00/49.17 (~node1(c_bit0, s34)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1063, 1052])).
% 49.00/49.17 tff(1065,plain,
% 49.00/49.17 (succ(s34, s35) <=> succ(s34, s35)),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1066,axiom,(succ(s34, s35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound35')).
% 49.00/49.17 tff(1067,plain,
% 49.00/49.17 (succ(s34, s35)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 49.00/49.17 tff(1068,plain,
% 49.00/49.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1069,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1070,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 49.00/49.17 tff(1071,plain,
% 49.00/49.17 (trans(s34, s35)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1070, 1067, 7])).
% 49.00/49.17 tff(1072,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1073,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1074,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 49.00/49.17 tff(1075,plain,
% 49.00/49.17 (node3(c_bit0, s34, s35)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1074, 21, 1071])).
% 49.00/49.17 tff(1076,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1077,plain,
% 49.00/49.17 ((node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35)) <=> (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1078,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1077])).
% 49.00/49.17 tff(1079,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1078, 1076])).
% 49.00/49.17 tff(1080,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s34) | (~node3(c_bit0, s34, s35)) | m_counter_cell_v_value(c_bit0, s35))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1081,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 49.00/49.17 tff(1082,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1081, 84, 1075])).
% 49.00/49.17 tff(1083,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s35)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1082, 1064])).
% 49.00/49.17 tff(1084,assumption,(~m_counter_cell_v_carry_in(c_bit0, s35)), introduced(assumption)).
% 49.00/49.17 tff(1085,plain,
% 49.00/49.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s35)),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1086,plain,
% 49.00/49.17 ($false),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1085, 43, 1084])).
% 49.00/49.17 tff(1087,plain,(m_counter_cell_v_carry_in(c_bit0, s35)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.17 tff(1088,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1089,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1090,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 49.00/49.17 tff(1091,plain,
% 49.00/49.17 ((~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1090, 104, 1087])).
% 49.00/49.17 tff(1092,plain,
% 49.00/49.17 (~node2(c_bit0, s35)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1091, 1083])).
% 49.00/49.17 tff(1093,plain,
% 49.00/49.17 (succ(s35, s36) <=> succ(s35, s36)),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1094,axiom,(succ(s35, s36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound36')).
% 49.00/49.17 tff(1095,plain,
% 49.00/49.17 (succ(s35, s36)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 49.00/49.17 tff(1096,plain,
% 49.00/49.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1097,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1098,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 49.00/49.17 tff(1099,plain,
% 49.00/49.17 (trans(s35, s36)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1098, 1095, 7])).
% 49.00/49.17 tff(1100,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1101,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1102,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 49.00/49.17 tff(1103,plain,
% 49.00/49.17 (node3(c_bit0, s35, s36)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1102, 21, 1099])).
% 49.00/49.17 tff(1104,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1105,plain,
% 49.00/49.17 ((node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36))) <=> ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1106,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1105])).
% 49.00/49.17 tff(1107,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1106, 1104])).
% 49.00/49.17 tff(1108,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s35) | (~node3(c_bit0, s35, s36)) | (~m_counter_cell_v_value(c_bit0, s36)))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1109,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 49.00/49.17 tff(1110,plain,
% 49.00/49.17 ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1109, 130, 1103])).
% 49.00/49.17 tff(1111,plain,
% 49.00/49.17 (~m_counter_cell_v_value(c_bit0, s36)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1110, 1092])).
% 49.00/49.17 tff(1112,assumption,(~m_counter_cell_v_carry_in(c_bit0, s36)), introduced(assumption)).
% 49.00/49.17 tff(1113,plain,
% 49.00/49.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s36)),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1114,plain,
% 49.00/49.17 ($false),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1113, 43, 1112])).
% 49.00/49.17 tff(1115,plain,(m_counter_cell_v_carry_in(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.17 tff(1116,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1117,plain,
% 49.00/49.17 (((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1118,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))))),
% 49.00/49.17 inference(monotonicity,[status(thm)],[1117])).
% 49.00/49.17 tff(1119,plain,
% 49.00/49.17 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36)))),
% 49.00/49.17 inference(transitivity,[status(thm)],[1118, 1116])).
% 49.00/49.17 tff(1120,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1121,plain,
% 49.00/49.17 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 49.00/49.17 tff(1122,plain,
% 49.00/49.17 (m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1121, 55, 1115])).
% 49.00/49.17 tff(1123,plain,
% 49.00/49.17 (~node1(c_bit0, s36)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1122, 1111])).
% 49.00/49.17 tff(1124,plain,
% 49.00/49.17 (succ(s36, s37) <=> succ(s36, s37)),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1125,axiom,(succ(s36, s37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound37')).
% 49.00/49.17 tff(1126,plain,
% 49.00/49.17 (succ(s36, s37)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 49.00/49.17 tff(1127,plain,
% 49.00/49.17 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1128,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1129,plain,
% 49.00/49.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 49.00/49.17 tff(1130,plain,
% 49.00/49.17 (trans(s36, s37)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1129, 1126, 7])).
% 49.00/49.17 tff(1131,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 49.00/49.17 inference(rewrite,[status(thm)],[])).
% 49.00/49.17 tff(1132,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 49.00/49.17 inference(quant_inst,[status(thm)],[])).
% 49.00/49.17 tff(1133,plain,
% 49.00/49.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37)),
% 49.00/49.17 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 49.00/49.17 tff(1134,plain,
% 49.00/49.17 (node3(c_bit0, s36, s37)),
% 49.00/49.17 inference(unit_resolution,[status(thm)],[1133, 21, 1130])).
% 49.00/49.17 tff(1135,plain,
% 49.00/49.17 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1136,plain,
% 49.00/49.18 ((node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37)) <=> (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1137,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1136])).
% 49.00/49.18 tff(1138,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1137, 1135])).
% 49.00/49.18 tff(1139,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s36) | (~node3(c_bit0, s36, s37)) | m_counter_cell_v_value(c_bit0, s37))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1140,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 49.00/49.18 tff(1141,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1140, 84, 1134])).
% 49.00/49.18 tff(1142,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s37)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1141, 1123])).
% 49.00/49.18 tff(1143,assumption,(~m_counter_cell_v_carry_in(c_bit0, s37)), introduced(assumption)).
% 49.00/49.18 tff(1144,plain,
% 49.00/49.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s37)),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1145,plain,
% 49.00/49.18 ($false),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1144, 43, 1143])).
% 49.00/49.18 tff(1146,plain,(m_counter_cell_v_carry_in(c_bit0, s37)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.18 tff(1147,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1148,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1149,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 49.00/49.18 tff(1150,plain,
% 49.00/49.18 ((~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1149, 104, 1146])).
% 49.00/49.18 tff(1151,plain,
% 49.00/49.18 (~node2(c_bit0, s37)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1150, 1142])).
% 49.00/49.18 tff(1152,plain,
% 49.00/49.18 (succ(s37, s38) <=> succ(s37, s38)),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1153,axiom,(succ(s37, s38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound38')).
% 49.00/49.18 tff(1154,plain,
% 49.00/49.18 (succ(s37, s38)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 49.00/49.18 tff(1155,plain,
% 49.00/49.18 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1156,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1157,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 49.00/49.18 tff(1158,plain,
% 49.00/49.18 (trans(s37, s38)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1157, 1154, 7])).
% 49.00/49.18 tff(1159,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1160,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1161,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 49.00/49.18 tff(1162,plain,
% 49.00/49.18 (node3(c_bit0, s37, s38)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1161, 21, 1158])).
% 49.00/49.18 tff(1163,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1164,plain,
% 49.00/49.18 ((node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38))) <=> ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1165,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1164])).
% 49.00/49.18 tff(1166,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1165, 1163])).
% 49.00/49.18 tff(1167,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s37) | (~node3(c_bit0, s37, s38)) | (~m_counter_cell_v_value(c_bit0, s38)))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1168,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 49.00/49.18 tff(1169,plain,
% 49.00/49.18 ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1168, 130, 1162])).
% 49.00/49.18 tff(1170,plain,
% 49.00/49.18 (~m_counter_cell_v_value(c_bit0, s38)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1169, 1151])).
% 49.00/49.18 tff(1171,assumption,(~m_counter_cell_v_carry_in(c_bit0, s38)), introduced(assumption)).
% 49.00/49.18 tff(1172,plain,
% 49.00/49.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s38)),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1173,plain,
% 49.00/49.18 ($false),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1172, 43, 1171])).
% 49.00/49.18 tff(1174,plain,(m_counter_cell_v_carry_in(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.18 tff(1175,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1176,plain,
% 49.00/49.18 (((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1177,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1176])).
% 49.00/49.18 tff(1178,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1177, 1175])).
% 49.00/49.18 tff(1179,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1180,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 49.00/49.18 tff(1181,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1180, 55, 1174])).
% 49.00/49.18 tff(1182,plain,
% 49.00/49.18 (~node1(c_bit0, s38)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1181, 1170])).
% 49.00/49.18 tff(1183,plain,
% 49.00/49.18 (succ(s38, s39) <=> succ(s38, s39)),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1184,axiom,(succ(s38, s39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound39')).
% 49.00/49.18 tff(1185,plain,
% 49.00/49.18 (succ(s38, s39)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 49.00/49.18 tff(1186,plain,
% 49.00/49.18 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1187,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1188,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 49.00/49.18 tff(1189,plain,
% 49.00/49.18 (trans(s38, s39)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1188, 1185, 7])).
% 49.00/49.18 tff(1190,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1191,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1192,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 49.00/49.18 tff(1193,plain,
% 49.00/49.18 (node3(c_bit0, s38, s39)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1192, 21, 1189])).
% 49.00/49.18 tff(1194,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1195,plain,
% 49.00/49.18 ((node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39)) <=> (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1196,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1195])).
% 49.00/49.18 tff(1197,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1196, 1194])).
% 49.00/49.18 tff(1198,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s38) | (~node3(c_bit0, s38, s39)) | m_counter_cell_v_value(c_bit0, s39))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1199,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 49.00/49.18 tff(1200,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1199, 84, 1193])).
% 49.00/49.18 tff(1201,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s39)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1200, 1182])).
% 49.00/49.18 tff(1202,assumption,(~m_counter_cell_v_carry_in(c_bit0, s39)), introduced(assumption)).
% 49.00/49.18 tff(1203,plain,
% 49.00/49.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s39)),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1204,plain,
% 49.00/49.18 ($false),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1203, 43, 1202])).
% 49.00/49.18 tff(1205,plain,(m_counter_cell_v_carry_in(c_bit0, s39)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.18 tff(1206,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1207,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1208,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 49.00/49.18 tff(1209,plain,
% 49.00/49.18 ((~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1208, 104, 1205])).
% 49.00/49.18 tff(1210,plain,
% 49.00/49.18 (~node2(c_bit0, s39)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1209, 1201])).
% 49.00/49.18 tff(1211,plain,
% 49.00/49.18 (succ(s39, s40) <=> succ(s39, s40)),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1212,axiom,(succ(s39, s40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound40')).
% 49.00/49.18 tff(1213,plain,
% 49.00/49.18 (succ(s39, s40)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 49.00/49.18 tff(1214,plain,
% 49.00/49.18 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1215,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1216,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 49.00/49.18 tff(1217,plain,
% 49.00/49.18 (trans(s39, s40)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1216, 1213, 7])).
% 49.00/49.18 tff(1218,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1219,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1220,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 49.00/49.18 tff(1221,plain,
% 49.00/49.18 (node3(c_bit0, s39, s40)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1220, 21, 1217])).
% 49.00/49.18 tff(1222,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1223,plain,
% 49.00/49.18 ((node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40))) <=> ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1224,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1223])).
% 49.00/49.18 tff(1225,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1224, 1222])).
% 49.00/49.18 tff(1226,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s39) | (~node3(c_bit0, s39, s40)) | (~m_counter_cell_v_value(c_bit0, s40)))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1227,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 49.00/49.18 tff(1228,plain,
% 49.00/49.18 ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1227, 130, 1221])).
% 49.00/49.18 tff(1229,plain,
% 49.00/49.18 (~m_counter_cell_v_value(c_bit0, s40)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1228, 1210])).
% 49.00/49.18 tff(1230,assumption,(~m_counter_cell_v_carry_in(c_bit0, s40)), introduced(assumption)).
% 49.00/49.18 tff(1231,plain,
% 49.00/49.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s40)),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1232,plain,
% 49.00/49.18 ($false),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1231, 43, 1230])).
% 49.00/49.18 tff(1233,plain,(m_counter_cell_v_carry_in(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.18 tff(1234,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1235,plain,
% 49.00/49.18 (((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1236,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1235])).
% 49.00/49.18 tff(1237,plain,
% 49.00/49.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1236, 1234])).
% 49.00/49.18 tff(1238,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1239,plain,
% 49.00/49.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 49.00/49.18 tff(1240,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1239, 55, 1233])).
% 49.00/49.18 tff(1241,plain,
% 49.00/49.18 (~node1(c_bit0, s40)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1240, 1229])).
% 49.00/49.18 tff(1242,plain,
% 49.00/49.18 (succ(s40, s41) <=> succ(s40, s41)),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1243,axiom,(succ(s40, s41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound41')).
% 49.00/49.18 tff(1244,plain,
% 49.00/49.18 (succ(s40, s41)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 49.00/49.18 tff(1245,plain,
% 49.00/49.18 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1246,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1247,plain,
% 49.00/49.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 49.00/49.18 tff(1248,plain,
% 49.00/49.18 (trans(s40, s41)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1247, 1244, 7])).
% 49.00/49.18 tff(1249,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1250,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1251,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41)),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 49.00/49.18 tff(1252,plain,
% 49.00/49.18 (node3(c_bit0, s40, s41)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1251, 21, 1248])).
% 49.00/49.18 tff(1253,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1254,plain,
% 49.00/49.18 ((node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41)) <=> (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 49.00/49.18 inference(rewrite,[status(thm)],[])).
% 49.00/49.18 tff(1255,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41))))),
% 49.00/49.18 inference(monotonicity,[status(thm)],[1254])).
% 49.00/49.18 tff(1256,plain,
% 49.00/49.18 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)))),
% 49.00/49.18 inference(transitivity,[status(thm)],[1255, 1253])).
% 49.00/49.18 tff(1257,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s40) | (~node3(c_bit0, s40, s41)) | m_counter_cell_v_value(c_bit0, s41))),
% 49.00/49.18 inference(quant_inst,[status(thm)],[])).
% 49.00/49.18 tff(1258,plain,
% 49.00/49.18 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41))),
% 49.00/49.18 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 49.00/49.18 tff(1259,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1258, 84, 1252])).
% 49.00/49.18 tff(1260,plain,
% 49.00/49.18 (m_counter_cell_v_value(c_bit0, s41)),
% 49.00/49.18 inference(unit_resolution,[status(thm)],[1259, 1241])).
% 49.00/49.19 tff(1261,assumption,(~m_counter_cell_v_carry_in(c_bit0, s41)), introduced(assumption)).
% 49.00/49.19 tff(1262,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s41)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1263,plain,
% 49.00/49.19 ($false),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1262, 43, 1261])).
% 49.00/49.19 tff(1264,plain,(m_counter_cell_v_carry_in(c_bit0, s41)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.19 tff(1265,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1266,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1267,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 49.00/49.19 tff(1268,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1267, 104, 1264])).
% 49.00/49.19 tff(1269,plain,
% 49.00/49.19 (~node2(c_bit0, s41)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1268, 1260])).
% 49.00/49.19 tff(1270,plain,
% 49.00/49.19 (succ(s41, s42) <=> succ(s41, s42)),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1271,axiom,(succ(s41, s42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound42')).
% 49.00/49.19 tff(1272,plain,
% 49.00/49.19 (succ(s41, s42)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 49.00/49.19 tff(1273,plain,
% 49.00/49.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1274,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1275,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 49.00/49.19 tff(1276,plain,
% 49.00/49.19 (trans(s41, s42)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1275, 1272, 7])).
% 49.00/49.19 tff(1277,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1278,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1279,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 49.00/49.19 tff(1280,plain,
% 49.00/49.19 (node3(c_bit0, s41, s42)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1279, 21, 1276])).
% 49.00/49.19 tff(1281,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1282,plain,
% 49.00/49.19 ((node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42))) <=> ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1283,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1282])).
% 49.00/49.19 tff(1284,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1283, 1281])).
% 49.00/49.19 tff(1285,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1286,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 49.00/49.19 tff(1287,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1286, 130, 1280])).
% 49.00/49.19 tff(1288,plain,
% 49.00/49.19 (~m_counter_cell_v_value(c_bit0, s42)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1287, 1269])).
% 49.00/49.19 tff(1289,assumption,(~m_counter_cell_v_carry_in(c_bit0, s42)), introduced(assumption)).
% 49.00/49.19 tff(1290,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s42)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1291,plain,
% 49.00/49.19 ($false),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1290, 43, 1289])).
% 49.00/49.19 tff(1292,plain,(m_counter_cell_v_carry_in(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.19 tff(1293,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1294,plain,
% 49.00/49.19 (((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1295,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1294])).
% 49.00/49.19 tff(1296,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1295, 1293])).
% 49.00/49.19 tff(1297,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1298,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 49.00/49.19 tff(1299,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1298, 55, 1292])).
% 49.00/49.19 tff(1300,plain,
% 49.00/49.19 (~node1(c_bit0, s42)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1299, 1288])).
% 49.00/49.19 tff(1301,plain,
% 49.00/49.19 (succ(s42, s43) <=> succ(s42, s43)),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1302,axiom,(succ(s42, s43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound43')).
% 49.00/49.19 tff(1303,plain,
% 49.00/49.19 (succ(s42, s43)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 49.00/49.19 tff(1304,plain,
% 49.00/49.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1305,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1306,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 49.00/49.19 tff(1307,plain,
% 49.00/49.19 (trans(s42, s43)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1306, 1303, 7])).
% 49.00/49.19 tff(1308,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1309,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1310,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 49.00/49.19 tff(1311,plain,
% 49.00/49.19 (node3(c_bit0, s42, s43)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1310, 21, 1307])).
% 49.00/49.19 tff(1312,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1313,plain,
% 49.00/49.19 ((node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43)) <=> (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1314,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1313])).
% 49.00/49.19 tff(1315,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1314, 1312])).
% 49.00/49.19 tff(1316,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1317,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 49.00/49.19 tff(1318,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1317, 84, 1311])).
% 49.00/49.19 tff(1319,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s43)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1318, 1300])).
% 49.00/49.19 tff(1320,assumption,(~m_counter_cell_v_carry_in(c_bit0, s43)), introduced(assumption)).
% 49.00/49.19 tff(1321,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s43)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1322,plain,
% 49.00/49.19 ($false),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1321, 43, 1320])).
% 49.00/49.19 tff(1323,plain,(m_counter_cell_v_carry_in(c_bit0, s43)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.19 tff(1324,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1325,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1326,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 49.00/49.19 tff(1327,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1326, 104, 1323])).
% 49.00/49.19 tff(1328,plain,
% 49.00/49.19 (~node2(c_bit0, s43)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1327, 1319])).
% 49.00/49.19 tff(1329,plain,
% 49.00/49.19 (succ(s43, s44) <=> succ(s43, s44)),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1330,axiom,(succ(s43, s44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound44')).
% 49.00/49.19 tff(1331,plain,
% 49.00/49.19 (succ(s43, s44)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 49.00/49.19 tff(1332,plain,
% 49.00/49.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1333,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1334,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 49.00/49.19 tff(1335,plain,
% 49.00/49.19 (trans(s43, s44)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1334, 1331, 7])).
% 49.00/49.19 tff(1336,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1337,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1338,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 49.00/49.19 tff(1339,plain,
% 49.00/49.19 (node3(c_bit0, s43, s44)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1338, 21, 1335])).
% 49.00/49.19 tff(1340,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1341,plain,
% 49.00/49.19 ((node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44))) <=> ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1342,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1341])).
% 49.00/49.19 tff(1343,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1342, 1340])).
% 49.00/49.19 tff(1344,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1345,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 49.00/49.19 tff(1346,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1345, 130, 1339])).
% 49.00/49.19 tff(1347,plain,
% 49.00/49.19 (~m_counter_cell_v_value(c_bit0, s44)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1346, 1328])).
% 49.00/49.19 tff(1348,assumption,(~m_counter_cell_v_carry_in(c_bit0, s44)), introduced(assumption)).
% 49.00/49.19 tff(1349,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s44)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1350,plain,
% 49.00/49.19 ($false),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1349, 43, 1348])).
% 49.00/49.19 tff(1351,plain,(m_counter_cell_v_carry_in(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.19 tff(1352,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1353,plain,
% 49.00/49.19 (((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1354,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1353])).
% 49.00/49.19 tff(1355,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1354, 1352])).
% 49.00/49.19 tff(1356,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1357,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 49.00/49.19 tff(1358,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1357, 55, 1351])).
% 49.00/49.19 tff(1359,plain,
% 49.00/49.19 (~node1(c_bit0, s44)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1358, 1347])).
% 49.00/49.19 tff(1360,plain,
% 49.00/49.19 (succ(s44, s45) <=> succ(s44, s45)),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1361,axiom,(succ(s44, s45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound45')).
% 49.00/49.19 tff(1362,plain,
% 49.00/49.19 (succ(s44, s45)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 49.00/49.19 tff(1363,plain,
% 49.00/49.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1364,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1365,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 49.00/49.19 tff(1366,plain,
% 49.00/49.19 (trans(s44, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1365, 1362, 7])).
% 49.00/49.19 tff(1367,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1368,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1369,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 49.00/49.19 tff(1370,plain,
% 49.00/49.19 (node3(c_bit0, s44, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1369, 21, 1366])).
% 49.00/49.19 tff(1371,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1372,plain,
% 49.00/49.19 ((node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45)) <=> (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1373,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1372])).
% 49.00/49.19 tff(1374,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1373, 1371])).
% 49.00/49.19 tff(1375,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s44) | (~node3(c_bit0, s44, s45)) | m_counter_cell_v_value(c_bit0, s45))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1376,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 49.00/49.19 tff(1377,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1376, 84, 1370])).
% 49.00/49.19 tff(1378,plain,
% 49.00/49.19 (m_counter_cell_v_value(c_bit0, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1377, 1359])).
% 49.00/49.19 tff(1379,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s45)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1380,plain,
% 49.00/49.19 (m_counter_cell_v_carry_in(c_bit0, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1379, 43])).
% 49.00/49.19 tff(1381,plain,
% 49.00/49.19 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1382,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1383,plain,
% 49.00/49.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 49.00/49.19 tff(1384,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1383, 104, 1380])).
% 49.00/49.19 tff(1385,plain,
% 49.00/49.19 (~node2(c_bit0, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1384, 1378])).
% 49.00/49.19 tff(1386,plain,
% 49.00/49.19 (succ(s45, s46) <=> succ(s45, s46)),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1387,axiom,(succ(s45, s46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound46')).
% 49.00/49.19 tff(1388,plain,
% 49.00/49.19 (succ(s45, s46)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 49.00/49.19 tff(1389,plain,
% 49.00/49.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1390,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1391,plain,
% 49.00/49.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 49.00/49.19 tff(1392,plain,
% 49.00/49.19 (trans(s45, s46)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1391, 1388, 7])).
% 49.00/49.19 tff(1393,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1394,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1395,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46)),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 49.00/49.19 tff(1396,plain,
% 49.00/49.19 (node3(c_bit0, s45, s46)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1395, 21, 1392])).
% 49.00/49.19 tff(1397,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1398,plain,
% 49.00/49.19 ((node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46))) <=> ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 49.00/49.19 inference(rewrite,[status(thm)],[])).
% 49.00/49.19 tff(1399,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46))))),
% 49.00/49.19 inference(monotonicity,[status(thm)],[1398])).
% 49.00/49.19 tff(1400,plain,
% 49.00/49.19 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)))),
% 49.00/49.19 inference(transitivity,[status(thm)],[1399, 1397])).
% 49.00/49.19 tff(1401,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s45) | (~node3(c_bit0, s45, s46)) | (~m_counter_cell_v_value(c_bit0, s46)))),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1402,plain,
% 49.00/49.19 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46))),
% 49.00/49.19 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 49.00/49.19 tff(1403,plain,
% 49.00/49.19 ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1402, 130, 1396])).
% 49.00/49.19 tff(1404,plain,
% 49.00/49.19 (~m_counter_cell_v_value(c_bit0, s46)),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1403, 1385])).
% 49.00/49.19 tff(1405,assumption,(~m_counter_cell_v_carry_in(c_bit0, s46)), introduced(assumption)).
% 49.00/49.19 tff(1406,plain,
% 49.00/49.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s46)),
% 49.00/49.19 inference(quant_inst,[status(thm)],[])).
% 49.00/49.19 tff(1407,plain,
% 49.00/49.19 ($false),
% 49.00/49.19 inference(unit_resolution,[status(thm)],[1406, 43, 1405])).
% 49.00/49.19 tff(1408,plain,(m_counter_cell_v_carry_in(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.20 tff(1409,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1410,plain,
% 49.00/49.20 (((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1411,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1410])).
% 49.00/49.20 tff(1412,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1411, 1409])).
% 49.00/49.20 tff(1413,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1414,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 49.00/49.20 tff(1415,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1414, 55, 1408])).
% 49.00/49.20 tff(1416,plain,
% 49.00/49.20 (~node1(c_bit0, s46)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1415, 1404])).
% 49.00/49.20 tff(1417,plain,
% 49.00/49.20 (succ(s46, s47) <=> succ(s46, s47)),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1418,axiom,(succ(s46, s47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound47')).
% 49.00/49.20 tff(1419,plain,
% 49.00/49.20 (succ(s46, s47)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 49.00/49.20 tff(1420,plain,
% 49.00/49.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1421,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1422,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 49.00/49.20 tff(1423,plain,
% 49.00/49.20 (trans(s46, s47)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1422, 1419, 7])).
% 49.00/49.20 tff(1424,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1425,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1426,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 49.00/49.20 tff(1427,plain,
% 49.00/49.20 (node3(c_bit0, s46, s47)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1426, 21, 1423])).
% 49.00/49.20 tff(1428,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1429,plain,
% 49.00/49.20 ((node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47)) <=> (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1430,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1429])).
% 49.00/49.20 tff(1431,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1430, 1428])).
% 49.00/49.20 tff(1432,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s46) | (~node3(c_bit0, s46, s47)) | m_counter_cell_v_value(c_bit0, s47))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1433,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 49.00/49.20 tff(1434,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1433, 84, 1427])).
% 49.00/49.20 tff(1435,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s47)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1434, 1416])).
% 49.00/49.20 tff(1436,assumption,(~m_counter_cell_v_carry_in(c_bit0, s47)), introduced(assumption)).
% 49.00/49.20 tff(1437,plain,
% 49.00/49.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s47)),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1438,plain,
% 49.00/49.20 ($false),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1437, 43, 1436])).
% 49.00/49.20 tff(1439,plain,(m_counter_cell_v_carry_in(c_bit0, s47)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.20 tff(1440,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1441,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1442,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 49.00/49.20 tff(1443,plain,
% 49.00/49.20 ((~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1442, 104, 1439])).
% 49.00/49.20 tff(1444,plain,
% 49.00/49.20 (~node2(c_bit0, s47)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1443, 1435])).
% 49.00/49.20 tff(1445,plain,
% 49.00/49.20 (succ(s47, s48) <=> succ(s47, s48)),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1446,axiom,(succ(s47, s48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound48')).
% 49.00/49.20 tff(1447,plain,
% 49.00/49.20 (succ(s47, s48)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 49.00/49.20 tff(1448,plain,
% 49.00/49.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1449,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1450,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 49.00/49.20 tff(1451,plain,
% 49.00/49.20 (trans(s47, s48)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1450, 1447, 7])).
% 49.00/49.20 tff(1452,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1453,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1454,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 49.00/49.20 tff(1455,plain,
% 49.00/49.20 (node3(c_bit0, s47, s48)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1454, 21, 1451])).
% 49.00/49.20 tff(1456,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1457,plain,
% 49.00/49.20 ((node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48))) <=> ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1458,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1457])).
% 49.00/49.20 tff(1459,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1458, 1456])).
% 49.00/49.20 tff(1460,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s47) | (~node3(c_bit0, s47, s48)) | (~m_counter_cell_v_value(c_bit0, s48)))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1461,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 49.00/49.20 tff(1462,plain,
% 49.00/49.20 ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1461, 130, 1455])).
% 49.00/49.20 tff(1463,plain,
% 49.00/49.20 (~m_counter_cell_v_value(c_bit0, s48)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1462, 1444])).
% 49.00/49.20 tff(1464,assumption,(~m_counter_cell_v_carry_in(c_bit0, s48)), introduced(assumption)).
% 49.00/49.20 tff(1465,plain,
% 49.00/49.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s48)),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1466,plain,
% 49.00/49.20 ($false),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1465, 43, 1464])).
% 49.00/49.20 tff(1467,plain,(m_counter_cell_v_carry_in(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.20 tff(1468,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1469,plain,
% 49.00/49.20 (((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1470,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1469])).
% 49.00/49.20 tff(1471,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1470, 1468])).
% 49.00/49.20 tff(1472,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1473,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 49.00/49.20 tff(1474,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1473, 55, 1467])).
% 49.00/49.20 tff(1475,plain,
% 49.00/49.20 (~node1(c_bit0, s48)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1474, 1463])).
% 49.00/49.20 tff(1476,plain,
% 49.00/49.20 (succ(s48, s49) <=> succ(s48, s49)),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1477,axiom,(succ(s48, s49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound49')).
% 49.00/49.20 tff(1478,plain,
% 49.00/49.20 (succ(s48, s49)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 49.00/49.20 tff(1479,plain,
% 49.00/49.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1480,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1481,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 49.00/49.20 tff(1482,plain,
% 49.00/49.20 (trans(s48, s49)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1481, 1478, 7])).
% 49.00/49.20 tff(1483,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1484,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1485,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 49.00/49.20 tff(1486,plain,
% 49.00/49.20 (node3(c_bit0, s48, s49)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1485, 21, 1482])).
% 49.00/49.20 tff(1487,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1488,plain,
% 49.00/49.20 ((node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49)) <=> (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1489,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1488])).
% 49.00/49.20 tff(1490,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1489, 1487])).
% 49.00/49.20 tff(1491,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1492,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 49.00/49.20 tff(1493,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1492, 84, 1486])).
% 49.00/49.20 tff(1494,plain,
% 49.00/49.20 (m_counter_cell_v_value(c_bit0, s49)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1493, 1475])).
% 49.00/49.20 tff(1495,assumption,(~m_counter_cell_v_carry_in(c_bit0, s49)), introduced(assumption)).
% 49.00/49.20 tff(1496,plain,
% 49.00/49.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s49)),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1497,plain,
% 49.00/49.20 ($false),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1496, 43, 1495])).
% 49.00/49.20 tff(1498,plain,(m_counter_cell_v_carry_in(c_bit0, s49)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.20 tff(1499,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1500,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1501,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 49.00/49.20 tff(1502,plain,
% 49.00/49.20 ((~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1501, 104, 1498])).
% 49.00/49.20 tff(1503,plain,
% 49.00/49.20 (~node2(c_bit0, s49)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1502, 1494])).
% 49.00/49.20 tff(1504,plain,
% 49.00/49.20 (succ(s49, s50) <=> succ(s49, s50)),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1505,axiom,(succ(s49, s50)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound50')).
% 49.00/49.20 tff(1506,plain,
% 49.00/49.20 (succ(s49, s50)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 49.00/49.20 tff(1507,plain,
% 49.00/49.20 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1508,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1509,plain,
% 49.00/49.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 49.00/49.20 tff(1510,plain,
% 49.00/49.20 (trans(s49, s50)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1509, 1506, 7])).
% 49.00/49.20 tff(1511,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1512,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1513,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50)),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 49.00/49.20 tff(1514,plain,
% 49.00/49.20 (node3(c_bit0, s49, s50)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1513, 21, 1510])).
% 49.00/49.20 tff(1515,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1516,plain,
% 49.00/49.20 ((node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50))) <=> ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1517,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1516])).
% 49.00/49.20 tff(1518,plain,
% 49.00/49.20 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1517, 1515])).
% 49.00/49.20 tff(1519,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1520,plain,
% 49.00/49.20 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))),
% 49.00/49.20 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 49.00/49.20 tff(1521,plain,
% 49.00/49.20 ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1520, 130, 1514])).
% 49.00/49.20 tff(1522,plain,
% 49.00/49.20 (~m_counter_cell_v_value(c_bit0, s50)),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1521, 1503])).
% 49.00/49.20 tff(1523,assumption,(~m_counter_cell_v_carry_in(c_bit0, s50)), introduced(assumption)).
% 49.00/49.20 tff(1524,plain,
% 49.00/49.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s50)),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.20 tff(1525,plain,
% 49.00/49.20 ($false),
% 49.00/49.20 inference(unit_resolution,[status(thm)],[1524, 43, 1523])).
% 49.00/49.20 tff(1526,plain,(m_counter_cell_v_carry_in(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.20 tff(1527,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1528,plain,
% 49.00/49.20 (((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 49.00/49.20 inference(rewrite,[status(thm)],[])).
% 49.00/49.20 tff(1529,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))))),
% 49.00/49.20 inference(monotonicity,[status(thm)],[1528])).
% 49.00/49.20 tff(1530,plain,
% 49.00/49.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50)))),
% 49.00/49.20 inference(transitivity,[status(thm)],[1529, 1527])).
% 49.00/49.20 tff(1531,plain,
% 49.00/49.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))),
% 49.00/49.20 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1532,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 49.00/49.21 tff(1533,plain,
% 49.00/49.21 (m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1532, 55, 1526])).
% 49.00/49.21 tff(1534,plain,
% 49.00/49.21 (~node1(c_bit0, s50)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1533, 1522])).
% 49.00/49.21 tff(1535,plain,
% 49.00/49.21 (succ(s50, s51) <=> succ(s50, s51)),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1536,axiom,(succ(s50, s51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound51')).
% 49.00/49.21 tff(1537,plain,
% 49.00/49.21 (succ(s50, s51)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 49.00/49.21 tff(1538,plain,
% 49.00/49.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1539,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1540,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 49.00/49.21 tff(1541,plain,
% 49.00/49.21 (trans(s50, s51)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1540, 1537, 7])).
% 49.00/49.21 tff(1542,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1543,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1544,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 49.00/49.21 tff(1545,plain,
% 49.00/49.21 (node3(c_bit0, s50, s51)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1544, 21, 1541])).
% 49.00/49.21 tff(1546,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1547,plain,
% 49.00/49.21 ((node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51)) <=> (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1548,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))))),
% 49.00/49.21 inference(monotonicity,[status(thm)],[1547])).
% 49.00/49.21 tff(1549,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 49.00/49.21 inference(transitivity,[status(thm)],[1548, 1546])).
% 49.00/49.21 tff(1550,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1551,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 49.00/49.21 tff(1552,plain,
% 49.00/49.21 (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1551, 84, 1545])).
% 49.00/49.21 tff(1553,plain,
% 49.00/49.21 (m_counter_cell_v_value(c_bit0, s51)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1552, 1534])).
% 49.00/49.21 tff(1554,assumption,(~m_counter_cell_v_carry_in(c_bit0, s51)), introduced(assumption)).
% 49.00/49.21 tff(1555,plain,
% 49.00/49.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s51)),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1556,plain,
% 49.00/49.21 ($false),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1555, 43, 1554])).
% 49.00/49.21 tff(1557,plain,(m_counter_cell_v_carry_in(c_bit0, s51)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.21 tff(1558,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1559,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1560,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 49.00/49.21 tff(1561,plain,
% 49.00/49.21 ((~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1560, 104, 1557])).
% 49.00/49.21 tff(1562,plain,
% 49.00/49.21 (~node2(c_bit0, s51)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1561, 1553])).
% 49.00/49.21 tff(1563,plain,
% 49.00/49.21 (succ(s51, s52) <=> succ(s51, s52)),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1564,axiom,(succ(s51, s52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound52')).
% 49.00/49.21 tff(1565,plain,
% 49.00/49.21 (succ(s51, s52)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 49.00/49.21 tff(1566,plain,
% 49.00/49.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1567,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1568,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 49.00/49.21 tff(1569,plain,
% 49.00/49.21 (trans(s51, s52)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1568, 1565, 7])).
% 49.00/49.21 tff(1570,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1571,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1572,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 49.00/49.21 tff(1573,plain,
% 49.00/49.21 (node3(c_bit0, s51, s52)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1572, 21, 1569])).
% 49.00/49.21 tff(1574,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1575,plain,
% 49.00/49.21 ((node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52))) <=> ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1576,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))))),
% 49.00/49.21 inference(monotonicity,[status(thm)],[1575])).
% 49.00/49.21 tff(1577,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)))),
% 49.00/49.21 inference(transitivity,[status(thm)],[1576, 1574])).
% 49.00/49.21 tff(1578,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s51) | (~node3(c_bit0, s51, s52)) | (~m_counter_cell_v_value(c_bit0, s52)))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1579,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 49.00/49.21 tff(1580,plain,
% 49.00/49.21 ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1579, 130, 1573])).
% 49.00/49.21 tff(1581,plain,
% 49.00/49.21 (~m_counter_cell_v_value(c_bit0, s52)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1580, 1562])).
% 49.00/49.21 tff(1582,assumption,(~m_counter_cell_v_carry_in(c_bit0, s52)), introduced(assumption)).
% 49.00/49.21 tff(1583,plain,
% 49.00/49.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s52)),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1584,plain,
% 49.00/49.21 ($false),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1583, 43, 1582])).
% 49.00/49.21 tff(1585,plain,(m_counter_cell_v_carry_in(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.21 tff(1586,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1587,plain,
% 49.00/49.21 (((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1588,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))))),
% 49.00/49.21 inference(monotonicity,[status(thm)],[1587])).
% 49.00/49.21 tff(1589,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52)))),
% 49.00/49.21 inference(transitivity,[status(thm)],[1588, 1586])).
% 49.00/49.21 tff(1590,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1591,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 49.00/49.21 tff(1592,plain,
% 49.00/49.21 (m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1591, 55, 1585])).
% 49.00/49.21 tff(1593,plain,
% 49.00/49.21 (~node1(c_bit0, s52)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1592, 1581])).
% 49.00/49.21 tff(1594,plain,
% 49.00/49.21 (succ(s52, s53) <=> succ(s52, s53)),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1595,axiom,(succ(s52, s53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound53')).
% 49.00/49.21 tff(1596,plain,
% 49.00/49.21 (succ(s52, s53)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 49.00/49.21 tff(1597,plain,
% 49.00/49.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1598,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1599,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 49.00/49.21 tff(1600,plain,
% 49.00/49.21 (trans(s52, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1599, 1596, 7])).
% 49.00/49.21 tff(1601,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1602,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1603,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 49.00/49.21 tff(1604,plain,
% 49.00/49.21 (node3(c_bit0, s52, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1603, 21, 1600])).
% 49.00/49.21 tff(1605,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1606,plain,
% 49.00/49.21 ((node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53)) <=> (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1607,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53))))),
% 49.00/49.21 inference(monotonicity,[status(thm)],[1606])).
% 49.00/49.21 tff(1608,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 49.00/49.21 inference(transitivity,[status(thm)],[1607, 1605])).
% 49.00/49.21 tff(1609,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1610,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 49.00/49.21 tff(1611,plain,
% 49.00/49.21 (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1610, 84, 1604])).
% 49.00/49.21 tff(1612,plain,
% 49.00/49.21 (m_counter_cell_v_value(c_bit0, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1611, 1593])).
% 49.00/49.21 tff(1613,assumption,(~m_counter_cell_v_carry_in(c_bit0, s53)), introduced(assumption)).
% 49.00/49.21 tff(1614,plain,
% 49.00/49.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s53)),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1615,plain,
% 49.00/49.21 ($false),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1614, 43, 1613])).
% 49.00/49.21 tff(1616,plain,(m_counter_cell_v_carry_in(c_bit0, s53)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.21 tff(1617,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1618,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1619,plain,
% 49.00/49.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 49.00/49.21 tff(1620,plain,
% 49.00/49.21 ((~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1619, 104, 1616])).
% 49.00/49.21 tff(1621,plain,
% 49.00/49.21 (~node2(c_bit0, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1620, 1612])).
% 49.00/49.21 tff(1622,plain,
% 49.00/49.21 (succ(s53, s54) <=> succ(s53, s54)),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1623,axiom,(succ(s53, s54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound54')).
% 49.00/49.21 tff(1624,plain,
% 49.00/49.21 (succ(s53, s54)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 49.00/49.21 tff(1625,plain,
% 49.00/49.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1626,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1627,plain,
% 49.00/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 49.00/49.21 tff(1628,plain,
% 49.00/49.21 (trans(s53, s54)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1627, 1624, 7])).
% 49.00/49.21 tff(1629,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1630,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1631,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54)),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 49.00/49.21 tff(1632,plain,
% 49.00/49.21 (node3(c_bit0, s53, s54)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1631, 21, 1628])).
% 49.00/49.21 tff(1633,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1634,plain,
% 49.00/49.21 ((node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54))) <=> ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 49.00/49.21 inference(rewrite,[status(thm)],[])).
% 49.00/49.21 tff(1635,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))))),
% 49.00/49.21 inference(monotonicity,[status(thm)],[1634])).
% 49.00/49.21 tff(1636,plain,
% 49.00/49.21 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)))),
% 49.00/49.21 inference(transitivity,[status(thm)],[1635, 1633])).
% 49.00/49.21 tff(1637,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s53) | (~node3(c_bit0, s53, s54)) | (~m_counter_cell_v_value(c_bit0, s54)))),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1638,plain,
% 49.00/49.21 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))),
% 49.00/49.21 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 49.00/49.21 tff(1639,plain,
% 49.00/49.21 ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1638, 130, 1632])).
% 49.00/49.21 tff(1640,plain,
% 49.00/49.21 (~m_counter_cell_v_value(c_bit0, s54)),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1639, 1621])).
% 49.00/49.21 tff(1641,assumption,(~m_counter_cell_v_carry_in(c_bit0, s54)), introduced(assumption)).
% 49.00/49.21 tff(1642,plain,
% 49.00/49.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s54)),
% 49.00/49.21 inference(quant_inst,[status(thm)],[])).
% 49.00/49.21 tff(1643,plain,
% 49.00/49.21 ($false),
% 49.00/49.21 inference(unit_resolution,[status(thm)],[1642, 43, 1641])).
% 49.00/49.21 tff(1644,plain,(m_counter_cell_v_carry_in(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 49.00/49.21 tff(1645,plain,
% 49.00/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1646,plain,
% 49.05/49.21 (((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1647,plain,
% 49.05/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))))),
% 49.05/49.21 inference(monotonicity,[status(thm)],[1646])).
% 49.05/49.21 tff(1648,plain,
% 49.05/49.21 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54)))),
% 49.05/49.21 inference(transitivity,[status(thm)],[1647, 1645])).
% 49.05/49.21 tff(1649,plain,
% 49.05/49.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))),
% 49.05/49.21 inference(quant_inst,[status(thm)],[])).
% 49.05/49.21 tff(1650,plain,
% 49.05/49.21 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 49.05/49.21 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 49.05/49.21 tff(1651,plain,
% 49.05/49.21 (m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1650, 55, 1644])).
% 49.05/49.21 tff(1652,plain,
% 49.05/49.21 (~node1(c_bit0, s54)),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1651, 1640])).
% 49.05/49.21 tff(1653,plain,
% 49.05/49.21 (succ(s54, s55) <=> succ(s54, s55)),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1654,axiom,(succ(s54, s55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound55')).
% 49.05/49.21 tff(1655,plain,
% 49.05/49.21 (succ(s54, s55)),
% 49.05/49.21 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 49.05/49.21 tff(1656,plain,
% 49.05/49.21 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1657,plain,
% 49.05/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 49.05/49.21 inference(quant_inst,[status(thm)],[])).
% 49.05/49.21 tff(1658,plain,
% 49.05/49.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 49.05/49.21 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 49.05/49.21 tff(1659,plain,
% 49.05/49.21 (trans(s54, s55)),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1658, 1655, 7])).
% 49.05/49.21 tff(1660,plain,
% 49.05/49.21 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1661,plain,
% 49.05/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 49.05/49.21 inference(quant_inst,[status(thm)],[])).
% 49.05/49.21 tff(1662,plain,
% 49.05/49.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55)),
% 49.05/49.21 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 49.05/49.21 tff(1663,plain,
% 49.05/49.21 (node3(c_bit0, s54, s55)),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1662, 21, 1659])).
% 49.05/49.21 tff(1664,plain,
% 49.05/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1665,plain,
% 49.05/49.21 ((node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55)) <=> (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 49.05/49.21 inference(rewrite,[status(thm)],[])).
% 49.05/49.21 tff(1666,plain,
% 49.05/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))))),
% 49.05/49.21 inference(monotonicity,[status(thm)],[1665])).
% 49.05/49.21 tff(1667,plain,
% 49.05/49.21 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)))),
% 49.05/49.21 inference(transitivity,[status(thm)],[1666, 1664])).
% 49.05/49.21 tff(1668,plain,
% 49.05/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s54) | (~node3(c_bit0, s54, s55)) | m_counter_cell_v_value(c_bit0, s55))),
% 49.05/49.21 inference(quant_inst,[status(thm)],[])).
% 49.05/49.21 tff(1669,plain,
% 49.05/49.21 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))),
% 49.05/49.21 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 49.05/49.21 tff(1670,plain,
% 49.05/49.21 (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54)),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1669, 84, 1663])).
% 49.05/49.21 tff(1671,plain,
% 49.05/49.21 (m_counter_cell_v_value(c_bit0, s55)),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1670, 1652])).
% 49.05/49.21 tff(1672,assumption,(~m_counter_cell_v_carry_in(c_bit0, s55)), introduced(assumption)).
% 49.05/49.21 tff(1673,plain,
% 49.05/49.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s55)),
% 49.05/49.21 inference(quant_inst,[status(thm)],[])).
% 49.05/49.21 tff(1674,plain,
% 49.05/49.21 ($false),
% 49.05/49.21 inference(unit_resolution,[status(thm)],[1673, 43, 1672])).
% 49.05/49.21 tff(1675,plain,(m_counter_cell_v_carry_in(c_bit0, s55)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.21 tff(1676,plain,
% 49.05/49.21 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1677,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1678,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 49.05/49.22 tff(1679,plain,
% 49.05/49.22 ((~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1678, 104, 1675])).
% 49.05/49.22 tff(1680,plain,
% 49.05/49.22 (~node2(c_bit0, s55)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1679, 1671])).
% 49.05/49.22 tff(1681,plain,
% 49.05/49.22 (succ(s55, s56) <=> succ(s55, s56)),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1682,axiom,(succ(s55, s56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound56')).
% 49.05/49.22 tff(1683,plain,
% 49.05/49.22 (succ(s55, s56)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 49.05/49.22 tff(1684,plain,
% 49.05/49.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1685,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1686,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 49.05/49.22 tff(1687,plain,
% 49.05/49.22 (trans(s55, s56)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1686, 1683, 7])).
% 49.05/49.22 tff(1688,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1689,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1690,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 49.05/49.22 tff(1691,plain,
% 49.05/49.22 (node3(c_bit0, s55, s56)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1690, 21, 1687])).
% 49.05/49.22 tff(1692,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1693,plain,
% 49.05/49.22 ((node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56))) <=> ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1694,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1693])).
% 49.05/49.22 tff(1695,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1694, 1692])).
% 49.05/49.22 tff(1696,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s55) | (~node3(c_bit0, s55, s56)) | (~m_counter_cell_v_value(c_bit0, s56)))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1697,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 49.05/49.22 tff(1698,plain,
% 49.05/49.22 ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1697, 130, 1691])).
% 49.05/49.22 tff(1699,plain,
% 49.05/49.22 (~m_counter_cell_v_value(c_bit0, s56)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1698, 1680])).
% 49.05/49.22 tff(1700,assumption,(~m_counter_cell_v_carry_in(c_bit0, s56)), introduced(assumption)).
% 49.05/49.22 tff(1701,plain,
% 49.05/49.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s56)),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1702,plain,
% 49.05/49.22 ($false),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1701, 43, 1700])).
% 49.05/49.22 tff(1703,plain,(m_counter_cell_v_carry_in(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.22 tff(1704,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1705,plain,
% 49.05/49.22 (((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1706,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1705])).
% 49.05/49.22 tff(1707,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1706, 1704])).
% 49.05/49.22 tff(1708,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1709,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 49.05/49.22 tff(1710,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1709, 55, 1703])).
% 49.05/49.22 tff(1711,plain,
% 49.05/49.22 (~node1(c_bit0, s56)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1710, 1699])).
% 49.05/49.22 tff(1712,plain,
% 49.05/49.22 (succ(s56, s57) <=> succ(s56, s57)),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1713,axiom,(succ(s56, s57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound57')).
% 49.05/49.22 tff(1714,plain,
% 49.05/49.22 (succ(s56, s57)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 49.05/49.22 tff(1715,plain,
% 49.05/49.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1716,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1717,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 49.05/49.22 tff(1718,plain,
% 49.05/49.22 (trans(s56, s57)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1717, 1714, 7])).
% 49.05/49.22 tff(1719,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1720,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1721,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 49.05/49.22 tff(1722,plain,
% 49.05/49.22 (node3(c_bit0, s56, s57)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1721, 21, 1718])).
% 49.05/49.22 tff(1723,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1724,plain,
% 49.05/49.22 ((node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57)) <=> (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1725,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1724])).
% 49.05/49.22 tff(1726,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1725, 1723])).
% 49.05/49.22 tff(1727,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s56) | (~node3(c_bit0, s56, s57)) | m_counter_cell_v_value(c_bit0, s57))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1728,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56) | (~node3(c_bit0, s56, s57))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 49.05/49.22 tff(1729,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1728, 84, 1722])).
% 49.05/49.22 tff(1730,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s57)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1729, 1711])).
% 49.05/49.22 tff(1731,assumption,(~m_counter_cell_v_carry_in(c_bit0, s57)), introduced(assumption)).
% 49.05/49.22 tff(1732,plain,
% 49.05/49.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s57)),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1733,plain,
% 49.05/49.22 ($false),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1732, 43, 1731])).
% 49.05/49.22 tff(1734,plain,(m_counter_cell_v_carry_in(c_bit0, s57)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.22 tff(1735,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1736,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1737,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 49.05/49.22 tff(1738,plain,
% 49.05/49.22 ((~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1737, 104, 1734])).
% 49.05/49.22 tff(1739,plain,
% 49.05/49.22 (~node2(c_bit0, s57)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1738, 1730])).
% 49.05/49.22 tff(1740,plain,
% 49.05/49.22 (succ(s57, s58) <=> succ(s57, s58)),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1741,axiom,(succ(s57, s58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound58')).
% 49.05/49.22 tff(1742,plain,
% 49.05/49.22 (succ(s57, s58)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 49.05/49.22 tff(1743,plain,
% 49.05/49.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1744,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1745,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 49.05/49.22 tff(1746,plain,
% 49.05/49.22 (trans(s57, s58)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1745, 1742, 7])).
% 49.05/49.22 tff(1747,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1748,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1749,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 49.05/49.22 tff(1750,plain,
% 49.05/49.22 (node3(c_bit0, s57, s58)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1749, 21, 1746])).
% 49.05/49.22 tff(1751,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1752,plain,
% 49.05/49.22 ((node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58))) <=> (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1753,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1752])).
% 49.05/49.22 tff(1754,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1753, 1751])).
% 49.05/49.22 tff(1755,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58)))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1756,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 49.05/49.22 tff(1757,plain,
% 49.05/49.22 (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1756, 130, 1750])).
% 49.05/49.22 tff(1758,plain,
% 49.05/49.22 (~m_counter_cell_v_value(c_bit0, s58)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1757, 1739])).
% 49.05/49.22 tff(1759,assumption,(~m_counter_cell_v_carry_in(c_bit0, s58)), introduced(assumption)).
% 49.05/49.22 tff(1760,plain,
% 49.05/49.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s58)),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1761,plain,
% 49.05/49.22 ($false),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1760, 43, 1759])).
% 49.05/49.22 tff(1762,plain,(m_counter_cell_v_carry_in(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.22 tff(1763,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1764,plain,
% 49.05/49.22 (((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1765,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1764])).
% 49.05/49.22 tff(1766,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1765, 1763])).
% 49.05/49.22 tff(1767,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1768,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 49.05/49.22 tff(1769,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1768, 55, 1762])).
% 49.05/49.22 tff(1770,plain,
% 49.05/49.22 (~node1(c_bit0, s58)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1769, 1758])).
% 49.05/49.22 tff(1771,plain,
% 49.05/49.22 (succ(s58, s59) <=> succ(s58, s59)),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1772,axiom,(succ(s58, s59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound59')).
% 49.05/49.22 tff(1773,plain,
% 49.05/49.22 (succ(s58, s59)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 49.05/49.22 tff(1774,plain,
% 49.05/49.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1775,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1776,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 49.05/49.22 tff(1777,plain,
% 49.05/49.22 (trans(s58, s59)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1776, 1773, 7])).
% 49.05/49.22 tff(1778,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1779,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1780,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 49.05/49.22 tff(1781,plain,
% 49.05/49.22 (node3(c_bit0, s58, s59)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1780, 21, 1777])).
% 49.05/49.22 tff(1782,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1783,plain,
% 49.05/49.22 ((node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59)) <=> (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1784,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59))))),
% 49.05/49.22 inference(monotonicity,[status(thm)],[1783])).
% 49.05/49.22 tff(1785,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)))),
% 49.05/49.22 inference(transitivity,[status(thm)],[1784, 1782])).
% 49.05/49.22 tff(1786,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s58) | (~node3(c_bit0, s58, s59)) | m_counter_cell_v_value(c_bit0, s59))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1787,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 49.05/49.22 tff(1788,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1787, 84, 1781])).
% 49.05/49.22 tff(1789,plain,
% 49.05/49.22 (m_counter_cell_v_value(c_bit0, s59)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1788, 1770])).
% 49.05/49.22 tff(1790,assumption,(~m_counter_cell_v_carry_in(c_bit0, s59)), introduced(assumption)).
% 49.05/49.22 tff(1791,plain,
% 49.05/49.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s59)),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1792,plain,
% 49.05/49.22 ($false),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1791, 43, 1790])).
% 49.05/49.22 tff(1793,plain,(m_counter_cell_v_carry_in(c_bit0, s59)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.22 tff(1794,plain,
% 49.05/49.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1795,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1796,plain,
% 49.05/49.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 49.05/49.22 tff(1797,plain,
% 49.05/49.22 ((~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1796, 104, 1793])).
% 49.05/49.22 tff(1798,plain,
% 49.05/49.22 (~node2(c_bit0, s59)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1797, 1789])).
% 49.05/49.22 tff(1799,plain,
% 49.05/49.22 (succ(s59, s60) <=> succ(s59, s60)),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1800,axiom,(succ(s59, s60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound60')).
% 49.05/49.22 tff(1801,plain,
% 49.05/49.22 (succ(s59, s60)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 49.05/49.22 tff(1802,plain,
% 49.05/49.22 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1803,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1804,plain,
% 49.05/49.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 49.05/49.22 tff(1805,plain,
% 49.05/49.22 (trans(s59, s60)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1804, 1801, 7])).
% 49.05/49.22 tff(1806,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit0, s59, s60))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit0, s59, s60))),
% 49.05/49.22 inference(rewrite,[status(thm)],[])).
% 49.05/49.22 tff(1807,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit0, s59, s60))),
% 49.05/49.22 inference(quant_inst,[status(thm)],[])).
% 49.05/49.22 tff(1808,plain,
% 49.05/49.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit0, s59, s60)),
% 49.05/49.22 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 49.05/49.22 tff(1809,plain,
% 49.05/49.22 (node3(c_bit0, s59, s60)),
% 49.05/49.22 inference(unit_resolution,[status(thm)],[1808, 21, 1805])).
% 49.05/49.22 tff(1810,plain,
% 49.05/49.22 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1811,plain,
% 49.05/49.23 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)) | (~m_counter_cell_v_value(c_bit0, s60))) <=> ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1812,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1811])).
% 49.05/49.23 tff(1813,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1812, 1810])).
% 49.05/49.23 tff(1814,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1815,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 49.05/49.23 tff(1816,plain,
% 49.05/49.23 ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1815, 130, 1809])).
% 49.05/49.23 tff(1817,plain,
% 49.05/49.23 (~m_counter_cell_v_value(c_bit0, s60)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1816, 1798])).
% 49.05/49.23 tff(1818,assumption,(~m_counter_cell_v_carry_in(c_bit0, s60)), introduced(assumption)).
% 49.05/49.23 tff(1819,plain,
% 49.05/49.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s60)),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1820,plain,
% 49.05/49.23 ($false),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1819, 43, 1818])).
% 49.05/49.23 tff(1821,plain,(m_counter_cell_v_carry_in(c_bit0, s60)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.23 tff(1822,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1823,plain,
% 49.05/49.23 (((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1824,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1823])).
% 49.05/49.23 tff(1825,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1824, 1822])).
% 49.05/49.23 tff(1826,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1827,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 49.05/49.23 tff(1828,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1827, 55, 1821])).
% 49.05/49.23 tff(1829,plain,
% 49.05/49.23 (~node1(c_bit0, s60)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1828, 1817])).
% 49.05/49.23 tff(1830,plain,
% 49.05/49.23 (succ(s60, s61) <=> succ(s60, s61)),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1831,axiom,(succ(s60, s61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound61')).
% 49.05/49.23 tff(1832,plain,
% 49.05/49.23 (succ(s60, s61)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 49.05/49.23 tff(1833,plain,
% 49.05/49.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1834,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1835,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 49.05/49.23 tff(1836,plain,
% 49.05/49.23 (trans(s60, s61)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1835, 1832, 7])).
% 49.05/49.23 tff(1837,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit0, s60, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit0, s60, s61))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1838,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit0, s60, s61))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1839,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit0, s60, s61)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 49.05/49.23 tff(1840,plain,
% 49.05/49.23 (node3(c_bit0, s60, s61)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1839, 21, 1836])).
% 49.05/49.23 tff(1841,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1842,plain,
% 49.05/49.23 ((node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61)) <=> (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1843,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1842])).
% 49.05/49.23 tff(1844,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1843, 1841])).
% 49.05/49.23 tff(1845,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1846,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 49.05/49.23 tff(1847,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1846, 84, 1840])).
% 49.05/49.23 tff(1848,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s61)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1847, 1829])).
% 49.05/49.23 tff(1849,assumption,(~m_counter_cell_v_carry_in(c_bit0, s61)), introduced(assumption)).
% 49.05/49.23 tff(1850,plain,
% 49.05/49.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s61)),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1851,plain,
% 49.05/49.23 ($false),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1850, 43, 1849])).
% 49.05/49.23 tff(1852,plain,(m_counter_cell_v_carry_in(c_bit0, s61)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.23 tff(1853,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1854,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1855,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 49.05/49.23 tff(1856,plain,
% 49.05/49.23 ((~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61))),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1855, 104, 1852])).
% 49.05/49.23 tff(1857,plain,
% 49.05/49.23 (~node2(c_bit0, s61)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1856, 1848])).
% 49.05/49.23 tff(1858,plain,
% 49.05/49.23 (succ(s61, s62) <=> succ(s61, s62)),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1859,axiom,(succ(s61, s62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound62')).
% 49.05/49.23 tff(1860,plain,
% 49.05/49.23 (succ(s61, s62)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 49.05/49.23 tff(1861,plain,
% 49.05/49.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1862,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1863,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 49.05/49.23 tff(1864,plain,
% 49.05/49.23 (trans(s61, s62)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1863, 1860, 7])).
% 49.05/49.23 tff(1865,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit0, s61, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit0, s61, s62))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1866,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit0, s61, s62))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1867,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit0, s61, s62)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 49.05/49.23 tff(1868,plain,
% 49.05/49.23 (node3(c_bit0, s61, s62)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1867, 21, 1864])).
% 49.05/49.23 tff(1869,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1870,plain,
% 49.05/49.23 ((node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62))) <=> ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1871,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1870])).
% 49.05/49.23 tff(1872,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1871, 1869])).
% 49.05/49.23 tff(1873,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1874,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 49.05/49.23 tff(1875,plain,
% 49.05/49.23 ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1874, 130, 1868])).
% 49.05/49.23 tff(1876,plain,
% 49.05/49.23 (~m_counter_cell_v_value(c_bit0, s62)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1875, 1857])).
% 49.05/49.23 tff(1877,assumption,(~m_counter_cell_v_carry_in(c_bit0, s62)), introduced(assumption)).
% 49.05/49.23 tff(1878,plain,
% 49.05/49.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s62)),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1879,plain,
% 49.05/49.23 ($false),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1878, 43, 1877])).
% 49.05/49.23 tff(1880,plain,(m_counter_cell_v_carry_in(c_bit0, s62)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.23 tff(1881,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1882,plain,
% 49.05/49.23 (((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1883,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1882])).
% 49.05/49.23 tff(1884,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1883, 1881])).
% 49.05/49.23 tff(1885,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1886,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 49.05/49.23 tff(1887,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1886, 55, 1880])).
% 49.05/49.23 tff(1888,plain,
% 49.05/49.23 (~node1(c_bit0, s62)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1887, 1876])).
% 49.05/49.23 tff(1889,plain,
% 49.05/49.23 (succ(s62, s63) <=> succ(s62, s63)),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1890,axiom,(succ(s62, s63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound63')).
% 49.05/49.23 tff(1891,plain,
% 49.05/49.23 (succ(s62, s63)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 49.05/49.23 tff(1892,plain,
% 49.05/49.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1893,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1894,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 49.05/49.23 tff(1895,plain,
% 49.05/49.23 (trans(s62, s63)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1894, 1891, 7])).
% 49.05/49.23 tff(1896,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit0, s62, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit0, s62, s63))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1897,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit0, s62, s63))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1898,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit0, s62, s63)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 49.05/49.23 tff(1899,plain,
% 49.05/49.23 (node3(c_bit0, s62, s63)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1898, 21, 1895])).
% 49.05/49.23 tff(1900,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1901,plain,
% 49.05/49.23 ((node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63)) <=> (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1902,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1901])).
% 49.05/49.23 tff(1903,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1902, 1900])).
% 49.05/49.23 tff(1904,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1905,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 49.05/49.23 tff(1906,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1905, 84, 1899])).
% 49.05/49.23 tff(1907,plain,
% 49.05/49.23 (m_counter_cell_v_value(c_bit0, s63)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1906, 1888])).
% 49.05/49.23 tff(1908,assumption,(~m_counter_cell_v_carry_in(c_bit0, s63)), introduced(assumption)).
% 49.05/49.23 tff(1909,plain,
% 49.05/49.23 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s63)),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1910,plain,
% 49.05/49.23 ($false),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1909, 43, 1908])).
% 49.05/49.23 tff(1911,plain,(m_counter_cell_v_carry_in(c_bit0, s63)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.23 tff(1912,plain,
% 49.05/49.23 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1913,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1914,plain,
% 49.05/49.23 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 49.05/49.23 tff(1915,plain,
% 49.05/49.23 ((~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63))),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1914, 104, 1911])).
% 49.05/49.23 tff(1916,plain,
% 49.05/49.23 (~node2(c_bit0, s63)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1915, 1907])).
% 49.05/49.23 tff(1917,plain,
% 49.05/49.23 (succ(s63, s64) <=> succ(s63, s64)),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1918,axiom,(succ(s63, s64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound64')).
% 49.05/49.23 tff(1919,plain,
% 49.05/49.23 (succ(s63, s64)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 49.05/49.23 tff(1920,plain,
% 49.05/49.23 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1921,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1922,plain,
% 49.05/49.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 49.05/49.23 tff(1923,plain,
% 49.05/49.23 (trans(s63, s64)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1922, 1919, 7])).
% 49.05/49.23 tff(1924,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit0, s63, s64))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit0, s63, s64))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1925,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit0, s63, s64))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1926,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit0, s63, s64)),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 49.05/49.23 tff(1927,plain,
% 49.05/49.23 (node3(c_bit0, s63, s64)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1926, 21, 1923])).
% 49.05/49.23 tff(1928,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1929,plain,
% 49.05/49.23 ((node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64))) <=> ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 49.05/49.23 inference(rewrite,[status(thm)],[])).
% 49.05/49.23 tff(1930,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64))))),
% 49.05/49.23 inference(monotonicity,[status(thm)],[1929])).
% 49.05/49.23 tff(1931,plain,
% 49.05/49.23 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 49.05/49.23 inference(transitivity,[status(thm)],[1930, 1928])).
% 49.05/49.23 tff(1932,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))),
% 49.05/49.23 inference(quant_inst,[status(thm)],[])).
% 49.05/49.23 tff(1933,plain,
% 49.05/49.23 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64))),
% 49.05/49.23 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 49.05/49.23 tff(1934,plain,
% 49.05/49.23 ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63)),
% 49.05/49.23 inference(unit_resolution,[status(thm)],[1933, 130, 1927])).
% 49.05/49.24 tff(1935,plain,
% 49.05/49.24 (~m_counter_cell_v_value(c_bit0, s64)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1934, 1916])).
% 49.05/49.24 tff(1936,assumption,(~m_counter_cell_v_carry_in(c_bit0, s64)), introduced(assumption)).
% 49.05/49.24 tff(1937,plain,
% 49.05/49.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s64)),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1938,plain,
% 49.05/49.24 ($false),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1937, 43, 1936])).
% 49.05/49.24 tff(1939,plain,(m_counter_cell_v_carry_in(c_bit0, s64)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.24 tff(1940,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1941,plain,
% 49.05/49.24 (((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1942,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[1941])).
% 49.05/49.24 tff(1943,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[1942, 1940])).
% 49.05/49.24 tff(1944,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1945,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 49.05/49.24 tff(1946,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1945, 55, 1939])).
% 49.05/49.24 tff(1947,plain,
% 49.05/49.24 (~node1(c_bit0, s64)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1946, 1935])).
% 49.05/49.24 tff(1948,plain,
% 49.05/49.24 (succ(s64, s65) <=> succ(s64, s65)),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1949,axiom,(succ(s64, s65)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound65')).
% 49.05/49.24 tff(1950,plain,
% 49.05/49.24 (succ(s64, s65)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 49.05/49.24 tff(1951,plain,
% 49.05/49.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1952,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1953,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 49.05/49.24 tff(1954,plain,
% 49.05/49.24 (trans(s64, s65)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1953, 1950, 7])).
% 49.05/49.24 tff(1955,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit0, s64, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit0, s64, s65))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1956,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit0, s64, s65))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1957,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit0, s64, s65)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 49.05/49.24 tff(1958,plain,
% 49.05/49.24 (node3(c_bit0, s64, s65)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1957, 21, 1954])).
% 49.05/49.24 tff(1959,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1960,plain,
% 49.05/49.24 ((node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65)) <=> (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1961,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[1960])).
% 49.05/49.24 tff(1962,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[1961, 1959])).
% 49.05/49.24 tff(1963,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1964,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 49.05/49.24 tff(1965,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1964, 84, 1958])).
% 49.05/49.24 tff(1966,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s65)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1965, 1947])).
% 49.05/49.24 tff(1967,assumption,(~m_counter_cell_v_carry_in(c_bit0, s65)), introduced(assumption)).
% 49.05/49.24 tff(1968,plain,
% 49.05/49.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s65)),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1969,plain,
% 49.05/49.24 ($false),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1968, 43, 1967])).
% 49.05/49.24 tff(1970,plain,(m_counter_cell_v_carry_in(c_bit0, s65)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.24 tff(1971,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1972,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1973,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 49.05/49.24 tff(1974,plain,
% 49.05/49.24 ((~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65))),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1973, 104, 1970])).
% 49.05/49.24 tff(1975,plain,
% 49.05/49.24 (~node2(c_bit0, s65)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1974, 1966])).
% 49.05/49.24 tff(1976,plain,
% 49.05/49.24 (succ(s65, s66) <=> succ(s65, s66)),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1977,axiom,(succ(s65, s66)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound66')).
% 49.05/49.24 tff(1978,plain,
% 49.05/49.24 (succ(s65, s66)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 49.05/49.24 tff(1979,plain,
% 49.05/49.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1980,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1981,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 49.05/49.24 tff(1982,plain,
% 49.05/49.24 (trans(s65, s66)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1981, 1978, 7])).
% 49.05/49.24 tff(1983,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit0, s65, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit0, s65, s66))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1984,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit0, s65, s66))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1985,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit0, s65, s66)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 49.05/49.24 tff(1986,plain,
% 49.05/49.24 (node3(c_bit0, s65, s66)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1985, 21, 1982])).
% 49.05/49.24 tff(1987,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1988,plain,
% 49.05/49.24 ((node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66))) <=> ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(1989,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[1988])).
% 49.05/49.24 tff(1990,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[1989, 1987])).
% 49.05/49.24 tff(1991,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1992,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 49.05/49.24 tff(1993,plain,
% 49.05/49.24 ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1992, 130, 1986])).
% 49.05/49.24 tff(1994,plain,
% 49.05/49.24 (~m_counter_cell_v_value(c_bit0, s66)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1993, 1975])).
% 49.05/49.24 tff(1995,assumption,(~m_counter_cell_v_carry_in(c_bit0, s66)), introduced(assumption)).
% 49.05/49.24 tff(1996,plain,
% 49.05/49.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s66)),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(1997,plain,
% 49.05/49.24 ($false),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[1996, 43, 1995])).
% 49.05/49.24 tff(1998,plain,(m_counter_cell_v_carry_in(c_bit0, s66)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.24 tff(1999,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2000,plain,
% 49.05/49.24 (((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2001,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[2000])).
% 49.05/49.24 tff(2002,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[2001, 1999])).
% 49.05/49.24 tff(2003,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2004,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 49.05/49.24 tff(2005,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2004, 55, 1998])).
% 49.05/49.24 tff(2006,plain,
% 49.05/49.24 (~node1(c_bit0, s66)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2005, 1994])).
% 49.05/49.24 tff(2007,plain,
% 49.05/49.24 (succ(s66, s67) <=> succ(s66, s67)),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2008,axiom,(succ(s66, s67)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound67')).
% 49.05/49.24 tff(2009,plain,
% 49.05/49.24 (succ(s66, s67)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 49.05/49.24 tff(2010,plain,
% 49.05/49.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2011,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2012,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 49.05/49.24 tff(2013,plain,
% 49.05/49.24 (trans(s66, s67)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2012, 2009, 7])).
% 49.05/49.24 tff(2014,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit0, s66, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit0, s66, s67))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2015,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit0, s66, s67))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2016,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit0, s66, s67)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 49.05/49.24 tff(2017,plain,
% 49.05/49.24 (node3(c_bit0, s66, s67)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2016, 21, 2013])).
% 49.05/49.24 tff(2018,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2019,plain,
% 49.05/49.24 ((node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67)) <=> (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2020,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[2019])).
% 49.05/49.24 tff(2021,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[2020, 2018])).
% 49.05/49.24 tff(2022,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2023,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 49.05/49.24 tff(2024,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2023, 84, 2017])).
% 49.05/49.24 tff(2025,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s67)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2024, 2006])).
% 49.05/49.24 tff(2026,assumption,(~m_counter_cell_v_carry_in(c_bit0, s67)), introduced(assumption)).
% 49.05/49.24 tff(2027,plain,
% 49.05/49.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s67)),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2028,plain,
% 49.05/49.24 ($false),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2027, 43, 2026])).
% 49.05/49.24 tff(2029,plain,(m_counter_cell_v_carry_in(c_bit0, s67)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.24 tff(2030,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2031,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2032,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 49.05/49.24 tff(2033,plain,
% 49.05/49.24 ((~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67))),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2032, 104, 2029])).
% 49.05/49.24 tff(2034,plain,
% 49.05/49.24 (~node2(c_bit0, s67)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2033, 2025])).
% 49.05/49.24 tff(2035,plain,
% 49.05/49.24 (succ(s67, s68) <=> succ(s67, s68)),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2036,axiom,(succ(s67, s68)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound68')).
% 49.05/49.24 tff(2037,plain,
% 49.05/49.24 (succ(s67, s68)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 49.05/49.24 tff(2038,plain,
% 49.05/49.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2039,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2040,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 49.05/49.24 tff(2041,plain,
% 49.05/49.24 (trans(s67, s68)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2040, 2037, 7])).
% 49.05/49.24 tff(2042,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit0, s67, s68))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit0, s67, s68))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2043,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit0, s67, s68))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2044,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit0, s67, s68)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 49.05/49.24 tff(2045,plain,
% 49.05/49.24 (node3(c_bit0, s67, s68)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2044, 21, 2041])).
% 49.05/49.24 tff(2046,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2047,plain,
% 49.05/49.24 ((node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68))) <=> ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2048,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[2047])).
% 49.05/49.24 tff(2049,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[2048, 2046])).
% 49.05/49.24 tff(2050,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2051,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 49.05/49.24 tff(2052,plain,
% 49.05/49.24 ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2051, 130, 2045])).
% 49.05/49.24 tff(2053,plain,
% 49.05/49.24 (~m_counter_cell_v_value(c_bit0, s68)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2052, 2034])).
% 49.05/49.24 tff(2054,assumption,(~m_counter_cell_v_carry_in(c_bit0, s68)), introduced(assumption)).
% 49.05/49.24 tff(2055,plain,
% 49.05/49.24 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s68)),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2056,plain,
% 49.05/49.24 ($false),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2055, 43, 2054])).
% 49.05/49.24 tff(2057,plain,(m_counter_cell_v_carry_in(c_bit0, s68)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.24 tff(2058,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2059,plain,
% 49.05/49.24 (((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2060,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[2059])).
% 49.05/49.24 tff(2061,plain,
% 49.05/49.24 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 49.05/49.24 inference(transitivity,[status(thm)],[2060, 2058])).
% 49.05/49.24 tff(2062,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2063,plain,
% 49.05/49.24 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 49.05/49.24 tff(2064,plain,
% 49.05/49.24 (m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2063, 55, 2057])).
% 49.05/49.24 tff(2065,plain,
% 49.05/49.24 (~node1(c_bit0, s68)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2064, 2053])).
% 49.05/49.24 tff(2066,plain,
% 49.05/49.24 (succ(s68, s69) <=> succ(s68, s69)),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2067,axiom,(succ(s68, s69)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound69')).
% 49.05/49.24 tff(2068,plain,
% 49.05/49.24 (succ(s68, s69)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 49.05/49.24 tff(2069,plain,
% 49.05/49.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2070,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2071,plain,
% 49.05/49.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 49.05/49.24 tff(2072,plain,
% 49.05/49.24 (trans(s68, s69)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2071, 2068, 7])).
% 49.05/49.24 tff(2073,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit0, s68, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit0, s68, s69))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2074,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit0, s68, s69))),
% 49.05/49.24 inference(quant_inst,[status(thm)],[])).
% 49.05/49.24 tff(2075,plain,
% 49.05/49.24 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit0, s68, s69)),
% 49.05/49.24 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 49.05/49.24 tff(2076,plain,
% 49.05/49.24 (node3(c_bit0, s68, s69)),
% 49.05/49.24 inference(unit_resolution,[status(thm)],[2075, 21, 2072])).
% 49.05/49.24 tff(2077,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2078,plain,
% 49.05/49.24 ((node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69)) <=> (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 49.05/49.24 inference(rewrite,[status(thm)],[])).
% 49.05/49.24 tff(2079,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69))))),
% 49.05/49.24 inference(monotonicity,[status(thm)],[2078])).
% 49.05/49.24 tff(2080,plain,
% 49.05/49.24 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 49.05/49.25 inference(transitivity,[status(thm)],[2079, 2077])).
% 49.05/49.25 tff(2081,plain,
% 49.05/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))),
% 49.05/49.25 inference(quant_inst,[status(thm)],[])).
% 49.05/49.25 tff(2082,plain,
% 49.05/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69))),
% 49.05/49.25 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 49.05/49.25 tff(2083,plain,
% 49.05/49.25 (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68)),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2082, 84, 2076])).
% 49.05/49.25 tff(2084,plain,
% 49.05/49.25 (m_counter_cell_v_value(c_bit0, s69)),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2083, 2065])).
% 49.05/49.25 tff(2085,assumption,(~m_counter_cell_v_carry_in(c_bit0, s69)), introduced(assumption)).
% 49.05/49.25 tff(2086,plain,
% 49.05/49.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s69)),
% 49.05/49.25 inference(quant_inst,[status(thm)],[])).
% 49.05/49.25 tff(2087,plain,
% 49.05/49.25 ($false),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2086, 43, 2085])).
% 49.05/49.25 tff(2088,plain,(m_counter_cell_v_carry_in(c_bit0, s69)), inference(lemma,lemma(discharge,[]))).
% 49.05/49.25 tff(2089,plain,
% 49.05/49.25 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))),
% 49.05/49.25 inference(rewrite,[status(thm)],[])).
% 49.05/49.25 tff(2090,plain,
% 49.05/49.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))),
% 49.05/49.25 inference(quant_inst,[status(thm)],[])).
% 49.05/49.25 tff(2091,plain,
% 49.05/49.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69))),
% 49.05/49.25 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 49.05/49.25 tff(2092,plain,
% 49.05/49.25 ((~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69))),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2091, 104, 2088])).
% 49.05/49.25 tff(2093,plain,
% 49.05/49.25 (~node2(c_bit0, s69)),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2092, 2084])).
% 49.05/49.25 tff(2094,plain,
% 49.05/49.25 (succ(s69, s70) <=> succ(s69, s70)),
% 49.05/49.25 inference(rewrite,[status(thm)],[])).
% 49.05/49.25 tff(2095,axiom,(succ(s69, s70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound70')).
% 49.05/49.25 tff(2096,plain,
% 49.05/49.25 (succ(s69, s70)),
% 49.05/49.25 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 49.05/49.25 tff(2097,plain,
% 49.05/49.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70))),
% 49.05/49.25 inference(rewrite,[status(thm)],[])).
% 49.05/49.25 tff(2098,plain,
% 49.05/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))),
% 49.05/49.25 inference(quant_inst,[status(thm)],[])).
% 49.05/49.25 tff(2099,plain,
% 49.05/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70)),
% 49.05/49.25 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 49.05/49.25 tff(2100,plain,
% 49.05/49.25 (trans(s69, s70)),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2099, 2096, 7])).
% 49.05/49.25 tff(2101,plain,
% 49.05/49.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit0, s69, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit0, s69, s70))),
% 49.05/49.25 inference(rewrite,[status(thm)],[])).
% 49.05/49.25 tff(2102,plain,
% 49.05/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit0, s69, s70))),
% 49.05/49.25 inference(quant_inst,[status(thm)],[])).
% 49.05/49.25 tff(2103,plain,
% 49.05/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit0, s69, s70)),
% 49.05/49.25 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 49.05/49.25 tff(2104,plain,
% 49.05/49.25 (node3(c_bit0, s69, s70)),
% 49.05/49.25 inference(unit_resolution,[status(thm)],[2103, 21, 2100])).
% 49.05/49.25 tff(2105,plain,
% 49.05/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2106,plain,
% 49.09/49.25 ((node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70))) <=> ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2107,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2106])).
% 49.09/49.25 tff(2108,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2107, 2105])).
% 49.09/49.25 tff(2109,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2110,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 49.09/49.25 tff(2111,plain,
% 49.09/49.25 ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2110, 130, 2104])).
% 49.09/49.25 tff(2112,plain,
% 49.09/49.25 (~m_counter_cell_v_value(c_bit0, s70)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2111, 2093])).
% 49.09/49.25 tff(2113,assumption,(~m_counter_cell_v_carry_in(c_bit0, s70)), introduced(assumption)).
% 49.09/49.25 tff(2114,plain,
% 49.09/49.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s70)),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2115,plain,
% 49.09/49.25 ($false),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2114, 43, 2113])).
% 49.09/49.25 tff(2116,plain,(m_counter_cell_v_carry_in(c_bit0, s70)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.25 tff(2117,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2118,plain,
% 49.09/49.25 (((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2119,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2118])).
% 49.09/49.25 tff(2120,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2119, 2117])).
% 49.09/49.25 tff(2121,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2122,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 49.09/49.25 tff(2123,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2122, 55, 2116])).
% 49.09/49.25 tff(2124,plain,
% 49.09/49.25 (~node1(c_bit0, s70)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2123, 2112])).
% 49.09/49.25 tff(2125,plain,
% 49.09/49.25 (succ(s70, s71) <=> succ(s70, s71)),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2126,axiom,(succ(s70, s71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound71')).
% 49.09/49.25 tff(2127,plain,
% 49.09/49.25 (succ(s70, s71)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 49.09/49.25 tff(2128,plain,
% 49.09/49.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2129,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2130,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 49.09/49.25 tff(2131,plain,
% 49.09/49.25 (trans(s70, s71)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2130, 2127, 7])).
% 49.09/49.25 tff(2132,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit0, s70, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit0, s70, s71))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2133,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit0, s70, s71))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2134,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit0, s70, s71)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 49.09/49.25 tff(2135,plain,
% 49.09/49.25 (node3(c_bit0, s70, s71)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2134, 21, 2131])).
% 49.09/49.25 tff(2136,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2137,plain,
% 49.09/49.25 ((node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71)) <=> (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2138,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2137])).
% 49.09/49.25 tff(2139,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2138, 2136])).
% 49.09/49.25 tff(2140,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2141,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 49.09/49.25 tff(2142,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2141, 84, 2135])).
% 49.09/49.25 tff(2143,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s71)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2142, 2124])).
% 49.09/49.25 tff(2144,assumption,(~m_counter_cell_v_carry_in(c_bit0, s71)), introduced(assumption)).
% 49.09/49.25 tff(2145,plain,
% 49.09/49.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s71)),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2146,plain,
% 49.09/49.25 ($false),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2145, 43, 2144])).
% 49.09/49.25 tff(2147,plain,(m_counter_cell_v_carry_in(c_bit0, s71)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.25 tff(2148,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2149,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2150,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 49.09/49.25 tff(2151,plain,
% 49.09/49.25 ((~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71))),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2150, 104, 2147])).
% 49.09/49.25 tff(2152,plain,
% 49.09/49.25 (~node2(c_bit0, s71)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2151, 2143])).
% 49.09/49.25 tff(2153,plain,
% 49.09/49.25 (succ(s71, s72) <=> succ(s71, s72)),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2154,axiom,(succ(s71, s72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound72')).
% 49.09/49.25 tff(2155,plain,
% 49.09/49.25 (succ(s71, s72)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 49.09/49.25 tff(2156,plain,
% 49.09/49.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2157,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2158,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 49.09/49.25 tff(2159,plain,
% 49.09/49.25 (trans(s71, s72)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2158, 2155, 7])).
% 49.09/49.25 tff(2160,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit0, s71, s72))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit0, s71, s72))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2161,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit0, s71, s72))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2162,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit0, s71, s72)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 49.09/49.25 tff(2163,plain,
% 49.09/49.25 (node3(c_bit0, s71, s72)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2162, 21, 2159])).
% 49.09/49.25 tff(2164,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2165,plain,
% 49.09/49.25 ((node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72))) <=> ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2166,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2165])).
% 49.09/49.25 tff(2167,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2166, 2164])).
% 49.09/49.25 tff(2168,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2169,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 49.09/49.25 tff(2170,plain,
% 49.09/49.25 ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2169, 130, 2163])).
% 49.09/49.25 tff(2171,plain,
% 49.09/49.25 (~m_counter_cell_v_value(c_bit0, s72)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2170, 2152])).
% 49.09/49.25 tff(2172,assumption,(~m_counter_cell_v_carry_in(c_bit0, s72)), introduced(assumption)).
% 49.09/49.25 tff(2173,plain,
% 49.09/49.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s72)),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2174,plain,
% 49.09/49.25 ($false),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2173, 43, 2172])).
% 49.09/49.25 tff(2175,plain,(m_counter_cell_v_carry_in(c_bit0, s72)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.25 tff(2176,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2177,plain,
% 49.09/49.25 (((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2178,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2177])).
% 49.09/49.25 tff(2179,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2178, 2176])).
% 49.09/49.25 tff(2180,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2181,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 49.09/49.25 tff(2182,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2181, 55, 2175])).
% 49.09/49.25 tff(2183,plain,
% 49.09/49.25 (~node1(c_bit0, s72)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2182, 2171])).
% 49.09/49.25 tff(2184,plain,
% 49.09/49.25 (succ(s72, s73) <=> succ(s72, s73)),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2185,axiom,(succ(s72, s73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound73')).
% 49.09/49.25 tff(2186,plain,
% 49.09/49.25 (succ(s72, s73)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 49.09/49.25 tff(2187,plain,
% 49.09/49.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2188,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2189,plain,
% 49.09/49.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 49.09/49.25 tff(2190,plain,
% 49.09/49.25 (trans(s72, s73)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2189, 2186, 7])).
% 49.09/49.25 tff(2191,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit0, s72, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit0, s72, s73))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2192,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit0, s72, s73))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2193,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit0, s72, s73)),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 49.09/49.25 tff(2194,plain,
% 49.09/49.25 (node3(c_bit0, s72, s73)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2193, 21, 2190])).
% 49.09/49.25 tff(2195,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2196,plain,
% 49.09/49.25 ((node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73)) <=> (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2197,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73))))),
% 49.09/49.25 inference(monotonicity,[status(thm)],[2196])).
% 49.09/49.25 tff(2198,plain,
% 49.09/49.25 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 49.09/49.25 inference(transitivity,[status(thm)],[2197, 2195])).
% 49.09/49.25 tff(2199,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2200,plain,
% 49.09/49.25 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73))),
% 49.09/49.25 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 49.09/49.25 tff(2201,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2200, 84, 2194])).
% 49.09/49.25 tff(2202,plain,
% 49.09/49.25 (m_counter_cell_v_value(c_bit0, s73)),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2201, 2183])).
% 49.09/49.25 tff(2203,assumption,(~m_counter_cell_v_carry_in(c_bit0, s73)), introduced(assumption)).
% 49.09/49.25 tff(2204,plain,
% 49.09/49.25 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s73)),
% 49.09/49.25 inference(quant_inst,[status(thm)],[])).
% 49.09/49.25 tff(2205,plain,
% 49.09/49.25 ($false),
% 49.09/49.25 inference(unit_resolution,[status(thm)],[2204, 43, 2203])).
% 49.09/49.25 tff(2206,plain,(m_counter_cell_v_carry_in(c_bit0, s73)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.25 tff(2207,plain,
% 49.09/49.25 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))),
% 49.09/49.25 inference(rewrite,[status(thm)],[])).
% 49.09/49.25 tff(2208,plain,
% 49.09/49.25 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2209,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 49.09/49.26 tff(2210,plain,
% 49.09/49.26 ((~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73))),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2209, 104, 2206])).
% 49.09/49.26 tff(2211,plain,
% 49.09/49.26 (~node2(c_bit0, s73)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2210, 2202])).
% 49.09/49.26 tff(2212,plain,
% 49.09/49.26 (succ(s73, s74) <=> succ(s73, s74)),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2213,axiom,(succ(s73, s74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound74')).
% 49.09/49.26 tff(2214,plain,
% 49.09/49.26 (succ(s73, s74)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 49.09/49.26 tff(2215,plain,
% 49.09/49.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2216,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2217,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 49.09/49.26 tff(2218,plain,
% 49.09/49.26 (trans(s73, s74)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2217, 2214, 7])).
% 49.09/49.26 tff(2219,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit0, s73, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit0, s73, s74))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2220,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit0, s73, s74))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2221,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit0, s73, s74)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 49.09/49.26 tff(2222,plain,
% 49.09/49.26 (node3(c_bit0, s73, s74)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2221, 21, 2218])).
% 49.09/49.26 tff(2223,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2224,plain,
% 49.09/49.26 ((node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74))) <=> ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2225,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2224])).
% 49.09/49.26 tff(2226,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2225, 2223])).
% 49.09/49.26 tff(2227,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2228,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 49.09/49.26 tff(2229,plain,
% 49.09/49.26 ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2228, 130, 2222])).
% 49.09/49.26 tff(2230,plain,
% 49.09/49.26 (~m_counter_cell_v_value(c_bit0, s74)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2229, 2211])).
% 49.09/49.26 tff(2231,assumption,(~m_counter_cell_v_carry_in(c_bit0, s74)), introduced(assumption)).
% 49.09/49.26 tff(2232,plain,
% 49.09/49.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s74)),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2233,plain,
% 49.09/49.26 ($false),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2232, 43, 2231])).
% 49.09/49.26 tff(2234,plain,(m_counter_cell_v_carry_in(c_bit0, s74)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.26 tff(2235,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2236,plain,
% 49.09/49.26 (((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2237,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2236])).
% 49.09/49.26 tff(2238,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2237, 2235])).
% 49.09/49.26 tff(2239,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2240,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 49.09/49.26 tff(2241,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2240, 55, 2234])).
% 49.09/49.26 tff(2242,plain,
% 49.09/49.26 (~node1(c_bit0, s74)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2241, 2230])).
% 49.09/49.26 tff(2243,plain,
% 49.09/49.26 (succ(s74, s75) <=> succ(s74, s75)),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2244,axiom,(succ(s74, s75)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound75')).
% 49.09/49.26 tff(2245,plain,
% 49.09/49.26 (succ(s74, s75)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 49.09/49.26 tff(2246,plain,
% 49.09/49.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2247,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2248,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 49.09/49.26 tff(2249,plain,
% 49.09/49.26 (trans(s74, s75)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2248, 2245, 7])).
% 49.09/49.26 tff(2250,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit0, s74, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit0, s74, s75))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2251,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit0, s74, s75))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2252,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit0, s74, s75)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 49.09/49.26 tff(2253,plain,
% 49.09/49.26 (node3(c_bit0, s74, s75)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2252, 21, 2249])).
% 49.09/49.26 tff(2254,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2255,plain,
% 49.09/49.26 ((node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75)) <=> (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2256,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2255])).
% 49.09/49.26 tff(2257,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2256, 2254])).
% 49.09/49.26 tff(2258,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2259,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 49.09/49.26 tff(2260,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2259, 84, 2253])).
% 49.09/49.26 tff(2261,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s75)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2260, 2242])).
% 49.09/49.26 tff(2262,assumption,(~m_counter_cell_v_carry_in(c_bit0, s75)), introduced(assumption)).
% 49.09/49.26 tff(2263,plain,
% 49.09/49.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s75)),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2264,plain,
% 49.09/49.26 ($false),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2263, 43, 2262])).
% 49.09/49.26 tff(2265,plain,(m_counter_cell_v_carry_in(c_bit0, s75)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.26 tff(2266,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2267,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2268,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 49.09/49.26 tff(2269,plain,
% 49.09/49.26 ((~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75))),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2268, 104, 2265])).
% 49.09/49.26 tff(2270,plain,
% 49.09/49.26 (~node2(c_bit0, s75)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2269, 2261])).
% 49.09/49.26 tff(2271,plain,
% 49.09/49.26 (succ(s75, s76) <=> succ(s75, s76)),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2272,axiom,(succ(s75, s76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound76')).
% 49.09/49.26 tff(2273,plain,
% 49.09/49.26 (succ(s75, s76)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 49.09/49.26 tff(2274,plain,
% 49.09/49.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2275,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2276,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 49.09/49.26 tff(2277,plain,
% 49.09/49.26 (trans(s75, s76)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2276, 2273, 7])).
% 49.09/49.26 tff(2278,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit0, s75, s76))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit0, s75, s76))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2279,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit0, s75, s76))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2280,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit0, s75, s76)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 49.09/49.26 tff(2281,plain,
% 49.09/49.26 (node3(c_bit0, s75, s76)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2280, 21, 2277])).
% 49.09/49.26 tff(2282,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2283,plain,
% 49.09/49.26 ((node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76))) <=> ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2284,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2283])).
% 49.09/49.26 tff(2285,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2284, 2282])).
% 49.09/49.26 tff(2286,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2287,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 49.09/49.26 tff(2288,plain,
% 49.09/49.26 ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2287, 130, 2281])).
% 49.09/49.26 tff(2289,plain,
% 49.09/49.26 (~m_counter_cell_v_value(c_bit0, s76)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2288, 2270])).
% 49.09/49.26 tff(2290,assumption,(~m_counter_cell_v_carry_in(c_bit0, s76)), introduced(assumption)).
% 49.09/49.26 tff(2291,plain,
% 49.09/49.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s76)),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2292,plain,
% 49.09/49.26 ($false),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2291, 43, 2290])).
% 49.09/49.26 tff(2293,plain,(m_counter_cell_v_carry_in(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.26 tff(2294,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2295,plain,
% 49.09/49.26 (((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2296,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2295])).
% 49.09/49.26 tff(2297,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2296, 2294])).
% 49.09/49.26 tff(2298,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2299,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 49.09/49.26 tff(2300,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2299, 55, 2293])).
% 49.09/49.26 tff(2301,plain,
% 49.09/49.26 (~node1(c_bit0, s76)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2300, 2289])).
% 49.09/49.26 tff(2302,plain,
% 49.09/49.26 (succ(s76, s77) <=> succ(s76, s77)),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2303,axiom,(succ(s76, s77)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound77')).
% 49.09/49.26 tff(2304,plain,
% 49.09/49.26 (succ(s76, s77)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 49.09/49.26 tff(2305,plain,
% 49.09/49.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2306,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2307,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 49.09/49.26 tff(2308,plain,
% 49.09/49.26 (trans(s76, s77)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2307, 2304, 7])).
% 49.09/49.26 tff(2309,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit0, s76, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit0, s76, s77))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2310,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit0, s76, s77))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2311,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit0, s76, s77)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 49.09/49.26 tff(2312,plain,
% 49.09/49.26 (node3(c_bit0, s76, s77)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2311, 21, 2308])).
% 49.09/49.26 tff(2313,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2314,plain,
% 49.09/49.26 ((node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77)) <=> (m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2315,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77))))),
% 49.09/49.26 inference(monotonicity,[status(thm)],[2314])).
% 49.09/49.26 tff(2316,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)))),
% 49.09/49.26 inference(transitivity,[status(thm)],[2315, 2313])).
% 49.09/49.26 tff(2317,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2318,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76) | (~node3(c_bit0, s76, s77))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 49.09/49.26 tff(2319,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2318, 84, 2312])).
% 49.09/49.26 tff(2320,plain,
% 49.09/49.26 (m_counter_cell_v_value(c_bit0, s77)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2319, 2301])).
% 49.09/49.26 tff(2321,assumption,(~m_counter_cell_v_carry_in(c_bit0, s77)), introduced(assumption)).
% 49.09/49.26 tff(2322,plain,
% 49.09/49.26 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s77)),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2323,plain,
% 49.09/49.26 ($false),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2322, 43, 2321])).
% 49.09/49.26 tff(2324,plain,(m_counter_cell_v_carry_in(c_bit0, s77)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.26 tff(2325,plain,
% 49.09/49.26 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2326,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2327,plain,
% 49.09/49.26 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77))),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 49.09/49.26 tff(2328,plain,
% 49.09/49.26 ((~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77))),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2327, 104, 2324])).
% 49.09/49.26 tff(2329,plain,
% 49.09/49.26 (~node2(c_bit0, s77)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2328, 2320])).
% 49.09/49.26 tff(2330,plain,
% 49.09/49.26 (succ(s77, s78) <=> succ(s77, s78)),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2331,axiom,(succ(s77, s78)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound78')).
% 49.09/49.26 tff(2332,plain,
% 49.09/49.26 (succ(s77, s78)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 49.09/49.26 tff(2333,plain,
% 49.09/49.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2334,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))),
% 49.09/49.26 inference(quant_inst,[status(thm)],[])).
% 49.09/49.26 tff(2335,plain,
% 49.09/49.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78)),
% 49.09/49.26 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 49.09/49.26 tff(2336,plain,
% 49.09/49.26 (trans(s77, s78)),
% 49.09/49.26 inference(unit_resolution,[status(thm)],[2335, 2332, 7])).
% 49.09/49.26 tff(2337,plain,
% 49.09/49.26 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit0, s77, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit0, s77, s78))),
% 49.09/49.26 inference(rewrite,[status(thm)],[])).
% 49.09/49.26 tff(2338,plain,
% 49.09/49.26 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit0, s77, s78))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2339,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit0, s77, s78)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 49.09/49.27 tff(2340,plain,
% 49.09/49.27 (node3(c_bit0, s77, s78)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2339, 21, 2336])).
% 49.09/49.27 tff(2341,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2342,plain,
% 49.09/49.27 ((node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78))) <=> (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2343,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2342])).
% 49.09/49.27 tff(2344,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2343, 2341])).
% 49.09/49.27 tff(2345,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2346,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 49.09/49.27 tff(2347,plain,
% 49.09/49.27 (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78))),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2346, 130, 2340])).
% 49.09/49.27 tff(2348,plain,
% 49.09/49.27 (~m_counter_cell_v_value(c_bit0, s78)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2347, 2329])).
% 49.09/49.27 tff(2349,assumption,(~m_counter_cell_v_carry_in(c_bit0, s78)), introduced(assumption)).
% 49.09/49.27 tff(2350,plain,
% 49.09/49.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s78)),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2351,plain,
% 49.09/49.27 ($false),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2350, 43, 2349])).
% 49.09/49.27 tff(2352,plain,(m_counter_cell_v_carry_in(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.27 tff(2353,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2354,plain,
% 49.09/49.27 (((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2355,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2354])).
% 49.09/49.27 tff(2356,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2355, 2353])).
% 49.09/49.27 tff(2357,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2358,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 49.09/49.27 tff(2359,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2358, 55, 2352])).
% 49.09/49.27 tff(2360,plain,
% 49.09/49.27 (~node1(c_bit0, s78)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2359, 2348])).
% 49.09/49.27 tff(2361,plain,
% 49.09/49.27 (succ(s78, s79) <=> succ(s78, s79)),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2362,axiom,(succ(s78, s79)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound79')).
% 49.09/49.27 tff(2363,plain,
% 49.09/49.27 (succ(s78, s79)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 49.09/49.27 tff(2364,plain,
% 49.09/49.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2365,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2366,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 49.09/49.27 tff(2367,plain,
% 49.09/49.27 (trans(s78, s79)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2366, 2363, 7])).
% 49.09/49.27 tff(2368,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit0, s78, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit0, s78, s79))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2369,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit0, s78, s79))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2370,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit0, s78, s79)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 49.09/49.27 tff(2371,plain,
% 49.09/49.27 (node3(c_bit0, s78, s79)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2370, 21, 2367])).
% 49.09/49.27 tff(2372,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2373,plain,
% 49.09/49.27 ((node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79)) <=> (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2374,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2373])).
% 49.09/49.27 tff(2375,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2374, 2372])).
% 49.09/49.27 tff(2376,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2377,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 49.09/49.27 tff(2378,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2377, 84, 2371])).
% 49.09/49.27 tff(2379,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s79)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2378, 2360])).
% 49.09/49.27 tff(2380,assumption,(~m_counter_cell_v_carry_in(c_bit0, s79)), introduced(assumption)).
% 49.09/49.27 tff(2381,plain,
% 49.09/49.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s79)),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2382,plain,
% 49.09/49.27 ($false),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2381, 43, 2380])).
% 49.09/49.27 tff(2383,plain,(m_counter_cell_v_carry_in(c_bit0, s79)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.27 tff(2384,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2385,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2386,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 49.09/49.27 tff(2387,plain,
% 49.09/49.27 ((~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79))),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2386, 104, 2383])).
% 49.09/49.27 tff(2388,plain,
% 49.09/49.27 (~node2(c_bit0, s79)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2387, 2379])).
% 49.09/49.27 tff(2389,plain,
% 49.09/49.27 (succ(s79, s80) <=> succ(s79, s80)),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2390,axiom,(succ(s79, s80)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound80')).
% 49.09/49.27 tff(2391,plain,
% 49.09/49.27 (succ(s79, s80)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 49.09/49.27 tff(2392,plain,
% 49.09/49.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2393,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2394,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 49.09/49.27 tff(2395,plain,
% 49.09/49.27 (trans(s79, s80)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2394, 2391, 7])).
% 49.09/49.27 tff(2396,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit0, s79, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit0, s79, s80))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2397,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit0, s79, s80))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2398,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit0, s79, s80)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 49.09/49.27 tff(2399,plain,
% 49.09/49.27 (node3(c_bit0, s79, s80)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2398, 21, 2395])).
% 49.09/49.27 tff(2400,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2401,plain,
% 49.09/49.27 ((node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80))) <=> ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2402,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2401])).
% 49.09/49.27 tff(2403,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2402, 2400])).
% 49.09/49.27 tff(2404,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2405,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 49.09/49.27 tff(2406,plain,
% 49.09/49.27 ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2405, 130, 2399])).
% 49.09/49.27 tff(2407,plain,
% 49.09/49.27 (~m_counter_cell_v_value(c_bit0, s80)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2406, 2388])).
% 49.09/49.27 tff(2408,assumption,(~m_counter_cell_v_carry_in(c_bit0, s80)), introduced(assumption)).
% 49.09/49.27 tff(2409,plain,
% 49.09/49.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s80)),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2410,plain,
% 49.09/49.27 ($false),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2409, 43, 2408])).
% 49.09/49.27 tff(2411,plain,(m_counter_cell_v_carry_in(c_bit0, s80)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.27 tff(2412,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2413,plain,
% 49.09/49.27 (((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2414,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2413])).
% 49.09/49.27 tff(2415,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2414, 2412])).
% 49.09/49.27 tff(2416,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2417,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 49.09/49.27 tff(2418,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2417, 55, 2411])).
% 49.09/49.27 tff(2419,plain,
% 49.09/49.27 (~node1(c_bit0, s80)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2418, 2407])).
% 49.09/49.27 tff(2420,plain,
% 49.09/49.27 (succ(s80, s81) <=> succ(s80, s81)),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2421,axiom,(succ(s80, s81)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound81')).
% 49.09/49.27 tff(2422,plain,
% 49.09/49.27 (succ(s80, s81)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 49.09/49.27 tff(2423,plain,
% 49.09/49.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2424,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2425,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 49.09/49.27 tff(2426,plain,
% 49.09/49.27 (trans(s80, s81)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2425, 2422, 7])).
% 49.09/49.27 tff(2427,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit0, s80, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit0, s80, s81))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2428,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit0, s80, s81))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2429,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit0, s80, s81)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 49.09/49.27 tff(2430,plain,
% 49.09/49.27 (node3(c_bit0, s80, s81)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2429, 21, 2426])).
% 49.09/49.27 tff(2431,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2432,plain,
% 49.09/49.27 ((node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81)) <=> (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2433,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2432])).
% 49.09/49.27 tff(2434,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2433, 2431])).
% 49.09/49.27 tff(2435,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2436,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2435, 2434])).
% 49.09/49.27 tff(2437,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2436, 84, 2430])).
% 49.09/49.27 tff(2438,plain,
% 49.09/49.27 (m_counter_cell_v_value(c_bit0, s81)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2437, 2419])).
% 49.09/49.27 tff(2439,assumption,(~m_counter_cell_v_carry_in(c_bit0, s81)), introduced(assumption)).
% 49.09/49.27 tff(2440,plain,
% 49.09/49.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s81)),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2441,plain,
% 49.09/49.27 ($false),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2440, 43, 2439])).
% 49.09/49.27 tff(2442,plain,(m_counter_cell_v_carry_in(c_bit0, s81)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.27 tff(2443,plain,
% 49.09/49.27 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2444,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2445,plain,
% 49.09/49.27 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81))),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 49.09/49.27 tff(2446,plain,
% 49.09/49.27 ((~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81))),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2445, 104, 2442])).
% 49.09/49.27 tff(2447,plain,
% 49.09/49.27 (~node2(c_bit0, s81)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2446, 2438])).
% 49.09/49.27 tff(2448,plain,
% 49.09/49.27 (succ(s81, s82) <=> succ(s81, s82)),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2449,axiom,(succ(s81, s82)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound82')).
% 49.09/49.27 tff(2450,plain,
% 49.09/49.27 (succ(s81, s82)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2449, 2448])).
% 49.09/49.27 tff(2451,plain,
% 49.09/49.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2452,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2453,plain,
% 49.09/49.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 49.09/49.27 tff(2454,plain,
% 49.09/49.27 (trans(s81, s82)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2453, 2450, 7])).
% 49.09/49.27 tff(2455,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit0, s81, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit0, s81, s82))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2456,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit0, s81, s82))),
% 49.09/49.27 inference(quant_inst,[status(thm)],[])).
% 49.09/49.27 tff(2457,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit0, s81, s82)),
% 49.09/49.27 inference(modus_ponens,[status(thm)],[2456, 2455])).
% 49.09/49.27 tff(2458,plain,
% 49.09/49.27 (node3(c_bit0, s81, s82)),
% 49.09/49.27 inference(unit_resolution,[status(thm)],[2457, 21, 2454])).
% 49.09/49.27 tff(2459,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2460,plain,
% 49.09/49.27 ((node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82))) <=> ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 49.09/49.27 inference(rewrite,[status(thm)],[])).
% 49.09/49.27 tff(2461,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82))))),
% 49.09/49.27 inference(monotonicity,[status(thm)],[2460])).
% 49.09/49.27 tff(2462,plain,
% 49.09/49.27 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 49.09/49.27 inference(transitivity,[status(thm)],[2461, 2459])).
% 49.09/49.27 tff(2463,plain,
% 49.09/49.27 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2464,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 49.09/49.28 tff(2465,plain,
% 49.09/49.28 ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2464, 130, 2458])).
% 49.09/49.28 tff(2466,plain,
% 49.09/49.28 (~m_counter_cell_v_value(c_bit0, s82)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2465, 2447])).
% 49.09/49.28 tff(2467,assumption,(~m_counter_cell_v_carry_in(c_bit0, s82)), introduced(assumption)).
% 49.09/49.28 tff(2468,plain,
% 49.09/49.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s82)),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2469,plain,
% 49.09/49.28 ($false),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2468, 43, 2467])).
% 49.09/49.28 tff(2470,plain,(m_counter_cell_v_carry_in(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.28 tff(2471,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2472,plain,
% 49.09/49.28 (((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2473,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2472])).
% 49.09/49.28 tff(2474,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2473, 2471])).
% 49.09/49.28 tff(2475,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2476,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2475, 2474])).
% 49.09/49.28 tff(2477,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2476, 55, 2470])).
% 49.09/49.28 tff(2478,plain,
% 49.09/49.28 (~node1(c_bit0, s82)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2477, 2466])).
% 49.09/49.28 tff(2479,plain,
% 49.09/49.28 (succ(s82, s83) <=> succ(s82, s83)),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2480,axiom,(succ(s82, s83)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound83')).
% 49.09/49.28 tff(2481,plain,
% 49.09/49.28 (succ(s82, s83)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 49.09/49.28 tff(2482,plain,
% 49.09/49.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2483,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2484,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 49.09/49.28 tff(2485,plain,
% 49.09/49.28 (trans(s82, s83)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2484, 2481, 7])).
% 49.09/49.28 tff(2486,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit0, s82, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit0, s82, s83))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2487,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit0, s82, s83))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2488,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit0, s82, s83)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 49.09/49.28 tff(2489,plain,
% 49.09/49.28 (node3(c_bit0, s82, s83)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2488, 21, 2485])).
% 49.09/49.28 tff(2490,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2491,plain,
% 49.09/49.28 ((node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83)) <=> (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2492,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2491])).
% 49.09/49.28 tff(2493,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2492, 2490])).
% 49.09/49.28 tff(2494,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2495,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 49.09/49.28 tff(2496,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2495, 84, 2489])).
% 49.09/49.28 tff(2497,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s83)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2496, 2478])).
% 49.09/49.28 tff(2498,assumption,(~m_counter_cell_v_carry_in(c_bit0, s83)), introduced(assumption)).
% 49.09/49.28 tff(2499,plain,
% 49.09/49.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s83)),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2500,plain,
% 49.09/49.28 ($false),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2499, 43, 2498])).
% 49.09/49.28 tff(2501,plain,(m_counter_cell_v_carry_in(c_bit0, s83)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.28 tff(2502,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2503,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2504,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 49.09/49.28 tff(2505,plain,
% 49.09/49.28 ((~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83))),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2504, 104, 2501])).
% 49.09/49.28 tff(2506,plain,
% 49.09/49.28 (~node2(c_bit0, s83)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2505, 2497])).
% 49.09/49.28 tff(2507,plain,
% 49.09/49.28 (succ(s83, s84) <=> succ(s83, s84)),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2508,axiom,(succ(s83, s84)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound84')).
% 49.09/49.28 tff(2509,plain,
% 49.09/49.28 (succ(s83, s84)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 49.09/49.28 tff(2510,plain,
% 49.09/49.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2511,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2512,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2511, 2510])).
% 49.09/49.28 tff(2513,plain,
% 49.09/49.28 (trans(s83, s84)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2512, 2509, 7])).
% 49.09/49.28 tff(2514,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit0, s83, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit0, s83, s84))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2515,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit0, s83, s84))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2516,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit0, s83, s84)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 49.09/49.28 tff(2517,plain,
% 49.09/49.28 (node3(c_bit0, s83, s84)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2516, 21, 2513])).
% 49.09/49.28 tff(2518,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2519,plain,
% 49.09/49.28 ((node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84))) <=> ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2520,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2519])).
% 49.09/49.28 tff(2521,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2520, 2518])).
% 49.09/49.28 tff(2522,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2523,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 49.09/49.28 tff(2524,plain,
% 49.09/49.28 ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2523, 130, 2517])).
% 49.09/49.28 tff(2525,plain,
% 49.09/49.28 (~m_counter_cell_v_value(c_bit0, s84)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2524, 2506])).
% 49.09/49.28 tff(2526,assumption,(~m_counter_cell_v_carry_in(c_bit0, s84)), introduced(assumption)).
% 49.09/49.28 tff(2527,plain,
% 49.09/49.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s84)),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2528,plain,
% 49.09/49.28 ($false),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2527, 43, 2526])).
% 49.09/49.28 tff(2529,plain,(m_counter_cell_v_carry_in(c_bit0, s84)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.28 tff(2530,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2531,plain,
% 49.09/49.28 (((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2532,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2531])).
% 49.09/49.28 tff(2533,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2532, 2530])).
% 49.09/49.28 tff(2534,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2535,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 49.09/49.28 tff(2536,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2535, 55, 2529])).
% 49.09/49.28 tff(2537,plain,
% 49.09/49.28 (~node1(c_bit0, s84)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2536, 2525])).
% 49.09/49.28 tff(2538,plain,
% 49.09/49.28 (succ(s84, s85) <=> succ(s84, s85)),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2539,axiom,(succ(s84, s85)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound85')).
% 49.09/49.28 tff(2540,plain,
% 49.09/49.28 (succ(s84, s85)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 49.09/49.28 tff(2541,plain,
% 49.09/49.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2542,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2543,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2542, 2541])).
% 49.09/49.28 tff(2544,plain,
% 49.09/49.28 (trans(s84, s85)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2543, 2540, 7])).
% 49.09/49.28 tff(2545,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit0, s84, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit0, s84, s85))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2546,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit0, s84, s85))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2547,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit0, s84, s85)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 49.09/49.28 tff(2548,plain,
% 49.09/49.28 (node3(c_bit0, s84, s85)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2547, 21, 2544])).
% 49.09/49.28 tff(2549,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2550,plain,
% 49.09/49.28 ((node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85)) <=> (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2551,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2550])).
% 49.09/49.28 tff(2552,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2551, 2549])).
% 49.09/49.28 tff(2553,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2554,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 49.09/49.28 tff(2555,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2554, 84, 2548])).
% 49.09/49.28 tff(2556,plain,
% 49.09/49.28 (m_counter_cell_v_value(c_bit0, s85)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2555, 2537])).
% 49.09/49.28 tff(2557,assumption,(~m_counter_cell_v_carry_in(c_bit0, s85)), introduced(assumption)).
% 49.09/49.28 tff(2558,plain,
% 49.09/49.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s85)),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2559,plain,
% 49.09/49.28 ($false),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2558, 43, 2557])).
% 49.09/49.28 tff(2560,plain,(m_counter_cell_v_carry_in(c_bit0, s85)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.28 tff(2561,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2562,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2563,plain,
% 49.09/49.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 49.09/49.28 tff(2564,plain,
% 49.09/49.28 ((~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85))),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2563, 104, 2560])).
% 49.09/49.28 tff(2565,plain,
% 49.09/49.28 (~node2(c_bit0, s85)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2564, 2556])).
% 49.09/49.28 tff(2566,plain,
% 49.09/49.28 (succ(s85, s86) <=> succ(s85, s86)),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2567,axiom,(succ(s85, s86)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound86')).
% 49.09/49.28 tff(2568,plain,
% 49.09/49.28 (succ(s85, s86)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 49.09/49.28 tff(2569,plain,
% 49.09/49.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2570,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2571,plain,
% 49.09/49.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 49.09/49.28 tff(2572,plain,
% 49.09/49.28 (trans(s85, s86)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2571, 2568, 7])).
% 49.09/49.28 tff(2573,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit0, s85, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit0, s85, s86))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2574,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit0, s85, s86))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2575,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit0, s85, s86)),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 49.09/49.28 tff(2576,plain,
% 49.09/49.28 (node3(c_bit0, s85, s86)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2575, 21, 2572])).
% 49.09/49.28 tff(2577,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2578,plain,
% 49.09/49.28 ((node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86))) <=> ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2579,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86))))),
% 49.09/49.28 inference(monotonicity,[status(thm)],[2578])).
% 49.09/49.28 tff(2580,plain,
% 49.09/49.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 49.09/49.28 inference(transitivity,[status(thm)],[2579, 2577])).
% 49.09/49.28 tff(2581,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2582,plain,
% 49.09/49.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86))),
% 49.09/49.28 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 49.09/49.28 tff(2583,plain,
% 49.09/49.28 ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2582, 130, 2576])).
% 49.09/49.28 tff(2584,plain,
% 49.09/49.28 (~m_counter_cell_v_value(c_bit0, s86)),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2583, 2565])).
% 49.09/49.28 tff(2585,assumption,(~m_counter_cell_v_carry_in(c_bit0, s86)), introduced(assumption)).
% 49.09/49.28 tff(2586,plain,
% 49.09/49.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s86)),
% 49.09/49.28 inference(quant_inst,[status(thm)],[])).
% 49.09/49.28 tff(2587,plain,
% 49.09/49.28 ($false),
% 49.09/49.28 inference(unit_resolution,[status(thm)],[2586, 43, 2585])).
% 49.09/49.28 tff(2588,plain,(m_counter_cell_v_carry_in(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.28 tff(2589,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2590,plain,
% 49.09/49.28 (((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 49.09/49.28 inference(rewrite,[status(thm)],[])).
% 49.09/49.28 tff(2591,plain,
% 49.09/49.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2590])).
% 49.09/49.29 tff(2592,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2591, 2589])).
% 49.09/49.29 tff(2593,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2594,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 49.09/49.29 tff(2595,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2594, 55, 2588])).
% 49.09/49.29 tff(2596,plain,
% 49.09/49.29 (~node1(c_bit0, s86)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2595, 2584])).
% 49.09/49.29 tff(2597,plain,
% 49.09/49.29 (succ(s86, s87) <=> succ(s86, s87)),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2598,axiom,(succ(s86, s87)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound87')).
% 49.09/49.29 tff(2599,plain,
% 49.09/49.29 (succ(s86, s87)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 49.09/49.29 tff(2600,plain,
% 49.09/49.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2601,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2602,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 49.09/49.29 tff(2603,plain,
% 49.09/49.29 (trans(s86, s87)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2602, 2599, 7])).
% 49.09/49.29 tff(2604,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit0, s86, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit0, s86, s87))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2605,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit0, s86, s87))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2606,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit0, s86, s87)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 49.09/49.29 tff(2607,plain,
% 49.09/49.29 (node3(c_bit0, s86, s87)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2606, 21, 2603])).
% 49.09/49.29 tff(2608,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2609,plain,
% 49.09/49.29 ((node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87)) <=> (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2610,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2609])).
% 49.09/49.29 tff(2611,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2610, 2608])).
% 49.09/49.29 tff(2612,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2613,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 49.09/49.29 tff(2614,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2613, 84, 2607])).
% 49.09/49.29 tff(2615,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s87)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2614, 2596])).
% 49.09/49.29 tff(2616,assumption,(~m_counter_cell_v_carry_in(c_bit0, s87)), introduced(assumption)).
% 49.09/49.29 tff(2617,plain,
% 49.09/49.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s87)),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2618,plain,
% 49.09/49.29 ($false),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2617, 43, 2616])).
% 49.09/49.29 tff(2619,plain,(m_counter_cell_v_carry_in(c_bit0, s87)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.29 tff(2620,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2621,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2622,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 49.09/49.29 tff(2623,plain,
% 49.09/49.29 ((~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87))),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2622, 104, 2619])).
% 49.09/49.29 tff(2624,plain,
% 49.09/49.29 (~node2(c_bit0, s87)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2623, 2615])).
% 49.09/49.29 tff(2625,plain,
% 49.09/49.29 (succ(s87, s88) <=> succ(s87, s88)),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2626,axiom,(succ(s87, s88)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound88')).
% 49.09/49.29 tff(2627,plain,
% 49.09/49.29 (succ(s87, s88)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 49.09/49.29 tff(2628,plain,
% 49.09/49.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2629,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2630,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 49.09/49.29 tff(2631,plain,
% 49.09/49.29 (trans(s87, s88)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2630, 2627, 7])).
% 49.09/49.29 tff(2632,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit0, s87, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit0, s87, s88))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2633,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit0, s87, s88))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2634,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit0, s87, s88)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 49.09/49.29 tff(2635,plain,
% 49.09/49.29 (node3(c_bit0, s87, s88)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2634, 21, 2631])).
% 49.09/49.29 tff(2636,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2637,plain,
% 49.09/49.29 ((node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88))) <=> ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2638,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2637])).
% 49.09/49.29 tff(2639,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2638, 2636])).
% 49.09/49.29 tff(2640,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2641,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 49.09/49.29 tff(2642,plain,
% 49.09/49.29 ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2641, 130, 2635])).
% 49.09/49.29 tff(2643,plain,
% 49.09/49.29 (~m_counter_cell_v_value(c_bit0, s88)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2642, 2624])).
% 49.09/49.29 tff(2644,assumption,(~m_counter_cell_v_carry_in(c_bit0, s88)), introduced(assumption)).
% 49.09/49.29 tff(2645,plain,
% 49.09/49.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s88)),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2646,plain,
% 49.09/49.29 ($false),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2645, 43, 2644])).
% 49.09/49.29 tff(2647,plain,(m_counter_cell_v_carry_in(c_bit0, s88)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.29 tff(2648,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2649,plain,
% 49.09/49.29 (((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2650,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2649])).
% 49.09/49.29 tff(2651,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2650, 2648])).
% 49.09/49.29 tff(2652,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2653,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 49.09/49.29 tff(2654,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2653, 55, 2647])).
% 49.09/49.29 tff(2655,plain,
% 49.09/49.29 (~node1(c_bit0, s88)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2654, 2643])).
% 49.09/49.29 tff(2656,plain,
% 49.09/49.29 (succ(s88, s89) <=> succ(s88, s89)),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2657,axiom,(succ(s88, s89)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound89')).
% 49.09/49.29 tff(2658,plain,
% 49.09/49.29 (succ(s88, s89)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 49.09/49.29 tff(2659,plain,
% 49.09/49.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2660,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2661,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 49.09/49.29 tff(2662,plain,
% 49.09/49.29 (trans(s88, s89)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2661, 2658, 7])).
% 49.09/49.29 tff(2663,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit0, s88, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit0, s88, s89))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2664,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit0, s88, s89))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2665,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit0, s88, s89)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 49.09/49.29 tff(2666,plain,
% 49.09/49.29 (node3(c_bit0, s88, s89)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2665, 21, 2662])).
% 49.09/49.29 tff(2667,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2668,plain,
% 49.09/49.29 ((node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89)) <=> (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2669,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2668])).
% 49.09/49.29 tff(2670,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2669, 2667])).
% 49.09/49.29 tff(2671,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2672,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 49.09/49.29 tff(2673,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2672, 84, 2666])).
% 49.09/49.29 tff(2674,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s89)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2673, 2655])).
% 49.09/49.29 tff(2675,assumption,(~m_counter_cell_v_carry_in(c_bit0, s89)), introduced(assumption)).
% 49.09/49.29 tff(2676,plain,
% 49.09/49.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s89)),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2677,plain,
% 49.09/49.29 ($false),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2676, 43, 2675])).
% 49.09/49.29 tff(2678,plain,(m_counter_cell_v_carry_in(c_bit0, s89)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.29 tff(2679,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2680,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2681,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 49.09/49.29 tff(2682,plain,
% 49.09/49.29 ((~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89))),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2681, 104, 2678])).
% 49.09/49.29 tff(2683,plain,
% 49.09/49.29 (~node2(c_bit0, s89)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2682, 2674])).
% 49.09/49.29 tff(2684,plain,
% 49.09/49.29 (succ(s89, s90) <=> succ(s89, s90)),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2685,axiom,(succ(s89, s90)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound90')).
% 49.09/49.29 tff(2686,plain,
% 49.09/49.29 (succ(s89, s90)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 49.09/49.29 tff(2687,plain,
% 49.09/49.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2688,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2689,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 49.09/49.29 tff(2690,plain,
% 49.09/49.29 (trans(s89, s90)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2689, 2686, 7])).
% 49.09/49.29 tff(2691,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit0, s89, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit0, s89, s90))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2692,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit0, s89, s90))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2693,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit0, s89, s90)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 49.09/49.29 tff(2694,plain,
% 49.09/49.29 (node3(c_bit0, s89, s90)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2693, 21, 2690])).
% 49.09/49.29 tff(2695,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2696,plain,
% 49.09/49.29 ((node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90))) <=> ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2697,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2696])).
% 49.09/49.29 tff(2698,plain,
% 49.09/49.29 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2697, 2695])).
% 49.09/49.29 tff(2699,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2700,plain,
% 49.09/49.29 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2699, 2698])).
% 49.09/49.29 tff(2701,plain,
% 49.09/49.29 ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2700, 130, 2694])).
% 49.09/49.29 tff(2702,plain,
% 49.09/49.29 (~m_counter_cell_v_value(c_bit0, s90)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2701, 2683])).
% 49.09/49.29 tff(2703,plain,
% 49.09/49.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s90)),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2704,plain,
% 49.09/49.29 (m_counter_cell_v_carry_in(c_bit0, s90)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2703, 43])).
% 49.09/49.29 tff(2705,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2706,plain,
% 49.09/49.29 (((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2707,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))))),
% 49.09/49.29 inference(monotonicity,[status(thm)],[2706])).
% 49.09/49.29 tff(2708,plain,
% 49.09/49.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 49.09/49.29 inference(transitivity,[status(thm)],[2707, 2705])).
% 49.09/49.29 tff(2709,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))),
% 49.09/49.29 inference(quant_inst,[status(thm)],[])).
% 49.09/49.29 tff(2710,plain,
% 49.09/49.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 49.09/49.29 tff(2711,plain,
% 49.09/49.29 (m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2710, 55, 2704])).
% 49.09/49.29 tff(2712,plain,
% 49.09/49.29 (~node1(c_bit0, s90)),
% 49.09/49.29 inference(unit_resolution,[status(thm)],[2711, 2702])).
% 49.09/49.29 tff(2713,plain,
% 49.09/49.29 (succ(s90, s91) <=> succ(s90, s91)),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2714,axiom,(succ(s90, s91)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound91')).
% 49.09/49.29 tff(2715,plain,
% 49.09/49.29 (succ(s90, s91)),
% 49.09/49.29 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 49.09/49.29 tff(2716,plain,
% 49.09/49.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91))),
% 49.09/49.29 inference(rewrite,[status(thm)],[])).
% 49.09/49.29 tff(2717,plain,
% 49.09/49.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2718,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 49.09/49.30 tff(2719,plain,
% 49.09/49.30 (trans(s90, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2718, 2715, 7])).
% 49.09/49.30 tff(2720,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit0, s90, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit0, s90, s91))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2721,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit0, s90, s91))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2722,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit0, s90, s91)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2721, 2720])).
% 49.09/49.30 tff(2723,plain,
% 49.09/49.30 (node3(c_bit0, s90, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2722, 21, 2719])).
% 49.09/49.30 tff(2724,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2725,plain,
% 49.09/49.30 ((node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91)) <=> (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2726,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91))))),
% 49.09/49.30 inference(monotonicity,[status(thm)],[2725])).
% 49.09/49.30 tff(2727,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 49.09/49.30 inference(transitivity,[status(thm)],[2726, 2724])).
% 49.09/49.30 tff(2728,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2729,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2728, 2727])).
% 49.09/49.30 tff(2730,plain,
% 49.09/49.30 (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2729, 84, 2723])).
% 49.09/49.30 tff(2731,plain,
% 49.09/49.30 (m_counter_cell_v_value(c_bit0, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2730, 2712])).
% 49.09/49.30 tff(2732,plain,
% 49.09/49.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s91)),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2733,plain,
% 49.09/49.30 (m_counter_cell_v_carry_in(c_bit0, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2732, 43])).
% 49.09/49.30 tff(2734,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2735,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2736,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 49.09/49.30 tff(2737,plain,
% 49.09/49.30 ((~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91))),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2736, 104, 2733])).
% 49.09/49.30 tff(2738,plain,
% 49.09/49.30 (~node2(c_bit0, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2737, 2731])).
% 49.09/49.30 tff(2739,plain,
% 49.09/49.30 (succ(s91, s92) <=> succ(s91, s92)),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2740,axiom,(succ(s91, s92)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound92')).
% 49.09/49.30 tff(2741,plain,
% 49.09/49.30 (succ(s91, s92)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 49.09/49.30 tff(2742,plain,
% 49.09/49.30 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2743,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2744,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 49.09/49.30 tff(2745,plain,
% 49.09/49.30 (trans(s91, s92)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2744, 2741, 7])).
% 49.09/49.30 tff(2746,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit0, s91, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit0, s91, s92))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2747,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit0, s91, s92))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2748,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit0, s91, s92)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 49.09/49.30 tff(2749,plain,
% 49.09/49.30 (node3(c_bit0, s91, s92)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2748, 21, 2745])).
% 49.09/49.30 tff(2750,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2751,plain,
% 49.09/49.30 ((node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92))) <=> ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2752,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92))))),
% 49.09/49.30 inference(monotonicity,[status(thm)],[2751])).
% 49.09/49.30 tff(2753,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 49.09/49.30 inference(transitivity,[status(thm)],[2752, 2750])).
% 49.09/49.30 tff(2754,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2755,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 49.09/49.30 tff(2756,plain,
% 49.09/49.30 ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2755, 130, 2749])).
% 49.09/49.30 tff(2757,plain,
% 49.09/49.30 (~m_counter_cell_v_value(c_bit0, s92)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2756, 2738])).
% 49.09/49.30 tff(2758,assumption,(~m_counter_cell_v_carry_in(c_bit0, s92)), introduced(assumption)).
% 49.09/49.30 tff(2759,plain,
% 49.09/49.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s92)),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2760,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2759, 43, 2758])).
% 49.09/49.30 tff(2761,plain,(m_counter_cell_v_carry_in(c_bit0, s92)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2762,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2763,plain,
% 49.09/49.30 (((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2764,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))))),
% 49.09/49.30 inference(monotonicity,[status(thm)],[2763])).
% 49.09/49.30 tff(2765,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 49.09/49.30 inference(transitivity,[status(thm)],[2764, 2762])).
% 49.09/49.30 tff(2766,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2767,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2766, 2765])).
% 49.09/49.30 tff(2768,plain,
% 49.09/49.30 (m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2767, 55, 2761])).
% 49.09/49.30 tff(2769,plain,
% 49.09/49.30 (~node1(c_bit0, s92)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2768, 2757])).
% 49.09/49.30 tff(2770,plain,
% 49.09/49.30 (succ(s92, s93) <=> succ(s92, s93)),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2771,axiom,(succ(s92, s93)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound93')).
% 49.09/49.30 tff(2772,plain,
% 49.09/49.30 (succ(s92, s93)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 49.09/49.30 tff(2773,plain,
% 49.09/49.30 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2774,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2775,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 49.09/49.30 tff(2776,plain,
% 49.09/49.30 (trans(s92, s93)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2775, 2772, 7])).
% 49.09/49.30 tff(2777,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit0, s92, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit0, s92, s93))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2778,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit0, s92, s93))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2779,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit0, s92, s93)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 49.09/49.30 tff(2780,plain,
% 49.09/49.30 (node3(c_bit0, s92, s93)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2779, 21, 2776])).
% 49.09/49.30 tff(2781,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2782,plain,
% 49.09/49.30 ((node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93)) <=> (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2783,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93))))),
% 49.09/49.30 inference(monotonicity,[status(thm)],[2782])).
% 49.09/49.30 tff(2784,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 49.09/49.30 inference(transitivity,[status(thm)],[2783, 2781])).
% 49.09/49.30 tff(2785,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2786,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 49.09/49.30 tff(2787,plain,
% 49.09/49.30 (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2786, 84, 2780])).
% 49.09/49.30 tff(2788,plain,
% 49.09/49.30 (m_counter_cell_v_value(c_bit0, s93)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2787, 2769])).
% 49.09/49.30 tff(2789,assumption,(~m_counter_cell_v_carry_in(c_bit0, s93)), introduced(assumption)).
% 49.09/49.30 tff(2790,plain,
% 49.09/49.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s93)),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2791,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2790, 43, 2789])).
% 49.09/49.30 tff(2792,plain,(m_counter_cell_v_carry_in(c_bit0, s93)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2793,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2794,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2795,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 49.09/49.30 tff(2796,plain,
% 49.09/49.30 ((~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93))),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2795, 104, 2792])).
% 49.09/49.30 tff(2797,plain,
% 49.09/49.30 (~node2(c_bit0, s93)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2796, 2788])).
% 49.09/49.30 tff(2798,plain,
% 49.09/49.30 (succ(s93, s94) <=> succ(s93, s94)),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2799,axiom,(succ(s93, s94)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound94')).
% 49.09/49.30 tff(2800,plain,
% 49.09/49.30 (succ(s93, s94)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 49.09/49.30 tff(2801,plain,
% 49.09/49.30 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2802,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2803,plain,
% 49.09/49.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2802, 2801])).
% 49.09/49.30 tff(2804,plain,
% 49.09/49.30 (trans(s93, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2803, 2800, 7])).
% 49.09/49.30 tff(2805,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit0, s93, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit0, s93, s94))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2806,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit0, s93, s94))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2807,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit0, s93, s94)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 49.09/49.30 tff(2808,plain,
% 49.09/49.30 (node3(c_bit0, s93, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2807, 21, 2804])).
% 49.09/49.30 tff(2809,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2810,plain,
% 49.09/49.30 ((node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94))) <=> ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2811,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94))))),
% 49.09/49.30 inference(monotonicity,[status(thm)],[2810])).
% 49.09/49.30 tff(2812,plain,
% 49.09/49.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 49.09/49.30 inference(transitivity,[status(thm)],[2811, 2809])).
% 49.09/49.30 tff(2813,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2814,plain,
% 49.09/49.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 49.09/49.30 tff(2815,plain,
% 49.09/49.30 ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2814, 130, 2808])).
% 49.09/49.30 tff(2816,plain,
% 49.09/49.30 (~m_counter_cell_v_value(c_bit0, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2815, 2797])).
% 49.09/49.30 tff(2817,plain,
% 49.09/49.30 (^[I0: $i, X: $i] : refl((m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> (m_counter_cell_v_value(I0, X) | (~node4(I0, X))))),
% 49.09/49.30 inference(bind,[status(th)],[])).
% 49.09/49.30 tff(2818,plain,
% 49.09/49.30 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 49.09/49.30 inference(quant_intro,[status(thm)],[2817])).
% 49.09/49.30 tff(2819,plain,
% 49.09/49.30 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2820,axiom,(![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_9')).
% 49.09/49.30 tff(2821,plain,
% 49.09/49.30 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2820, 2819])).
% 49.09/49.30 tff(2822,plain,(
% 49.09/49.30 ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 49.09/49.30 inference(skolemize,[status(sab)],[2821])).
% 49.09/49.30 tff(2823,plain,
% 49.09/49.30 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2822, 2818])).
% 49.09/49.30 tff(2824,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2825,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2826,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2825, 2824])).
% 49.09/49.30 tff(2827,plain,
% 49.09/49.30 (~node4(c_bit0, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2826, 2823, 2816])).
% 49.09/49.30 tff(2828,assumption,(~node4(c_bit0, s94)), introduced(assumption)).
% 49.09/49.30 tff(2829,assumption,(m_counter_cell_v_carry_out(c_bit0, s94)), introduced(assumption)).
% 49.09/49.30 tff(2830,plain,
% 49.09/49.30 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)))),
% 49.09/49.30 inference(bind,[status(th)],[])).
% 49.09/49.30 tff(2831,plain,
% 49.09/49.30 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 49.09/49.30 inference(quant_intro,[status(thm)],[2830])).
% 49.09/49.30 tff(2832,plain,
% 49.09/49.30 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2833,axiom,(![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_12')).
% 49.09/49.30 tff(2834,plain,
% 49.09/49.30 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 49.09/49.30 tff(2835,plain,(
% 49.09/49.30 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 49.09/49.30 inference(skolemize,[status(sab)],[2834])).
% 49.09/49.30 tff(2836,plain,
% 49.09/49.30 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2835, 2831])).
% 49.09/49.30 tff(2837,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2838,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2839,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 49.09/49.30 tff(2840,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2839, 2836, 2829, 2828])).
% 49.09/49.30 tff(2841,plain,((~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2842,plain,
% 49.09/49.30 (~m_counter_cell_v_carry_out(c_bit0, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2841, 2827])).
% 49.09/49.30 tff(2843,assumption,(m_counter_cell_v_carry_in(c_bit1, s94)), introduced(assumption)).
% 49.09/49.30 tff(2844,assumption,(~m_counter_cell_v_carry_out(c_bit0, s94)), introduced(assumption)).
% 49.09/49.30 tff(2845,plain,
% 49.09/49.30 (^[X: $i] : refl(((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)))),
% 49.09/49.30 inference(bind,[status(th)],[])).
% 49.09/49.30 tff(2846,plain,
% 49.09/49.30 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 49.09/49.30 inference(quant_intro,[status(thm)],[2845])).
% 49.09/49.30 tff(2847,plain,
% 49.09/49.30 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2848,axiom,(![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_3')).
% 49.09/49.30 tff(2849,plain,
% 49.09/49.30 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 49.09/49.30 tff(2850,plain,(
% 49.09/49.30 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 49.09/49.30 inference(skolemize,[status(sab)],[2849])).
% 49.09/49.30 tff(2851,plain,
% 49.09/49.30 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2850, 2846])).
% 49.09/49.30 tff(2852,plain,
% 49.09/49.30 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2853,plain,
% 49.09/49.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2854,plain,
% 49.09/49.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 49.09/49.30 tff(2855,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2854, 2851, 2844, 2843])).
% 49.09/49.30 tff(2856,plain,(m_counter_cell_v_carry_out(c_bit0, s94) | (~m_counter_cell_v_carry_in(c_bit1, s94))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2857,plain,
% 49.09/49.30 (~m_counter_cell_v_carry_in(c_bit1, s94)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2856, 2842])).
% 49.09/49.30 tff(2858,assumption,(node4(c_bit0, s64)), introduced(assumption)).
% 49.09/49.30 tff(2859,assumption,(~m_counter_cell_v_value(c_bit0, s64)), introduced(assumption)).
% 49.09/49.30 tff(2860,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2861,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2862,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 49.09/49.30 tff(2863,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2862, 2823, 2859, 2858])).
% 49.09/49.30 tff(2864,plain,(m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2865,plain,
% 49.09/49.30 (~node4(c_bit0, s64)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2864, 1935])).
% 49.09/49.30 tff(2866,assumption,(~node4(c_bit0, s64)), introduced(assumption)).
% 49.09/49.30 tff(2867,assumption,(m_counter_cell_v_carry_out(c_bit0, s64)), introduced(assumption)).
% 49.09/49.30 tff(2868,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2869,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2870,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 49.09/49.30 tff(2871,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2870, 2836, 2867, 2866])).
% 49.09/49.30 tff(2872,plain,((~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2873,plain,
% 49.09/49.30 (~m_counter_cell_v_carry_out(c_bit0, s64)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2872, 2865])).
% 49.09/49.30 tff(2874,assumption,(m_counter_cell_v_carry_in(c_bit1, s64)), introduced(assumption)).
% 49.09/49.30 tff(2875,assumption,(~m_counter_cell_v_carry_out(c_bit0, s64)), introduced(assumption)).
% 49.09/49.30 tff(2876,plain,
% 49.09/49.30 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2877,plain,
% 49.09/49.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2878,plain,
% 49.09/49.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s64)) | m_counter_cell_v_carry_out(c_bit0, s64)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 49.09/49.30 tff(2879,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2878, 2851, 2875, 2874])).
% 49.09/49.30 tff(2880,plain,(m_counter_cell_v_carry_out(c_bit0, s64) | (~m_counter_cell_v_carry_in(c_bit1, s64))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2881,plain,
% 49.09/49.30 (~m_counter_cell_v_carry_in(c_bit1, s64)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2880, 2873])).
% 49.09/49.30 tff(2882,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2883,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52)))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2884,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52))),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 49.09/49.30 tff(2885,plain,
% 49.09/49.30 (~node4(c_bit0, s52)),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2884, 2823, 1581])).
% 49.09/49.30 tff(2886,assumption,(m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 49.09/49.30 tff(2887,plain,
% 49.09/49.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2888,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.30 tff(2889,plain,
% 49.09/49.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52)),
% 49.09/49.30 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 49.09/49.30 tff(2890,plain,
% 49.09/49.30 ($false),
% 49.09/49.30 inference(unit_resolution,[status(thm)],[2889, 2836, 2886, 2885])).
% 49.09/49.30 tff(2891,plain,(~m_counter_cell_v_carry_out(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.30 tff(2892,plain,
% 49.09/49.30 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))),
% 49.09/49.30 inference(rewrite,[status(thm)],[])).
% 49.09/49.30 tff(2893,plain,
% 49.09/49.30 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52))),
% 49.09/49.30 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2894,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 49.09/49.31 tff(2895,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s52)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2894, 2851, 2891])).
% 49.09/49.31 tff(2896,assumption,(node2(c_bit1, s52)), introduced(assumption)).
% 49.09/49.31 tff(2897,plain,
% 49.09/49.31 (^[I0: $i, X: $i] : refl(((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(2898,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[2897])).
% 49.09/49.31 tff(2899,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2900,plain,
% 49.09/49.31 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))), (((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))))), rewrite((((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))), (((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(2901,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X))) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[2900])).
% 49.09/49.31 tff(2902,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_carry_out(I0, X) | (~m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_11')).
% 49.09/49.31 tff(2903,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 49.09/49.31 tff(2904,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2903, 2899])).
% 49.09/49.31 tff(2905,plain,(
% 49.09/49.31 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(skolemize,[status(sab)],[2904])).
% 49.09/49.31 tff(2906,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2905, 2898])).
% 49.09/49.31 tff(2907,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2908,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2909,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 49.09/49.31 tff(2910,plain,
% 49.09/49.31 ((~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2909, 2906, 1205])).
% 49.09/49.31 tff(2911,plain,
% 49.09/49.31 (m_counter_cell_v_carry_out(c_bit0, s39)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2910, 1201])).
% 49.09/49.31 tff(2912,plain,
% 49.09/49.31 (^[X: $i] : refl(((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(2913,plain,
% 49.09/49.31 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[2912])).
% 49.09/49.31 tff(2914,plain,
% 49.09/49.31 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2915,plain,
% 49.09/49.31 (^[X: $i] : rewrite((m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X))) <=> ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X)))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(2916,plain,
% 49.09/49.31 (![X: $i] : (m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X))) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[2915])).
% 49.09/49.31 tff(2917,axiom,(![X: $i] : (m_counter_cell_v_carry_in(c_bit1, X) | (~m_counter_cell_v_carry_out(c_bit0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_2')).
% 49.09/49.31 tff(2918,plain,
% 49.09/49.31 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 49.09/49.31 tff(2919,plain,
% 49.09/49.31 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2918, 2914])).
% 49.09/49.31 tff(2920,plain,(
% 49.09/49.31 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(skolemize,[status(sab)],[2919])).
% 49.09/49.31 tff(2921,plain,
% 49.09/49.31 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2920, 2913])).
% 49.09/49.31 tff(2922,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2923,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2924,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s39)) | m_counter_cell_v_carry_in(c_bit1, s39)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 49.09/49.31 tff(2925,plain,
% 49.09/49.31 (m_counter_cell_v_carry_in(c_bit1, s39)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2924, 2921, 2911])).
% 49.09/49.31 tff(2926,assumption,(node2(c_bit1, s39)), introduced(assumption)).
% 49.09/49.31 tff(2927,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2928,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2929,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s22) | (~node4(c_bit0, s22))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2928, 2927])).
% 49.09/49.31 tff(2930,plain,
% 49.09/49.31 (~node4(c_bit0, s22)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2929, 2823, 702])).
% 49.09/49.31 tff(2931,assumption,(m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 49.09/49.31 tff(2932,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2933,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2934,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 49.09/49.31 tff(2935,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2934, 2836, 2931, 2930])).
% 49.09/49.31 tff(2936,plain,(~m_counter_cell_v_carry_out(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2937,assumption,(m_counter_cell_v_carry_in(c_bit1, s22)), introduced(assumption)).
% 49.09/49.31 tff(2938,assumption,(~m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 49.09/49.31 tff(2939,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2940,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2941,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2940, 2939])).
% 49.09/49.31 tff(2942,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2941, 2851, 2938, 2937])).
% 49.09/49.31 tff(2943,plain,(m_counter_cell_v_carry_out(c_bit0, s22) | (~m_counter_cell_v_carry_in(c_bit1, s22))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2944,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s22)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2943, 2936])).
% 49.09/49.31 tff(2945,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2946,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2947,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s12) | (~node4(c_bit0, s12))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 49.09/49.31 tff(2948,plain,
% 49.09/49.31 (~node4(c_bit0, s12)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2947, 2823, 411])).
% 49.09/49.31 tff(2949,assumption,(m_counter_cell_v_carry_out(c_bit0, s12)), introduced(assumption)).
% 49.09/49.31 tff(2950,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2951,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2952,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 49.09/49.31 tff(2953,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2952, 2836, 2949, 2948])).
% 49.09/49.31 tff(2954,plain,(~m_counter_cell_v_carry_out(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2955,assumption,(m_counter_cell_v_carry_in(c_bit1, s12)), introduced(assumption)).
% 49.09/49.31 tff(2956,assumption,(~m_counter_cell_v_carry_out(c_bit0, s12)), introduced(assumption)).
% 49.09/49.31 tff(2957,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2958,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2959,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2958, 2957])).
% 49.09/49.31 tff(2960,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2959, 2851, 2956, 2955])).
% 49.09/49.31 tff(2961,plain,((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2962,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s12)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2961, 2954])).
% 49.09/49.31 tff(2963,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2964,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2965,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s10) | (~node4(c_bit0, s10))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 49.09/49.31 tff(2966,plain,
% 49.09/49.31 (~node4(c_bit0, s10)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2965, 2823, 352])).
% 49.09/49.31 tff(2967,assumption,(m_counter_cell_v_carry_out(c_bit0, s10)), introduced(assumption)).
% 49.09/49.31 tff(2968,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2969,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2970,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 49.09/49.31 tff(2971,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2970, 2836, 2967, 2966])).
% 49.09/49.31 tff(2972,plain,(~m_counter_cell_v_carry_out(c_bit0, s10)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2973,assumption,(m_counter_cell_v_carry_in(c_bit1, s10)), introduced(assumption)).
% 49.09/49.31 tff(2974,assumption,(~m_counter_cell_v_carry_out(c_bit0, s10)), introduced(assumption)).
% 49.09/49.31 tff(2975,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2976,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2977,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 49.09/49.31 tff(2978,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2977, 2851, 2974, 2973])).
% 49.09/49.31 tff(2979,plain,(m_counter_cell_v_carry_out(c_bit0, s10) | (~m_counter_cell_v_carry_in(c_bit1, s10))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2980,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s10)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2979, 2972])).
% 49.09/49.31 tff(2981,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2982,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2983,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 49.09/49.31 tff(2984,plain,
% 49.09/49.31 (~node4(c_bit0, s6)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2983, 2823, 250])).
% 49.09/49.31 tff(2985,assumption,(m_counter_cell_v_carry_out(c_bit0, s6)), introduced(assumption)).
% 49.09/49.31 tff(2986,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2987,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2988,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 49.09/49.31 tff(2989,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2988, 2836, 2985, 2984])).
% 49.09/49.31 tff(2990,plain,(~m_counter_cell_v_carry_out(c_bit0, s6)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2991,assumption,(m_counter_cell_v_carry_in(c_bit1, s6)), introduced(assumption)).
% 49.09/49.31 tff(2992,assumption,(~m_counter_cell_v_carry_out(c_bit0, s6)), introduced(assumption)).
% 49.09/49.31 tff(2993,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(2994,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(2995,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s6)) | m_counter_cell_v_carry_out(c_bit0, s6)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 49.09/49.31 tff(2996,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2995, 2851, 2992, 2991])).
% 49.09/49.31 tff(2997,plain,(m_counter_cell_v_carry_out(c_bit0, s6) | (~m_counter_cell_v_carry_in(c_bit1, s6))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(2998,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s6)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[2997, 2990])).
% 49.09/49.31 tff(2999,assumption,(m_counter_cell_v_value(c_bit1, s0)), introduced(assumption)).
% 49.09/49.31 tff(3000,plain,
% 49.09/49.31 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit1, s0))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3001,plain,
% 49.09/49.31 ($false),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3000, 33, 2999])).
% 49.09/49.31 tff(3002,plain,(~m_counter_cell_v_value(c_bit1, s0)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.31 tff(3003,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3004,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3005,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s0) | (~node4(c_bit0, s0))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 49.09/49.31 tff(3006,plain,
% 49.09/49.31 (~node4(c_bit0, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3005, 2823, 36])).
% 49.09/49.31 tff(3007,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3008,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3009,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s0)) | node4(c_bit0, s0)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 49.09/49.31 tff(3010,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_out(c_bit0, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3009, 2836, 3006])).
% 49.09/49.31 tff(3011,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3012,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3013,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s0)) | m_counter_cell_v_carry_out(c_bit0, s0)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 49.09/49.31 tff(3014,plain,
% 49.09/49.31 (~m_counter_cell_v_carry_in(c_bit1, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3013, 2851, 3010])).
% 49.09/49.31 tff(3015,plain,
% 49.09/49.31 (^[I0: $i, X: $i] : refl((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(3016,plain,
% 49.09/49.31 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[3015])).
% 49.09/49.31 tff(3017,plain,
% 49.09/49.31 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3018,plain,
% 49.09/49.31 (^[I0: $i, X: $i] : trans(monotonicity(rewrite((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X))), (((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> ((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X)) | (~node2(I0, X))))), rewrite(((m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X)) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))), (((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))))),
% 49.09/49.31 inference(bind,[status(th)],[])).
% 49.09/49.31 tff(3019,plain,
% 49.09/49.31 (![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(quant_intro,[status(thm)],[3018])).
% 49.09/49.31 tff(3020,axiom,(![I0: $i, X: $i] : ((m_counter_cell_v_value(I0, X) | m_counter_cell_v_carry_in(I0, X)) | (~node2(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_4')).
% 49.09/49.31 tff(3021,plain,
% 49.09/49.31 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 49.09/49.31 tff(3022,plain,
% 49.09/49.31 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3021, 3017])).
% 49.09/49.31 tff(3023,plain,(
% 49.09/49.31 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(skolemize,[status(sab)],[3022])).
% 49.09/49.31 tff(3024,plain,
% 49.09/49.31 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3023, 3016])).
% 49.09/49.31 tff(3025,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3026,plain,
% 49.09/49.31 ((m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))) <=> ((~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3027,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0)))),
% 49.09/49.31 inference(monotonicity,[status(thm)],[3026])).
% 49.09/49.31 tff(3028,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0))),
% 49.09/49.31 inference(transitivity,[status(thm)],[3027, 3025])).
% 49.09/49.31 tff(3029,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3030,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3029, 3028])).
% 49.09/49.31 tff(3031,plain,
% 49.09/49.31 ((~node2(c_bit1, s0)) | m_counter_cell_v_value(c_bit1, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3030, 3024, 3014])).
% 49.09/49.31 tff(3032,plain,
% 49.09/49.31 (~node2(c_bit1, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3031, 3002])).
% 49.09/49.31 tff(3033,plain,
% 49.09/49.31 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3034,plain,
% 49.09/49.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3035,plain,
% 49.09/49.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 49.09/49.31 tff(3036,plain,
% 49.09/49.31 (node3(c_bit1, s0, s1)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3035, 21, 70])).
% 49.09/49.31 tff(3037,plain,
% 49.09/49.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3038,plain,
% 49.09/49.31 ((node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1))) <=> ((~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3039,plain,
% 49.09/49.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0)))),
% 49.09/49.31 inference(monotonicity,[status(thm)],[3038])).
% 49.09/49.31 tff(3040,plain,
% 49.09/49.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0))),
% 49.09/49.31 inference(transitivity,[status(thm)],[3039, 3037])).
% 49.09/49.31 tff(3041,plain,
% 49.09/49.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3042,plain,
% 49.09/49.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 49.09/49.31 tff(3043,plain,
% 49.09/49.31 ((~m_counter_cell_v_value(c_bit1, s1)) | node2(c_bit1, s0)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3042, 130, 3036])).
% 49.09/49.31 tff(3044,plain,
% 49.09/49.31 (~m_counter_cell_v_value(c_bit1, s1)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3043, 3032])).
% 49.09/49.31 tff(3045,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3046,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3047,plain,
% 49.09/49.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 49.09/49.31 tff(3048,plain,
% 49.09/49.31 ((~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3047, 2906, 94])).
% 49.09/49.31 tff(3049,plain,
% 49.09/49.31 (m_counter_cell_v_carry_out(c_bit0, s1)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3048, 92])).
% 49.09/49.31 tff(3050,plain,
% 49.09/49.31 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))),
% 49.09/49.31 inference(rewrite,[status(thm)],[])).
% 49.09/49.31 tff(3051,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1))),
% 49.09/49.31 inference(quant_inst,[status(thm)],[])).
% 49.09/49.31 tff(3052,plain,
% 49.09/49.31 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s1)) | m_counter_cell_v_carry_in(c_bit1, s1)),
% 49.09/49.31 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 49.09/49.31 tff(3053,plain,
% 49.09/49.31 (m_counter_cell_v_carry_in(c_bit1, s1)),
% 49.09/49.31 inference(unit_resolution,[status(thm)],[3052, 2921, 3049])).
% 49.09/49.31 tff(3054,plain,
% 49.09/49.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3055,plain,
% 49.09/49.32 (((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3056,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3055])).
% 49.09/49.32 tff(3057,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3056, 3054])).
% 49.09/49.32 tff(3058,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s1)) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3059,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 49.09/49.32 tff(3060,plain,
% 49.09/49.32 (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3059, 55, 3053])).
% 49.09/49.32 tff(3061,plain,
% 49.09/49.32 (~node1(c_bit1, s1)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3060, 3044])).
% 49.09/49.32 tff(3062,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3063,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3064,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 49.09/49.32 tff(3065,plain,
% 49.09/49.32 (node3(c_bit1, s1, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3064, 21, 116])).
% 49.09/49.32 tff(3066,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3067,plain,
% 49.09/49.32 ((node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2)) <=> (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3068,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3067])).
% 49.09/49.32 tff(3069,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3068, 3066])).
% 49.09/49.32 tff(3070,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3071,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1) | (~node3(c_bit1, s1, s2))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 49.09/49.32 tff(3072,plain,
% 49.09/49.32 (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3071, 84, 3065])).
% 49.09/49.32 tff(3073,plain,
% 49.09/49.32 (m_counter_cell_v_value(c_bit1, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3072, 3061])).
% 49.09/49.32 tff(3074,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3075,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3076,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s2) | (~node4(c_bit0, s2))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 49.09/49.32 tff(3077,plain,
% 49.09/49.32 (~node4(c_bit0, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3076, 2823, 138])).
% 49.09/49.32 tff(3078,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3079,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3080,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s2)) | node4(c_bit0, s2)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 49.09/49.32 tff(3081,plain,
% 49.09/49.32 (~m_counter_cell_v_carry_out(c_bit0, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3080, 2836, 3077])).
% 49.09/49.32 tff(3082,plain,
% 49.09/49.32 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3083,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3084,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s2)) | m_counter_cell_v_carry_out(c_bit0, s2)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 49.09/49.32 tff(3085,plain,
% 49.09/49.32 (~m_counter_cell_v_carry_in(c_bit1, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3084, 2851, 3081])).
% 49.09/49.32 tff(3086,plain,
% 49.09/49.32 (^[I0: $i, X: $i] : refl(((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))))),
% 49.09/49.32 inference(bind,[status(th)],[])).
% 49.09/49.32 tff(3087,plain,
% 49.09/49.32 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(quant_intro,[status(thm)],[3086])).
% 49.09/49.32 tff(3088,plain,
% 49.09/49.32 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3089,plain,
% 49.09/49.32 (^[I0: $i, X: $i] : rewrite((((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X))) <=> ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X))))),
% 49.09/49.32 inference(bind,[status(th)],[])).
% 49.09/49.32 tff(3090,plain,
% 49.09/49.32 (![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X))) <=> ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(quant_intro,[status(thm)],[3089])).
% 49.09/49.32 tff(3091,axiom,(![I0: $i, X: $i] : (((~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_in(I0, X)) | (~node1(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_3')).
% 49.09/49.32 tff(3092,plain,
% 49.09/49.32 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 49.09/49.32 tff(3093,plain,
% 49.09/49.32 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3092, 3088])).
% 49.09/49.32 tff(3094,plain,(
% 49.09/49.32 ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(skolemize,[status(sab)],[3093])).
% 49.09/49.32 tff(3095,plain,
% 49.09/49.32 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3094, 3087])).
% 49.09/49.32 tff(3096,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3097,plain,
% 49.09/49.32 (((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2))) <=> (m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3098,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3097])).
% 49.09/49.32 tff(3099,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3098, 3096])).
% 49.09/49.32 tff(3100,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3101,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 49.09/49.32 tff(3102,plain,
% 49.09/49.32 ((~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3101, 3095, 3085])).
% 49.09/49.32 tff(3103,plain,
% 49.09/49.32 (~node1(c_bit1, s2)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3102, 3073])).
% 49.09/49.32 tff(3104,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3105,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3106,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 49.09/49.32 tff(3107,plain,
% 49.09/49.32 (node3(c_bit1, s2, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3106, 21, 155])).
% 49.09/49.32 tff(3108,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3109,plain,
% 49.09/49.32 ((node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3110,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3109])).
% 49.09/49.32 tff(3111,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3110, 3108])).
% 49.09/49.32 tff(3112,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3113,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3112, 3111])).
% 49.09/49.32 tff(3114,plain,
% 49.09/49.32 (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3113, 84, 3107])).
% 49.09/49.32 tff(3115,plain,
% 49.09/49.32 (m_counter_cell_v_value(c_bit1, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3114, 3103])).
% 49.09/49.32 tff(3116,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3117,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3118,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3117, 3116])).
% 49.09/49.32 tff(3119,plain,
% 49.09/49.32 ((~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3118, 2906, 169])).
% 49.09/49.32 tff(3120,plain,
% 49.09/49.32 (m_counter_cell_v_carry_out(c_bit0, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3119, 167])).
% 49.09/49.32 tff(3121,plain,
% 49.09/49.32 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3122,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3123,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s3)) | m_counter_cell_v_carry_in(c_bit1, s3)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 49.09/49.32 tff(3124,plain,
% 49.09/49.32 (m_counter_cell_v_carry_in(c_bit1, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3123, 2921, 3120])).
% 49.09/49.32 tff(3125,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3126,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3127,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 49.09/49.32 tff(3128,plain,
% 49.09/49.32 ((~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3127, 104, 3124])).
% 49.09/49.32 tff(3129,plain,
% 49.09/49.32 (~node2(c_bit1, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3128, 3115])).
% 49.09/49.32 tff(3130,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3131,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3132,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 49.09/49.32 tff(3133,plain,
% 49.09/49.32 (node3(c_bit1, s3, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3132, 21, 181])).
% 49.09/49.32 tff(3134,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3135,plain,
% 49.09/49.32 ((node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4))) <=> ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3136,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3135])).
% 49.09/49.32 tff(3137,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3136, 3134])).
% 49.09/49.32 tff(3138,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3139,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3138, 3137])).
% 49.09/49.32 tff(3140,plain,
% 49.09/49.32 ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3139, 130, 3133])).
% 49.09/49.32 tff(3141,plain,
% 49.09/49.32 (~m_counter_cell_v_value(c_bit1, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3140, 3129])).
% 49.09/49.32 tff(3142,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3143,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3144,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s4) | (~node4(c_bit0, s4))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 49.09/49.32 tff(3145,plain,
% 49.09/49.32 (~node4(c_bit0, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3144, 2823, 193])).
% 49.09/49.32 tff(3146,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3147,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3148,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s4)) | node4(c_bit0, s4)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 49.09/49.32 tff(3149,plain,
% 49.09/49.32 (~m_counter_cell_v_carry_out(c_bit0, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3148, 2836, 3145])).
% 49.09/49.32 tff(3150,plain,
% 49.09/49.32 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3151,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3152,plain,
% 49.09/49.32 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s4)) | m_counter_cell_v_carry_out(c_bit0, s4)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3151, 3150])).
% 49.09/49.32 tff(3153,plain,
% 49.09/49.32 (~m_counter_cell_v_carry_in(c_bit1, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3152, 2851, 3149])).
% 49.09/49.32 tff(3154,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3155,plain,
% 49.09/49.32 ((m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))) <=> (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3156,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4)))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3155])).
% 49.09/49.32 tff(3157,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3156, 3154])).
% 49.09/49.32 tff(3158,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3159,plain,
% 49.09/49.32 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 49.09/49.32 tff(3160,plain,
% 49.09/49.32 (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3159, 3024, 3153])).
% 49.09/49.32 tff(3161,plain,
% 49.09/49.32 (~node2(c_bit1, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3160, 3141])).
% 49.09/49.32 tff(3162,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3163,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3164,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5)),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3163, 3162])).
% 49.09/49.32 tff(3165,plain,
% 49.09/49.32 (node3(c_bit1, s4, s5)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3164, 21, 210])).
% 49.09/49.32 tff(3166,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3167,plain,
% 49.09/49.32 ((node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5))) <=> ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 49.09/49.32 inference(rewrite,[status(thm)],[])).
% 49.09/49.32 tff(3168,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5))))),
% 49.09/49.32 inference(monotonicity,[status(thm)],[3167])).
% 49.09/49.32 tff(3169,plain,
% 49.09/49.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 49.09/49.32 inference(transitivity,[status(thm)],[3168, 3166])).
% 49.09/49.32 tff(3170,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))),
% 49.09/49.32 inference(quant_inst,[status(thm)],[])).
% 49.09/49.32 tff(3171,plain,
% 49.09/49.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5))),
% 49.09/49.32 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 49.09/49.32 tff(3172,plain,
% 49.09/49.32 ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3171, 130, 3165])).
% 49.09/49.32 tff(3173,plain,
% 49.09/49.32 (~m_counter_cell_v_value(c_bit1, s5)),
% 49.09/49.32 inference(unit_resolution,[status(thm)],[3172, 3161])).
% 49.09/49.32 tff(3174,plain,
% 49.09/49.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3175,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3176,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 49.09/49.33 tff(3177,plain,
% 49.09/49.33 ((~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3176, 2906, 226])).
% 49.09/49.33 tff(3178,plain,
% 49.09/49.33 (m_counter_cell_v_carry_out(c_bit0, s5)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3177, 222])).
% 49.09/49.33 tff(3179,plain,
% 49.09/49.33 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3180,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3181,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s5)) | m_counter_cell_v_carry_in(c_bit1, s5)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3180, 3179])).
% 49.09/49.33 tff(3182,plain,
% 49.09/49.33 (m_counter_cell_v_carry_in(c_bit1, s5)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3181, 2921, 3178])).
% 49.09/49.33 tff(3183,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3184,plain,
% 49.09/49.33 (((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3185,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3184])).
% 49.09/49.33 tff(3186,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3185, 3183])).
% 49.09/49.33 tff(3187,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s5)) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3188,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 49.09/49.33 tff(3189,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5))),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3188, 55, 3182])).
% 49.09/49.33 tff(3190,plain,
% 49.09/49.33 (~node1(c_bit1, s5)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3189, 3173])).
% 49.09/49.33 tff(3191,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3192,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3193,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3192, 3191])).
% 49.09/49.33 tff(3194,plain,
% 49.09/49.33 (node3(c_bit1, s5, s6)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3193, 21, 238])).
% 49.09/49.33 tff(3195,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3196,plain,
% 49.09/49.33 ((node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6)) <=> (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3197,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3196])).
% 49.09/49.33 tff(3198,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3197, 3195])).
% 49.09/49.33 tff(3199,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3200,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 49.09/49.33 tff(3201,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3200, 84, 3194])).
% 49.09/49.33 tff(3202,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s6)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3201, 3190])).
% 49.09/49.33 tff(3203,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3204,plain,
% 49.09/49.33 (((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6))) <=> (m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3205,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3204])).
% 49.09/49.33 tff(3206,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3205, 3203])).
% 49.09/49.33 tff(3207,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s6)) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3208,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 49.09/49.33 tff(3209,plain,
% 49.09/49.33 (m_counter_cell_v_carry_in(c_bit1, s6) | (~node1(c_bit1, s6))),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3208, 3095, 3202])).
% 49.09/49.33 tff(3210,plain,
% 49.09/49.33 (~node1(c_bit1, s6)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3209, 2998])).
% 49.09/49.33 tff(3211,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3212,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3213,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 49.09/49.33 tff(3214,plain,
% 49.09/49.33 (node3(c_bit1, s6, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3213, 21, 14])).
% 49.09/49.33 tff(3215,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3216,plain,
% 49.09/49.33 ((node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7)) <=> (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3217,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3216])).
% 49.09/49.33 tff(3218,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3217, 3215])).
% 49.09/49.33 tff(3219,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3220,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 49.09/49.33 tff(3221,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3220, 84, 3214])).
% 49.09/49.33 tff(3222,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3221, 3210])).
% 49.09/49.33 tff(3223,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3224,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3225,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 49.09/49.33 tff(3226,plain,
% 49.09/49.33 ((~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3225, 2906, 273])).
% 49.09/49.33 tff(3227,plain,
% 49.09/49.33 (m_counter_cell_v_carry_out(c_bit0, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3226, 269])).
% 49.09/49.33 tff(3228,plain,
% 49.09/49.33 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3229,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3230,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s7)) | m_counter_cell_v_carry_in(c_bit1, s7)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 49.09/49.33 tff(3231,plain,
% 49.09/49.33 (m_counter_cell_v_carry_in(c_bit1, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3230, 2921, 3227])).
% 49.09/49.33 tff(3232,assumption,(m_counter_cell_v_value(c_bit1, s7)), introduced(assumption)).
% 49.09/49.33 tff(3233,assumption,(node2(c_bit1, s7)), introduced(assumption)).
% 49.09/49.33 tff(3234,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3235,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3236,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 49.09/49.33 tff(3237,plain,
% 49.09/49.33 ($false),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3236, 104, 3233, 3232, 3231])).
% 49.09/49.33 tff(3238,plain,((~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.33 tff(3239,plain,
% 49.09/49.33 (~node2(c_bit1, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3238, 3222])).
% 49.09/49.33 tff(3240,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3241,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3242,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3241, 3240])).
% 49.09/49.33 tff(3243,plain,
% 49.09/49.33 (node3(c_bit1, s7, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3242, 21, 285])).
% 49.09/49.33 tff(3244,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3245,plain,
% 49.09/49.33 ((node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8))) <=> ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3246,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3245])).
% 49.09/49.33 tff(3247,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3246, 3244])).
% 49.09/49.33 tff(3248,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3249,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 49.09/49.33 tff(3250,plain,
% 49.09/49.33 ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3249, 130, 3243])).
% 49.09/49.33 tff(3251,plain,
% 49.09/49.33 (~m_counter_cell_v_value(c_bit1, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3250, 3239])).
% 49.09/49.33 tff(3252,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3253,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3254,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s8) | (~node4(c_bit0, s8))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 49.09/49.33 tff(3255,plain,
% 49.09/49.33 (~node4(c_bit0, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3254, 2823, 297])).
% 49.09/49.33 tff(3256,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3257,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3258,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s8)) | node4(c_bit0, s8)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3257, 3256])).
% 49.09/49.33 tff(3259,plain,
% 49.09/49.33 (~m_counter_cell_v_carry_out(c_bit0, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3258, 2836, 3255])).
% 49.09/49.33 tff(3260,plain,
% 49.09/49.33 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3261,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3262,plain,
% 49.09/49.33 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s8)) | m_counter_cell_v_carry_out(c_bit0, s8)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 49.09/49.33 tff(3263,plain,
% 49.09/49.33 (~m_counter_cell_v_carry_in(c_bit1, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3262, 2851, 3259])).
% 49.09/49.33 tff(3264,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3265,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3266,plain,
% 49.09/49.33 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 49.09/49.33 tff(3267,plain,
% 49.09/49.33 (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3266, 3024, 3263])).
% 49.09/49.33 tff(3268,plain,
% 49.09/49.33 (~node2(c_bit1, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3267, 3251])).
% 49.09/49.33 tff(3269,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3270,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3271,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9)),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 49.09/49.33 tff(3272,plain,
% 49.09/49.33 (node3(c_bit1, s8, s9)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3271, 21, 314])).
% 49.09/49.33 tff(3273,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3274,plain,
% 49.09/49.33 ((node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9))) <=> ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 49.09/49.33 inference(rewrite,[status(thm)],[])).
% 49.09/49.33 tff(3275,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))))),
% 49.09/49.33 inference(monotonicity,[status(thm)],[3274])).
% 49.09/49.33 tff(3276,plain,
% 49.09/49.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 49.09/49.33 inference(transitivity,[status(thm)],[3275, 3273])).
% 49.09/49.33 tff(3277,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))),
% 49.09/49.33 inference(quant_inst,[status(thm)],[])).
% 49.09/49.33 tff(3278,plain,
% 49.09/49.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))),
% 49.09/49.33 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 49.09/49.33 tff(3279,plain,
% 49.09/49.33 ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3278, 130, 3272])).
% 49.09/49.33 tff(3280,plain,
% 49.09/49.33 (~m_counter_cell_v_value(c_bit1, s9)),
% 49.09/49.33 inference(unit_resolution,[status(thm)],[3279, 3268])).
% 49.09/49.33 tff(3281,plain,
% 49.09/49.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3282,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3283,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 49.09/49.34 tff(3284,plain,
% 49.09/49.34 ((~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3283, 2906, 328])).
% 49.09/49.34 tff(3285,plain,
% 49.09/49.34 (m_counter_cell_v_carry_out(c_bit0, s9)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3284, 326])).
% 49.09/49.34 tff(3286,plain,
% 49.09/49.34 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3287,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3288,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s9)) | m_counter_cell_v_carry_in(c_bit1, s9)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 49.09/49.34 tff(3289,plain,
% 49.09/49.34 (m_counter_cell_v_carry_in(c_bit1, s9)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3288, 2921, 3285])).
% 49.09/49.34 tff(3290,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3291,plain,
% 49.09/49.34 (((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3292,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3291])).
% 49.09/49.34 tff(3293,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3292, 3290])).
% 49.09/49.34 tff(3294,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s9)) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3295,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s9)) | m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3294, 3293])).
% 49.09/49.34 tff(3296,plain,
% 49.09/49.34 (m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3295, 55, 3289])).
% 49.09/49.34 tff(3297,plain,
% 49.09/49.34 (~node1(c_bit1, s9)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3296, 3280])).
% 49.09/49.34 tff(3298,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3299,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3300,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 49.09/49.34 tff(3301,plain,
% 49.09/49.34 (node3(c_bit1, s9, s10)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3300, 21, 340])).
% 49.09/49.34 tff(3302,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3303,plain,
% 49.09/49.34 ((node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10)) <=> (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3304,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3303])).
% 49.09/49.34 tff(3305,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3304, 3302])).
% 49.09/49.34 tff(3306,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s9) | (~node3(c_bit1, s9, s10)) | m_counter_cell_v_value(c_bit1, s10))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3307,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9) | (~node3(c_bit1, s9, s10))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3306, 3305])).
% 49.09/49.34 tff(3308,plain,
% 49.09/49.34 (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3307, 84, 3301])).
% 49.09/49.34 tff(3309,plain,
% 49.09/49.34 (m_counter_cell_v_value(c_bit1, s10)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3308, 3297])).
% 49.09/49.34 tff(3310,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3311,plain,
% 49.09/49.34 (((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10))) <=> (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3312,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3311])).
% 49.09/49.34 tff(3313,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3312, 3310])).
% 49.09/49.34 tff(3314,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s10)) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3315,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 49.09/49.34 tff(3316,plain,
% 49.09/49.34 (m_counter_cell_v_carry_in(c_bit1, s10) | (~node1(c_bit1, s10))),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3315, 3095, 3309])).
% 49.09/49.34 tff(3317,plain,
% 49.09/49.34 (~node1(c_bit1, s10)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3316, 2980])).
% 49.09/49.34 tff(3318,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3319,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3320,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3319, 3318])).
% 49.09/49.34 tff(3321,plain,
% 49.09/49.34 (node3(c_bit1, s10, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3320, 21, 371])).
% 49.09/49.34 tff(3322,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3323,plain,
% 49.09/49.34 ((node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11)) <=> (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3324,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3323])).
% 49.09/49.34 tff(3325,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3324, 3322])).
% 49.09/49.34 tff(3326,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s10) | (~node3(c_bit1, s10, s11)) | m_counter_cell_v_value(c_bit1, s11))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3327,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10) | (~node3(c_bit1, s10, s11))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 49.09/49.34 tff(3328,plain,
% 49.09/49.34 (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3327, 84, 3321])).
% 49.09/49.34 tff(3329,plain,
% 49.09/49.34 (m_counter_cell_v_value(c_bit1, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3328, 3317])).
% 49.09/49.34 tff(3330,assumption,(m_counter_cell_v_value(c_bit1, s11)), introduced(assumption)).
% 49.09/49.34 tff(3331,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3332,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3333,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3332, 3331])).
% 49.09/49.34 tff(3334,plain,
% 49.09/49.34 ((~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3333, 2906, 387])).
% 49.09/49.34 tff(3335,plain,
% 49.09/49.34 (m_counter_cell_v_carry_out(c_bit0, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3334, 383])).
% 49.09/49.34 tff(3336,plain,
% 49.09/49.34 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3337,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3338,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 49.09/49.34 tff(3339,plain,
% 49.09/49.34 (m_counter_cell_v_carry_in(c_bit1, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3338, 2921, 3335])).
% 49.09/49.34 tff(3340,assumption,(node2(c_bit1, s11)), introduced(assumption)).
% 49.09/49.34 tff(3341,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3342,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11)))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3343,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 49.09/49.34 tff(3344,plain,
% 49.09/49.34 ($false),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3343, 104, 3340, 3339, 3330])).
% 49.09/49.34 tff(3345,plain,((~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.34 tff(3346,plain,
% 49.09/49.34 (~node2(c_bit1, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3345, 3329])).
% 49.09/49.34 tff(3347,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3348,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3349,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 49.09/49.34 tff(3350,plain,
% 49.09/49.34 (node3(c_bit1, s11, s12)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3349, 21, 399])).
% 49.09/49.34 tff(3351,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3352,plain,
% 49.09/49.34 ((node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12))) <=> ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3353,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3352])).
% 49.09/49.34 tff(3354,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3353, 3351])).
% 49.09/49.34 tff(3355,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s11) | (~node3(c_bit1, s11, s12)) | (~m_counter_cell_v_value(c_bit1, s12)))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3356,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11) | (~node3(c_bit1, s11, s12))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 49.09/49.34 tff(3357,plain,
% 49.09/49.34 ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3356, 130, 3350])).
% 49.09/49.34 tff(3358,plain,
% 49.09/49.34 (~m_counter_cell_v_value(c_bit1, s12)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3357, 3346])).
% 49.09/49.34 tff(3359,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3360,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12)))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3361,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s12) | m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 49.09/49.34 tff(3362,plain,
% 49.09/49.34 (m_counter_cell_v_carry_in(c_bit1, s12) | (~node2(c_bit1, s12))),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3361, 3024, 3358])).
% 49.09/49.34 tff(3363,plain,
% 49.09/49.34 (~node2(c_bit1, s12)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3362, 2962])).
% 49.09/49.34 tff(3364,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3365,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3366,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3365, 3364])).
% 49.09/49.34 tff(3367,plain,
% 49.09/49.34 (node3(c_bit1, s12, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3366, 21, 430])).
% 49.09/49.34 tff(3368,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3369,plain,
% 49.09/49.34 ((node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13))) <=> ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3370,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3369])).
% 49.09/49.34 tff(3371,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3370, 3368])).
% 49.09/49.34 tff(3372,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s12) | (~node3(c_bit1, s12, s13)) | (~m_counter_cell_v_value(c_bit1, s13)))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3373,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12) | (~node3(c_bit1, s12, s13))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 49.09/49.34 tff(3374,plain,
% 49.09/49.34 ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3373, 130, 3367])).
% 49.09/49.34 tff(3375,plain,
% 49.09/49.34 (~m_counter_cell_v_value(c_bit1, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3374, 3363])).
% 49.09/49.34 tff(3376,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3377,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3378,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3377, 3376])).
% 49.09/49.34 tff(3379,plain,
% 49.09/49.34 ((~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3378, 2906, 446])).
% 49.09/49.34 tff(3380,plain,
% 49.09/49.34 (m_counter_cell_v_carry_out(c_bit0, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3379, 442])).
% 49.09/49.34 tff(3381,assumption,(~m_counter_cell_v_carry_in(c_bit1, s13)), introduced(assumption)).
% 49.09/49.34 tff(3382,assumption,(m_counter_cell_v_carry_out(c_bit0, s13)), introduced(assumption)).
% 49.09/49.34 tff(3383,plain,
% 49.09/49.34 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3384,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3385,plain,
% 49.09/49.34 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 49.09/49.34 tff(3386,plain,
% 49.09/49.34 ($false),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3385, 2921, 3382, 3381])).
% 49.09/49.34 tff(3387,plain,((~m_counter_cell_v_carry_out(c_bit0, s13)) | m_counter_cell_v_carry_in(c_bit1, s13)), inference(lemma,lemma(discharge,[]))).
% 49.09/49.34 tff(3388,plain,
% 49.09/49.34 (m_counter_cell_v_carry_in(c_bit1, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3387, 3380])).
% 49.09/49.34 tff(3389,assumption,(m_counter_cell_v_carry_in(c_bit1, s13)), introduced(assumption)).
% 49.09/49.34 tff(3390,assumption,(node1(c_bit1, s13)), introduced(assumption)).
% 49.09/49.34 tff(3391,assumption,(~m_counter_cell_v_value(c_bit1, s13)), introduced(assumption)).
% 49.09/49.34 tff(3392,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3393,plain,
% 49.09/49.34 (((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3394,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))))),
% 49.09/49.34 inference(monotonicity,[status(thm)],[3393])).
% 49.09/49.34 tff(3395,plain,
% 49.09/49.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13)))),
% 49.09/49.34 inference(transitivity,[status(thm)],[3394, 3392])).
% 49.09/49.34 tff(3396,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s13)) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3397,plain,
% 49.09/49.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 49.09/49.34 tff(3398,plain,
% 49.09/49.34 ($false),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3397, 55, 3391, 3390, 3389])).
% 49.09/49.34 tff(3399,plain,((~node1(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13) | (~m_counter_cell_v_carry_in(c_bit1, s13))), inference(lemma,lemma(discharge,[]))).
% 49.09/49.34 tff(3400,plain,
% 49.09/49.34 ((~node1(c_bit1, s13)) | m_counter_cell_v_value(c_bit1, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3399, 3388])).
% 49.09/49.34 tff(3401,plain,
% 49.09/49.34 (~node1(c_bit1, s13)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3400, 3375])).
% 49.09/49.34 tff(3402,plain,
% 49.09/49.34 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 49.09/49.34 inference(rewrite,[status(thm)],[])).
% 49.09/49.34 tff(3403,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 49.09/49.34 inference(quant_inst,[status(thm)],[])).
% 49.09/49.34 tff(3404,plain,
% 49.09/49.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14)),
% 49.09/49.34 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 49.09/49.34 tff(3405,plain,
% 49.09/49.34 (node3(c_bit1, s13, s14)),
% 49.09/49.34 inference(unit_resolution,[status(thm)],[3404, 21, 458])).
% 49.18/49.35 tff(3406,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3407,plain,
% 49.18/49.35 ((node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14)) <=> (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3408,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14))))),
% 49.18/49.35 inference(monotonicity,[status(thm)],[3407])).
% 49.18/49.35 tff(3409,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)))),
% 49.18/49.35 inference(transitivity,[status(thm)],[3408, 3406])).
% 49.18/49.35 tff(3410,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s13) | (~node3(c_bit1, s13, s14)) | m_counter_cell_v_value(c_bit1, s14))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3411,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13) | (~node3(c_bit1, s13, s14))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 49.18/49.35 tff(3412,plain,
% 49.18/49.35 (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3411, 84, 3405])).
% 49.18/49.35 tff(3413,plain,
% 49.18/49.35 (m_counter_cell_v_value(c_bit1, s14)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3412, 3401])).
% 49.18/49.35 tff(3414,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3415,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3416,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s14) | (~node4(c_bit0, s14))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 49.18/49.35 tff(3417,plain,
% 49.18/49.35 (~node4(c_bit0, s14)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3416, 2823, 470])).
% 49.18/49.35 tff(3418,assumption,(m_counter_cell_v_carry_out(c_bit0, s14)), introduced(assumption)).
% 49.18/49.35 tff(3419,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3420,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3421,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3420, 3419])).
% 49.18/49.35 tff(3422,plain,
% 49.18/49.35 ($false),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3421, 2836, 3418, 3417])).
% 49.18/49.35 tff(3423,plain,(~m_counter_cell_v_carry_out(c_bit0, s14)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.35 tff(3424,plain,
% 49.18/49.35 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3425,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3426,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 49.18/49.35 tff(3427,plain,
% 49.18/49.35 (~m_counter_cell_v_carry_in(c_bit1, s14)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3426, 2851, 3423])).
% 49.18/49.35 tff(3428,assumption,(node1(c_bit1, s14)), introduced(assumption)).
% 49.18/49.35 tff(3429,assumption,(m_counter_cell_v_value(c_bit1, s14)), introduced(assumption)).
% 49.18/49.35 tff(3430,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3431,plain,
% 49.18/49.35 (((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14))) <=> (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3432,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))))),
% 49.18/49.35 inference(monotonicity,[status(thm)],[3431])).
% 49.18/49.35 tff(3433,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14)))),
% 49.18/49.35 inference(transitivity,[status(thm)],[3432, 3430])).
% 49.18/49.35 tff(3434,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3435,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3434, 3433])).
% 49.18/49.35 tff(3436,plain,
% 49.18/49.35 ($false),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3435, 3095, 3429, 3428, 3427])).
% 49.18/49.35 tff(3437,plain,((~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.35 tff(3438,plain,
% 49.18/49.35 (~node1(c_bit1, s14)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3437, 3413])).
% 49.18/49.35 tff(3439,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3440,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3441,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 49.18/49.35 tff(3442,plain,
% 49.18/49.35 (node3(c_bit1, s14, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3441, 21, 489])).
% 49.18/49.35 tff(3443,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3444,plain,
% 49.18/49.35 ((node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15)) <=> (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3445,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15))))),
% 49.18/49.35 inference(monotonicity,[status(thm)],[3444])).
% 49.18/49.35 tff(3446,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)))),
% 49.18/49.35 inference(transitivity,[status(thm)],[3445, 3443])).
% 49.18/49.35 tff(3447,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s14) | (~node3(c_bit1, s14, s15)) | m_counter_cell_v_value(c_bit1, s15))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3448,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14) | (~node3(c_bit1, s14, s15))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 49.18/49.35 tff(3449,plain,
% 49.18/49.35 (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3448, 84, 3442])).
% 49.18/49.35 tff(3450,plain,
% 49.18/49.35 (m_counter_cell_v_value(c_bit1, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3449, 3438])).
% 49.18/49.35 tff(3451,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3452,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3453,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 49.18/49.35 tff(3454,plain,
% 49.18/49.35 ((~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3453, 2906, 505])).
% 49.18/49.35 tff(3455,plain,
% 49.18/49.35 (m_counter_cell_v_carry_out(c_bit0, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3454, 501])).
% 49.18/49.35 tff(3456,plain,
% 49.18/49.35 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3457,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3458,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s15)) | m_counter_cell_v_carry_in(c_bit1, s15)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 49.18/49.35 tff(3459,plain,
% 49.18/49.35 (m_counter_cell_v_carry_in(c_bit1, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3458, 2921, 3455])).
% 49.18/49.35 tff(3460,assumption,(node2(c_bit1, s15)), introduced(assumption)).
% 49.18/49.35 tff(3461,assumption,(m_counter_cell_v_value(c_bit1, s15)), introduced(assumption)).
% 49.18/49.35 tff(3462,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3463,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3464,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 49.18/49.35 tff(3465,plain,
% 49.18/49.35 ($false),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3464, 104, 3461, 3460, 3459])).
% 49.18/49.35 tff(3466,plain,((~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.35 tff(3467,plain,
% 49.18/49.35 (~node2(c_bit1, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3466, 3450])).
% 49.18/49.35 tff(3468,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3469,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3470,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 49.18/49.35 tff(3471,plain,
% 49.18/49.35 (node3(c_bit1, s15, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3470, 21, 517])).
% 49.18/49.35 tff(3472,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3473,plain,
% 49.18/49.35 ((node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16))) <=> ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3474,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16))))),
% 49.18/49.35 inference(monotonicity,[status(thm)],[3473])).
% 49.18/49.35 tff(3475,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)))),
% 49.18/49.35 inference(transitivity,[status(thm)],[3474, 3472])).
% 49.18/49.35 tff(3476,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s15) | (~node3(c_bit1, s15, s16)) | (~m_counter_cell_v_value(c_bit1, s16)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3477,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15) | (~node3(c_bit1, s15, s16))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 49.18/49.35 tff(3478,plain,
% 49.18/49.35 ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3477, 130, 3471])).
% 49.18/49.35 tff(3479,plain,
% 49.18/49.35 (~m_counter_cell_v_value(c_bit1, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3478, 3467])).
% 49.18/49.35 tff(3480,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3481,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3482,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s16) | (~node4(c_bit0, s16))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 49.18/49.35 tff(3483,plain,
% 49.18/49.35 (~node4(c_bit0, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3482, 2823, 529])).
% 49.18/49.35 tff(3484,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3485,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3486,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s16)) | node4(c_bit0, s16)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 49.18/49.35 tff(3487,plain,
% 49.18/49.35 (~m_counter_cell_v_carry_out(c_bit0, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3486, 2836, 3483])).
% 49.18/49.35 tff(3488,plain,
% 49.18/49.35 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3489,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3490,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 49.18/49.35 tff(3491,plain,
% 49.18/49.35 (~m_counter_cell_v_carry_in(c_bit1, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3490, 2851, 3487])).
% 49.18/49.35 tff(3492,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3493,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3494,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 49.18/49.35 tff(3495,plain,
% 49.18/49.35 (m_counter_cell_v_value(c_bit1, s16) | (~node2(c_bit1, s16))),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3494, 3024, 3491])).
% 49.18/49.35 tff(3496,plain,
% 49.18/49.35 (~node2(c_bit1, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3495, 3479])).
% 49.18/49.35 tff(3497,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3498,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3499,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3498, 3497])).
% 49.18/49.35 tff(3500,plain,
% 49.18/49.35 (node3(c_bit1, s16, s17)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3499, 21, 546])).
% 49.18/49.35 tff(3501,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3502,plain,
% 49.18/49.35 ((node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17))) <=> ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3503,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17))))),
% 49.18/49.35 inference(monotonicity,[status(thm)],[3502])).
% 49.18/49.35 tff(3504,plain,
% 49.18/49.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)))),
% 49.18/49.35 inference(transitivity,[status(thm)],[3503, 3501])).
% 49.18/49.35 tff(3505,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s16) | (~node3(c_bit1, s16, s17)) | (~m_counter_cell_v_value(c_bit1, s17)))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3506,plain,
% 49.18/49.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16) | (~node3(c_bit1, s16, s17))),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 49.18/49.35 tff(3507,plain,
% 49.18/49.35 ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3506, 130, 3500])).
% 49.18/49.35 tff(3508,plain,
% 49.18/49.35 (~m_counter_cell_v_value(c_bit1, s17)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3507, 3496])).
% 49.18/49.35 tff(3509,plain,
% 49.18/49.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3510,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3511,plain,
% 49.18/49.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 49.18/49.35 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 49.18/49.35 tff(3512,plain,
% 49.18/49.35 ((~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3511, 2906, 562])).
% 49.18/49.35 tff(3513,plain,
% 49.18/49.35 (m_counter_cell_v_carry_out(c_bit0, s17)),
% 49.18/49.35 inference(unit_resolution,[status(thm)],[3512, 558])).
% 49.18/49.35 tff(3514,plain,
% 49.18/49.35 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))),
% 49.18/49.35 inference(rewrite,[status(thm)],[])).
% 49.18/49.35 tff(3515,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17))),
% 49.18/49.35 inference(quant_inst,[status(thm)],[])).
% 49.18/49.35 tff(3516,plain,
% 49.18/49.35 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s17)) | m_counter_cell_v_carry_in(c_bit1, s17)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 49.18/49.36 tff(3517,plain,
% 49.18/49.36 (m_counter_cell_v_carry_in(c_bit1, s17)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3516, 2921, 3513])).
% 49.18/49.36 tff(3518,assumption,(node1(c_bit1, s17)), introduced(assumption)).
% 49.18/49.36 tff(3519,assumption,(~m_counter_cell_v_value(c_bit1, s17)), introduced(assumption)).
% 49.18/49.36 tff(3520,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3521,plain,
% 49.18/49.36 (((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3522,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3521])).
% 49.18/49.36 tff(3523,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3522, 3520])).
% 49.18/49.36 tff(3524,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s17)) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3525,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3524, 3523])).
% 49.18/49.36 tff(3526,plain,
% 49.18/49.36 ($false),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3525, 55, 3519, 3518, 3517])).
% 49.18/49.36 tff(3527,plain,((~node1(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.36 tff(3528,plain,
% 49.18/49.36 (~node1(c_bit1, s17)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3527, 3508])).
% 49.18/49.36 tff(3529,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3530,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3531,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3530, 3529])).
% 49.18/49.36 tff(3532,plain,
% 49.18/49.36 (node3(c_bit1, s17, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3531, 21, 574])).
% 49.18/49.36 tff(3533,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3534,plain,
% 49.18/49.36 ((node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18)) <=> (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3535,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3534])).
% 49.18/49.36 tff(3536,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3535, 3533])).
% 49.18/49.36 tff(3537,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | m_counter_cell_v_value(c_bit1, s18))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3538,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17) | (~node3(c_bit1, s17, s18))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 49.18/49.36 tff(3539,plain,
% 49.18/49.36 (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3538, 84, 3532])).
% 49.18/49.36 tff(3540,plain,
% 49.18/49.36 (m_counter_cell_v_value(c_bit1, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3539, 3528])).
% 49.18/49.36 tff(3541,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3542,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3543,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s18) | (~node4(c_bit0, s18))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 49.18/49.36 tff(3544,plain,
% 49.18/49.36 (~node4(c_bit0, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3543, 2823, 586])).
% 49.18/49.36 tff(3545,assumption,(m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 49.18/49.36 tff(3546,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3547,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3548,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3547, 3546])).
% 49.18/49.36 tff(3549,plain,
% 49.18/49.36 ($false),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3548, 2836, 3545, 3544])).
% 49.18/49.36 tff(3550,plain,(~m_counter_cell_v_carry_out(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.36 tff(3551,plain,
% 49.18/49.36 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3552,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3553,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 49.18/49.36 tff(3554,plain,
% 49.18/49.36 (~m_counter_cell_v_carry_in(c_bit1, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3553, 2851, 3550])).
% 49.18/49.36 tff(3555,assumption,(node1(c_bit1, s18)), introduced(assumption)).
% 49.18/49.36 tff(3556,assumption,(m_counter_cell_v_value(c_bit1, s18)), introduced(assumption)).
% 49.18/49.36 tff(3557,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3558,plain,
% 49.18/49.36 (((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18))) <=> (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3559,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3558])).
% 49.18/49.36 tff(3560,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3559, 3557])).
% 49.18/49.36 tff(3561,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3562,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~node1(c_bit1, s18))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 49.18/49.36 tff(3563,plain,
% 49.18/49.36 ($false),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3562, 3095, 3556, 3555, 3554])).
% 49.18/49.36 tff(3564,plain,((~node1(c_bit1, s18)) | (~m_counter_cell_v_value(c_bit1, s18))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.36 tff(3565,plain,
% 49.18/49.36 (~node1(c_bit1, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3564, 3540])).
% 49.18/49.36 tff(3566,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3567,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3568,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 49.18/49.36 tff(3569,plain,
% 49.18/49.36 (node3(c_bit1, s18, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3568, 21, 605])).
% 49.18/49.36 tff(3570,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3571,plain,
% 49.18/49.36 ((node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19)) <=> (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3572,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3571])).
% 49.18/49.36 tff(3573,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3572, 3570])).
% 49.18/49.36 tff(3574,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s18) | (~node3(c_bit1, s18, s19)) | m_counter_cell_v_value(c_bit1, s19))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3575,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18) | (~node3(c_bit1, s18, s19))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3574, 3573])).
% 49.18/49.36 tff(3576,plain,
% 49.18/49.36 (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3575, 84, 3569])).
% 49.18/49.36 tff(3577,plain,
% 49.18/49.36 (m_counter_cell_v_value(c_bit1, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3576, 3565])).
% 49.18/49.36 tff(3578,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3579,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3580,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 49.18/49.36 tff(3581,plain,
% 49.18/49.36 ((~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3580, 2906, 621])).
% 49.18/49.36 tff(3582,plain,
% 49.18/49.36 (m_counter_cell_v_carry_out(c_bit0, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3581, 617])).
% 49.18/49.36 tff(3583,plain,
% 49.18/49.36 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3584,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3585,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s19)) | m_counter_cell_v_carry_in(c_bit1, s19)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3584, 3583])).
% 49.18/49.36 tff(3586,plain,
% 49.18/49.36 (m_counter_cell_v_carry_in(c_bit1, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3585, 2921, 3582])).
% 49.18/49.36 tff(3587,assumption,(m_counter_cell_v_value(c_bit1, s19)), introduced(assumption)).
% 49.18/49.36 tff(3588,assumption,(node2(c_bit1, s19)), introduced(assumption)).
% 49.18/49.36 tff(3589,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3590,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3591,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3590, 3589])).
% 49.18/49.36 tff(3592,plain,
% 49.18/49.36 ($false),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3591, 104, 3588, 3587, 3586])).
% 49.18/49.36 tff(3593,plain,((~node2(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.36 tff(3594,plain,
% 49.18/49.36 (~node2(c_bit1, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3593, 3577])).
% 49.18/49.36 tff(3595,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3596,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3597,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 49.18/49.36 tff(3598,plain,
% 49.18/49.36 (node3(c_bit1, s19, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3597, 21, 633])).
% 49.18/49.36 tff(3599,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3600,plain,
% 49.18/49.36 ((node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20))) <=> ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3601,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3600])).
% 49.18/49.36 tff(3602,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3601, 3599])).
% 49.18/49.36 tff(3603,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s19) | (~node3(c_bit1, s19, s20)) | (~m_counter_cell_v_value(c_bit1, s20)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3604,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19) | (~node3(c_bit1, s19, s20))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 49.18/49.36 tff(3605,plain,
% 49.18/49.36 ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3604, 130, 3598])).
% 49.18/49.36 tff(3606,plain,
% 49.18/49.36 (~m_counter_cell_v_value(c_bit1, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3605, 3594])).
% 49.18/49.36 tff(3607,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3608,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3609,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3608, 3607])).
% 49.18/49.36 tff(3610,plain,
% 49.18/49.36 (~node4(c_bit0, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3609, 2823, 645])).
% 49.18/49.36 tff(3611,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3612,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3613,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 49.18/49.36 tff(3614,plain,
% 49.18/49.36 (~m_counter_cell_v_carry_out(c_bit0, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3613, 2836, 3610])).
% 49.18/49.36 tff(3615,plain,
% 49.18/49.36 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3616,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3617,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 49.18/49.36 tff(3618,plain,
% 49.18/49.36 (~m_counter_cell_v_carry_in(c_bit1, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3617, 2851, 3614])).
% 49.18/49.36 tff(3619,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3620,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3621,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 49.18/49.36 tff(3622,plain,
% 49.18/49.36 (m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20))),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3621, 3024, 3618])).
% 49.18/49.36 tff(3623,plain,
% 49.18/49.36 (~node2(c_bit1, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3622, 3606])).
% 49.18/49.36 tff(3624,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3625,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3626,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 49.18/49.36 tff(3627,plain,
% 49.18/49.36 (node3(c_bit1, s20, s21)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3626, 21, 662])).
% 49.18/49.36 tff(3628,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3629,plain,
% 49.18/49.36 ((node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21))) <=> ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3630,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21))))),
% 49.18/49.36 inference(monotonicity,[status(thm)],[3629])).
% 49.18/49.36 tff(3631,plain,
% 49.18/49.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)))),
% 49.18/49.36 inference(transitivity,[status(thm)],[3630, 3628])).
% 49.18/49.36 tff(3632,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s20) | (~node3(c_bit1, s20, s21)) | (~m_counter_cell_v_value(c_bit1, s21)))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3633,plain,
% 49.18/49.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20) | (~node3(c_bit1, s20, s21))),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 49.18/49.36 tff(3634,plain,
% 49.18/49.36 ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3633, 130, 3627])).
% 49.18/49.36 tff(3635,plain,
% 49.18/49.36 (~m_counter_cell_v_value(c_bit1, s21)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3634, 3623])).
% 49.18/49.36 tff(3636,plain,
% 49.18/49.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3637,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3638,plain,
% 49.18/49.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 49.18/49.36 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 49.18/49.36 tff(3639,plain,
% 49.18/49.36 ((~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3638, 2906, 678])).
% 49.18/49.36 tff(3640,plain,
% 49.18/49.36 (m_counter_cell_v_carry_out(c_bit0, s21)),
% 49.18/49.36 inference(unit_resolution,[status(thm)],[3639, 674])).
% 49.18/49.36 tff(3641,plain,
% 49.18/49.36 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))),
% 49.18/49.36 inference(rewrite,[status(thm)],[])).
% 49.18/49.36 tff(3642,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21))),
% 49.18/49.36 inference(quant_inst,[status(thm)],[])).
% 49.18/49.36 tff(3643,plain,
% 49.18/49.36 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s21)) | m_counter_cell_v_carry_in(c_bit1, s21)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 49.18/49.37 tff(3644,plain,
% 49.18/49.37 (m_counter_cell_v_carry_in(c_bit1, s21)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3643, 2921, 3640])).
% 49.18/49.37 tff(3645,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3646,plain,
% 49.18/49.37 (((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3647,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3646])).
% 49.18/49.37 tff(3648,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3647, 3645])).
% 49.18/49.37 tff(3649,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s21)) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3650,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3649, 3648])).
% 49.18/49.37 tff(3651,plain,
% 49.18/49.37 (m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3650, 55, 3644])).
% 49.18/49.37 tff(3652,plain,
% 49.18/49.37 (~node1(c_bit1, s21)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3651, 3635])).
% 49.18/49.37 tff(3653,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3654,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3655,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3654, 3653])).
% 49.18/49.37 tff(3656,plain,
% 49.18/49.37 (node3(c_bit1, s21, s22)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3655, 21, 690])).
% 49.18/49.37 tff(3657,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3658,plain,
% 49.18/49.37 ((node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22)) <=> (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3659,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3658])).
% 49.18/49.37 tff(3660,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3659, 3657])).
% 49.18/49.37 tff(3661,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s21) | (~node3(c_bit1, s21, s22)) | m_counter_cell_v_value(c_bit1, s22))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3662,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21) | (~node3(c_bit1, s21, s22))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3661, 3660])).
% 49.18/49.37 tff(3663,plain,
% 49.18/49.37 (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3662, 84, 3656])).
% 49.18/49.37 tff(3664,plain,
% 49.18/49.37 (m_counter_cell_v_value(c_bit1, s22)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3663, 3652])).
% 49.18/49.37 tff(3665,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3666,plain,
% 49.18/49.37 (((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22))) <=> (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3667,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3666])).
% 49.18/49.37 tff(3668,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3667, 3665])).
% 49.18/49.37 tff(3669,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s22)) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3670,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 49.18/49.37 tff(3671,plain,
% 49.18/49.37 (m_counter_cell_v_carry_in(c_bit1, s22) | (~node1(c_bit1, s22))),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3670, 3095, 3664])).
% 49.18/49.37 tff(3672,plain,
% 49.18/49.37 (~node1(c_bit1, s22)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3671, 2944])).
% 49.18/49.37 tff(3673,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3674,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3675,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3674, 3673])).
% 49.18/49.37 tff(3676,plain,
% 49.18/49.37 (node3(c_bit1, s22, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3675, 21, 721])).
% 49.18/49.37 tff(3677,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3678,plain,
% 49.18/49.37 ((node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23)) <=> (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3679,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3678])).
% 49.18/49.37 tff(3680,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3679, 3677])).
% 49.18/49.37 tff(3681,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s22) | (~node3(c_bit1, s22, s23)) | m_counter_cell_v_value(c_bit1, s23))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3682,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22) | (~node3(c_bit1, s22, s23))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3681, 3680])).
% 49.18/49.37 tff(3683,plain,
% 49.18/49.37 (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3682, 84, 3676])).
% 49.18/49.37 tff(3684,plain,
% 49.18/49.37 (m_counter_cell_v_value(c_bit1, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3683, 3672])).
% 49.18/49.37 tff(3685,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3686,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3687,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 49.18/49.37 tff(3688,plain,
% 49.18/49.37 ((~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3687, 2906, 737])).
% 49.18/49.37 tff(3689,plain,
% 49.18/49.37 (m_counter_cell_v_carry_out(c_bit0, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3688, 733])).
% 49.18/49.37 tff(3690,plain,
% 49.18/49.37 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3691,plain,
% 49.18/49.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3692,plain,
% 49.18/49.37 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s23)) | m_counter_cell_v_carry_in(c_bit1, s23)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3691, 3690])).
% 49.18/49.37 tff(3693,plain,
% 49.18/49.37 (m_counter_cell_v_carry_in(c_bit1, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3692, 2921, 3689])).
% 49.18/49.37 tff(3694,assumption,(node2(c_bit1, s23)), introduced(assumption)).
% 49.18/49.37 tff(3695,assumption,(m_counter_cell_v_value(c_bit1, s23)), introduced(assumption)).
% 49.18/49.37 tff(3696,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3697,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3698,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 49.18/49.37 tff(3699,plain,
% 49.18/49.37 ($false),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3698, 104, 3695, 3694, 3693])).
% 49.18/49.37 tff(3700,plain,((~node2(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.37 tff(3701,plain,
% 49.18/49.37 (~node2(c_bit1, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3700, 3684])).
% 49.18/49.37 tff(3702,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3703,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3704,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 49.18/49.37 tff(3705,plain,
% 49.18/49.37 (node3(c_bit1, s23, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3704, 21, 749])).
% 49.18/49.37 tff(3706,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3707,plain,
% 49.18/49.37 ((node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24))) <=> ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3708,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3707])).
% 49.18/49.37 tff(3709,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3708, 3706])).
% 49.18/49.37 tff(3710,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | (~m_counter_cell_v_value(c_bit1, s24)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3711,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23) | (~node3(c_bit1, s23, s24))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3710, 3709])).
% 49.18/49.37 tff(3712,plain,
% 49.18/49.37 ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3711, 130, 3705])).
% 49.18/49.37 tff(3713,plain,
% 49.18/49.37 (~m_counter_cell_v_value(c_bit1, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3712, 3701])).
% 49.18/49.37 tff(3714,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3715,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3716,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s24) | (~node4(c_bit0, s24))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 49.18/49.37 tff(3717,plain,
% 49.18/49.37 (~node4(c_bit0, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3716, 2823, 761])).
% 49.18/49.37 tff(3718,assumption,(m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 49.18/49.37 tff(3719,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3720,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3721,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3720, 3719])).
% 49.18/49.37 tff(3722,plain,
% 49.18/49.37 ($false),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3721, 2836, 3718, 3717])).
% 49.18/49.37 tff(3723,plain,(~m_counter_cell_v_carry_out(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.37 tff(3724,plain,
% 49.18/49.37 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3725,plain,
% 49.18/49.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3726,plain,
% 49.18/49.37 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 49.18/49.37 tff(3727,plain,
% 49.18/49.37 (~m_counter_cell_v_carry_in(c_bit1, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3726, 2851, 3723])).
% 49.18/49.37 tff(3728,assumption,(node2(c_bit1, s24)), introduced(assumption)).
% 49.18/49.37 tff(3729,assumption,(~m_counter_cell_v_value(c_bit1, s24)), introduced(assumption)).
% 49.18/49.37 tff(3730,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3731,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3732,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 49.18/49.37 tff(3733,plain,
% 49.18/49.37 ($false),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3732, 3024, 3729, 3728, 3727])).
% 49.18/49.37 tff(3734,plain,(m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.37 tff(3735,plain,
% 49.18/49.37 (~node2(c_bit1, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3734, 3713])).
% 49.18/49.37 tff(3736,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3737,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3738,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 49.18/49.37 tff(3739,plain,
% 49.18/49.37 (node3(c_bit1, s24, s25)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3738, 21, 780])).
% 49.18/49.37 tff(3740,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3741,plain,
% 49.18/49.37 ((node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25))) <=> ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3742,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25))))),
% 49.18/49.37 inference(monotonicity,[status(thm)],[3741])).
% 49.18/49.37 tff(3743,plain,
% 49.18/49.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 49.18/49.37 inference(transitivity,[status(thm)],[3742, 3740])).
% 49.18/49.37 tff(3744,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | (~m_counter_cell_v_value(c_bit1, s25)))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3745,plain,
% 49.18/49.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24) | (~node3(c_bit1, s24, s25))),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 49.18/49.37 tff(3746,plain,
% 49.18/49.37 ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3745, 130, 3739])).
% 49.18/49.37 tff(3747,plain,
% 49.18/49.37 (~m_counter_cell_v_value(c_bit1, s25)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3746, 3735])).
% 49.18/49.37 tff(3748,plain,
% 49.18/49.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))),
% 49.18/49.37 inference(rewrite,[status(thm)],[])).
% 49.18/49.37 tff(3749,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25))),
% 49.18/49.37 inference(quant_inst,[status(thm)],[])).
% 49.18/49.37 tff(3750,plain,
% 49.18/49.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 49.18/49.37 inference(modus_ponens,[status(thm)],[3749, 3748])).
% 49.18/49.37 tff(3751,plain,
% 49.18/49.37 ((~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3750, 2906, 794])).
% 49.18/49.37 tff(3752,plain,
% 49.18/49.37 (m_counter_cell_v_carry_out(c_bit0, s25)),
% 49.18/49.37 inference(unit_resolution,[status(thm)],[3751, 792])).
% 49.18/49.38 tff(3753,plain,
% 49.18/49.38 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3754,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3755,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 49.18/49.38 tff(3756,plain,
% 49.18/49.38 (m_counter_cell_v_carry_in(c_bit1, s25)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3755, 2921, 3752])).
% 49.18/49.38 tff(3757,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3758,plain,
% 49.18/49.38 (((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3759,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3758])).
% 49.18/49.38 tff(3760,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3759, 3757])).
% 49.18/49.38 tff(3761,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s25)) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3762,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s25)) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 49.18/49.38 tff(3763,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3762, 55, 3756])).
% 49.18/49.38 tff(3764,plain,
% 49.18/49.38 (~node1(c_bit1, s25)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3763, 3747])).
% 49.18/49.38 tff(3765,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3766,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3767,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 49.18/49.38 tff(3768,plain,
% 49.18/49.38 (node3(c_bit1, s25, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3767, 21, 806])).
% 49.18/49.38 tff(3769,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3770,plain,
% 49.18/49.38 ((node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26)) <=> (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3771,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3770])).
% 49.18/49.38 tff(3772,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3771, 3769])).
% 49.18/49.38 tff(3773,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | m_counter_cell_v_value(c_bit1, s26))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3774,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25) | (~node3(c_bit1, s25, s26))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 49.18/49.38 tff(3775,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3774, 84, 3768])).
% 49.18/49.38 tff(3776,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3775, 3764])).
% 49.18/49.38 tff(3777,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3778,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3779,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s26) | (~node4(c_bit0, s26))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 49.18/49.38 tff(3780,plain,
% 49.18/49.38 (~node4(c_bit0, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3779, 2823, 818])).
% 49.18/49.38 tff(3781,assumption,(m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 49.18/49.38 tff(3782,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3783,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3784,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3783, 3782])).
% 49.18/49.38 tff(3785,plain,
% 49.18/49.38 ($false),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3784, 2836, 3781, 3780])).
% 49.18/49.38 tff(3786,plain,(~m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.38 tff(3787,assumption,(m_counter_cell_v_carry_in(c_bit1, s26)), introduced(assumption)).
% 49.18/49.38 tff(3788,assumption,(~m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 49.18/49.38 tff(3789,plain,
% 49.18/49.38 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3790,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3791,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 49.18/49.38 tff(3792,plain,
% 49.18/49.38 ($false),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3791, 2851, 3788, 3787])).
% 49.18/49.38 tff(3793,plain,((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.38 tff(3794,plain,
% 49.18/49.38 (~m_counter_cell_v_carry_in(c_bit1, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3793, 3786])).
% 49.18/49.38 tff(3795,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3796,plain,
% 49.18/49.38 (((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26))) <=> (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3797,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3796])).
% 49.18/49.38 tff(3798,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3797, 3795])).
% 49.18/49.38 tff(3799,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s26)) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3800,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 49.18/49.38 tff(3801,plain,
% 49.18/49.38 ((~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3800, 3095, 3794])).
% 49.18/49.38 tff(3802,plain,
% 49.18/49.38 (~node1(c_bit1, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3801, 3776])).
% 49.18/49.38 tff(3803,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3804,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3805,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 49.18/49.38 tff(3806,plain,
% 49.18/49.38 (node3(c_bit1, s26, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3805, 21, 837])).
% 49.18/49.38 tff(3807,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3808,plain,
% 49.18/49.38 ((node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27)) <=> (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3809,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3808])).
% 49.18/49.38 tff(3810,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3809, 3807])).
% 49.18/49.38 tff(3811,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | m_counter_cell_v_value(c_bit1, s27))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3812,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26) | (~node3(c_bit1, s26, s27))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3811, 3810])).
% 49.18/49.38 tff(3813,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3812, 84, 3806])).
% 49.18/49.38 tff(3814,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3813, 3802])).
% 49.18/49.38 tff(3815,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3816,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3817,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 49.18/49.38 tff(3818,plain,
% 49.18/49.38 ((~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3817, 2906, 853])).
% 49.18/49.38 tff(3819,plain,
% 49.18/49.38 (m_counter_cell_v_carry_out(c_bit0, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3818, 849])).
% 49.18/49.38 tff(3820,plain,
% 49.18/49.38 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3821,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3822,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s27)) | m_counter_cell_v_carry_in(c_bit1, s27)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3821, 3820])).
% 49.18/49.38 tff(3823,plain,
% 49.18/49.38 (m_counter_cell_v_carry_in(c_bit1, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3822, 2921, 3819])).
% 49.18/49.38 tff(3824,assumption,(node2(c_bit1, s27)), introduced(assumption)).
% 49.18/49.38 tff(3825,assumption,(m_counter_cell_v_value(c_bit1, s27)), introduced(assumption)).
% 49.18/49.38 tff(3826,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3827,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3828,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 49.18/49.38 tff(3829,plain,
% 49.18/49.38 ($false),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3828, 104, 3825, 3824, 3823])).
% 49.18/49.38 tff(3830,plain,((~node2(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.38 tff(3831,plain,
% 49.18/49.38 (~node2(c_bit1, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3830, 3814])).
% 49.18/49.38 tff(3832,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3833,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3834,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 49.18/49.38 tff(3835,plain,
% 49.18/49.38 (node3(c_bit1, s27, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3834, 21, 865])).
% 49.18/49.38 tff(3836,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3837,plain,
% 49.18/49.38 ((node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28))) <=> ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3838,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3837])).
% 49.18/49.38 tff(3839,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3838, 3836])).
% 49.18/49.38 tff(3840,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s27) | (~node3(c_bit1, s27, s28)) | (~m_counter_cell_v_value(c_bit1, s28)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3841,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27) | (~node3(c_bit1, s27, s28))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3840, 3839])).
% 49.18/49.38 tff(3842,plain,
% 49.18/49.38 ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3841, 130, 3835])).
% 49.18/49.38 tff(3843,plain,
% 49.18/49.38 (~m_counter_cell_v_value(c_bit1, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3842, 3831])).
% 49.18/49.38 tff(3844,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3845,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3846,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s28) | (~node4(c_bit0, s28))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 49.18/49.38 tff(3847,plain,
% 49.18/49.38 (~node4(c_bit0, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3846, 2823, 877])).
% 49.18/49.38 tff(3848,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3849,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3850,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 49.18/49.38 tff(3851,plain,
% 49.18/49.38 (~m_counter_cell_v_carry_out(c_bit0, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3850, 2836, 3847])).
% 49.18/49.38 tff(3852,plain,
% 49.18/49.38 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3853,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3854,plain,
% 49.18/49.38 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 49.18/49.38 tff(3855,plain,
% 49.18/49.38 (~m_counter_cell_v_carry_in(c_bit1, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3854, 2851, 3851])).
% 49.18/49.38 tff(3856,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3857,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3858,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 49.18/49.38 tff(3859,plain,
% 49.18/49.38 (m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3858, 3024, 3855])).
% 49.18/49.38 tff(3860,plain,
% 49.18/49.38 (~node2(c_bit1, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3859, 3843])).
% 49.18/49.38 tff(3861,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3862,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3863,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 49.18/49.38 tff(3864,plain,
% 49.18/49.38 (node3(c_bit1, s28, s29)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3863, 21, 894])).
% 49.18/49.38 tff(3865,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3866,plain,
% 49.18/49.38 ((node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29))) <=> ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3867,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29))))),
% 49.18/49.38 inference(monotonicity,[status(thm)],[3866])).
% 49.18/49.38 tff(3868,plain,
% 49.18/49.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)))),
% 49.18/49.38 inference(transitivity,[status(thm)],[3867, 3865])).
% 49.18/49.38 tff(3869,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s28) | (~node3(c_bit1, s28, s29)) | (~m_counter_cell_v_value(c_bit1, s29)))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3870,plain,
% 49.18/49.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28) | (~node3(c_bit1, s28, s29))),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 49.18/49.38 tff(3871,plain,
% 49.18/49.38 ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3870, 130, 3864])).
% 49.18/49.38 tff(3872,plain,
% 49.18/49.38 (~m_counter_cell_v_value(c_bit1, s29)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3871, 3860])).
% 49.18/49.38 tff(3873,assumption,(node1(c_bit1, s29)), introduced(assumption)).
% 49.18/49.38 tff(3874,plain,
% 49.18/49.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))),
% 49.18/49.38 inference(rewrite,[status(thm)],[])).
% 49.18/49.38 tff(3875,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29))),
% 49.18/49.38 inference(quant_inst,[status(thm)],[])).
% 49.18/49.38 tff(3876,plain,
% 49.18/49.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 49.18/49.38 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 49.18/49.38 tff(3877,plain,
% 49.18/49.38 ((~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3876, 2906, 910])).
% 49.18/49.38 tff(3878,plain,
% 49.18/49.38 (m_counter_cell_v_carry_out(c_bit0, s29)),
% 49.18/49.38 inference(unit_resolution,[status(thm)],[3877, 906])).
% 49.18/49.38 tff(3879,plain,
% 49.18/49.38 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3880,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3881,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s29)) | m_counter_cell_v_carry_in(c_bit1, s29)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3880, 3879])).
% 49.18/49.39 tff(3882,plain,
% 49.18/49.39 (m_counter_cell_v_carry_in(c_bit1, s29)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3881, 2921, 3878])).
% 49.18/49.39 tff(3883,assumption,(~m_counter_cell_v_value(c_bit1, s29)), introduced(assumption)).
% 49.18/49.39 tff(3884,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3885,plain,
% 49.18/49.39 (((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3886,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))))),
% 49.18/49.39 inference(monotonicity,[status(thm)],[3885])).
% 49.18/49.39 tff(3887,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29)))),
% 49.18/49.39 inference(transitivity,[status(thm)],[3886, 3884])).
% 49.18/49.39 tff(3888,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s29)) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3889,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 49.18/49.39 tff(3890,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3889, 55, 3883, 3882, 3873])).
% 49.18/49.39 tff(3891,plain,((~node1(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3892,plain,
% 49.18/49.39 (~node1(c_bit1, s29)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3891, 3872])).
% 49.18/49.39 tff(3893,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3894,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3895,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 49.18/49.39 tff(3896,plain,
% 49.18/49.39 (node3(c_bit1, s29, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3895, 21, 922])).
% 49.18/49.39 tff(3897,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3898,plain,
% 49.18/49.39 ((node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30)) <=> (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3899,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30))))),
% 49.18/49.39 inference(monotonicity,[status(thm)],[3898])).
% 49.18/49.39 tff(3900,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)))),
% 49.18/49.39 inference(transitivity,[status(thm)],[3899, 3897])).
% 49.18/49.39 tff(3901,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s29) | (~node3(c_bit1, s29, s30)) | m_counter_cell_v_value(c_bit1, s30))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3902,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29) | (~node3(c_bit1, s29, s30))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3901, 3900])).
% 49.18/49.39 tff(3903,plain,
% 49.18/49.39 (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3902, 84, 3896])).
% 49.18/49.39 tff(3904,plain,
% 49.18/49.39 (m_counter_cell_v_value(c_bit1, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3903, 3892])).
% 49.18/49.39 tff(3905,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3906,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3907,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s30) | (~node4(c_bit0, s30))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3906, 3905])).
% 49.18/49.39 tff(3908,plain,
% 49.18/49.39 (~node4(c_bit0, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3907, 2823, 934])).
% 49.18/49.39 tff(3909,assumption,(m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 49.18/49.39 tff(3910,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3911,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3912,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 49.18/49.39 tff(3913,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3912, 2836, 3909, 3908])).
% 49.18/49.39 tff(3914,plain,(~m_counter_cell_v_carry_out(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3915,assumption,(m_counter_cell_v_carry_in(c_bit1, s30)), introduced(assumption)).
% 49.18/49.39 tff(3916,assumption,(~m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 49.18/49.39 tff(3917,plain,
% 49.18/49.39 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3918,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3919,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3918, 3917])).
% 49.18/49.39 tff(3920,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3919, 2851, 3916, 3915])).
% 49.18/49.39 tff(3921,plain,(m_counter_cell_v_carry_out(c_bit0, s30) | (~m_counter_cell_v_carry_in(c_bit1, s30))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3922,plain,
% 49.18/49.39 (~m_counter_cell_v_carry_in(c_bit1, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3921, 3914])).
% 49.18/49.39 tff(3923,assumption,(m_counter_cell_v_value(c_bit1, s30)), introduced(assumption)).
% 49.18/49.39 tff(3924,assumption,(node1(c_bit1, s30)), introduced(assumption)).
% 49.18/49.39 tff(3925,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3926,plain,
% 49.18/49.39 (((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30))) <=> (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3927,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))))),
% 49.18/49.39 inference(monotonicity,[status(thm)],[3926])).
% 49.18/49.39 tff(3928,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30)))),
% 49.18/49.39 inference(transitivity,[status(thm)],[3927, 3925])).
% 49.18/49.39 tff(3929,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s30)) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3930,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 49.18/49.39 tff(3931,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3930, 3095, 3924, 3923, 3922])).
% 49.18/49.39 tff(3932,plain,((~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3933,plain,
% 49.18/49.39 (~node1(c_bit1, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3932, 3904])).
% 49.18/49.39 tff(3934,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3935,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3936,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3935, 3934])).
% 49.18/49.39 tff(3937,plain,
% 49.18/49.39 (node3(c_bit1, s30, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3936, 21, 953])).
% 49.18/49.39 tff(3938,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3939,plain,
% 49.18/49.39 ((node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31)) <=> (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3940,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31))))),
% 49.18/49.39 inference(monotonicity,[status(thm)],[3939])).
% 49.18/49.39 tff(3941,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)))),
% 49.18/49.39 inference(transitivity,[status(thm)],[3940, 3938])).
% 49.18/49.39 tff(3942,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s30) | (~node3(c_bit1, s30, s31)) | m_counter_cell_v_value(c_bit1, s31))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3943,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30) | (~node3(c_bit1, s30, s31))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 49.18/49.39 tff(3944,plain,
% 49.18/49.39 (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3943, 84, 3937])).
% 49.18/49.39 tff(3945,plain,
% 49.18/49.39 (m_counter_cell_v_value(c_bit1, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3944, 3933])).
% 49.18/49.39 tff(3946,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3947,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3948,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3947, 3946])).
% 49.18/49.39 tff(3949,plain,
% 49.18/49.39 ((~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3948, 2906, 969])).
% 49.18/49.39 tff(3950,plain,
% 49.18/49.39 (m_counter_cell_v_carry_out(c_bit0, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3949, 965])).
% 49.18/49.39 tff(3951,plain,
% 49.18/49.39 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3952,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3953,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 49.18/49.39 tff(3954,plain,
% 49.18/49.39 (m_counter_cell_v_carry_in(c_bit1, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3953, 2921, 3950])).
% 49.18/49.39 tff(3955,assumption,(node2(c_bit1, s31)), introduced(assumption)).
% 49.18/49.39 tff(3956,assumption,(m_counter_cell_v_value(c_bit1, s31)), introduced(assumption)).
% 49.18/49.39 tff(3957,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3958,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3959,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 49.18/49.39 tff(3960,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3959, 104, 3956, 3955, 3954])).
% 49.18/49.39 tff(3961,plain,((~node2(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31))), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3962,plain,
% 49.18/49.39 (~node2(c_bit1, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3961, 3945])).
% 49.18/49.39 tff(3963,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3964,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3965,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3964, 3963])).
% 49.18/49.39 tff(3966,plain,
% 49.18/49.39 (node3(c_bit1, s31, s32)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3965, 21, 981])).
% 49.18/49.39 tff(3967,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3968,plain,
% 49.18/49.39 ((node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32))) <=> ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3969,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32))))),
% 49.18/49.39 inference(monotonicity,[status(thm)],[3968])).
% 49.18/49.39 tff(3970,plain,
% 49.18/49.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)))),
% 49.18/49.39 inference(transitivity,[status(thm)],[3969, 3967])).
% 49.18/49.39 tff(3971,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s31) | (~node3(c_bit1, s31, s32)) | (~m_counter_cell_v_value(c_bit1, s32)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3972,plain,
% 49.18/49.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31) | (~node3(c_bit1, s31, s32))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3971, 3970])).
% 49.18/49.39 tff(3973,plain,
% 49.18/49.39 ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3972, 130, 3966])).
% 49.18/49.39 tff(3974,plain,
% 49.18/49.39 (~m_counter_cell_v_value(c_bit1, s32)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3973, 3962])).
% 49.18/49.39 tff(3975,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3976,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3977,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s32) | (~node4(c_bit0, s32))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 49.18/49.39 tff(3978,plain,
% 49.18/49.39 (~node4(c_bit0, s32)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3977, 2823, 993])).
% 49.18/49.39 tff(3979,assumption,(m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 49.18/49.39 tff(3980,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3981,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3982,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3981, 3980])).
% 49.18/49.39 tff(3983,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3982, 2836, 3979, 3978])).
% 49.18/49.39 tff(3984,plain,(~m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3985,assumption,(m_counter_cell_v_carry_in(c_bit1, s32)), introduced(assumption)).
% 49.18/49.39 tff(3986,assumption,(~m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 49.18/49.39 tff(3987,plain,
% 49.18/49.39 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3988,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3989,plain,
% 49.18/49.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 49.18/49.39 tff(3990,plain,
% 49.18/49.39 ($false),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3989, 2851, 3986, 3985])).
% 49.18/49.39 tff(3991,plain,((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 49.18/49.39 tff(3992,plain,
% 49.18/49.39 (~m_counter_cell_v_carry_in(c_bit1, s32)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3991, 3984])).
% 49.18/49.39 tff(3993,plain,
% 49.18/49.39 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))),
% 49.18/49.39 inference(rewrite,[status(thm)],[])).
% 49.18/49.39 tff(3994,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32)))),
% 49.18/49.39 inference(quant_inst,[status(thm)],[])).
% 49.18/49.39 tff(3995,plain,
% 49.18/49.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 49.18/49.39 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 49.18/49.39 tff(3996,plain,
% 49.18/49.39 (m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3995, 3024, 3992])).
% 49.18/49.39 tff(3997,plain,
% 49.18/49.39 (~node2(c_bit1, s32)),
% 49.18/49.39 inference(unit_resolution,[status(thm)],[3996, 3974])).
% 49.23/49.39 tff(3998,plain,
% 49.23/49.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 49.23/49.39 inference(rewrite,[status(thm)],[])).
% 49.23/49.39 tff(3999,plain,
% 49.23/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 49.23/49.39 inference(quant_inst,[status(thm)],[])).
% 49.23/49.39 tff(4000,plain,
% 49.23/49.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33)),
% 49.23/49.39 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 49.23/49.39 tff(4001,plain,
% 49.23/49.39 (node3(c_bit1, s32, s33)),
% 49.23/49.39 inference(unit_resolution,[status(thm)],[4000, 21, 1012])).
% 49.23/49.39 tff(4002,plain,
% 49.23/49.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4003,plain,
% 49.23/49.40 ((node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33))) <=> ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4004,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4003])).
% 49.23/49.40 tff(4005,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4004, 4002])).
% 49.23/49.40 tff(4006,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s32) | (~node3(c_bit1, s32, s33)) | (~m_counter_cell_v_value(c_bit1, s33)))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4007,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32) | (~node3(c_bit1, s32, s33))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4006, 4005])).
% 49.23/49.40 tff(4008,plain,
% 49.23/49.40 ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4007, 130, 4001])).
% 49.23/49.40 tff(4009,plain,
% 49.23/49.40 (~m_counter_cell_v_value(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4008, 3997])).
% 49.23/49.40 tff(4010,assumption,(~m_counter_cell_v_value(c_bit1, s33)), introduced(assumption)).
% 49.23/49.40 tff(4011,assumption,(node1(c_bit1, s34)), introduced(assumption)).
% 49.23/49.40 tff(4012,assumption,(~m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 49.23/49.40 tff(4013,assumption,(m_counter_cell_v_carry_in(c_bit1, s34)), introduced(assumption)).
% 49.23/49.40 tff(4014,plain,
% 49.23/49.40 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4015,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4016,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 49.23/49.40 tff(4017,plain,
% 49.23/49.40 ($false),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4016, 2851, 4012, 4013])).
% 49.23/49.40 tff(4018,plain,((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.40 tff(4019,plain,
% 49.23/49.40 (~m_counter_cell_v_carry_in(c_bit1, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4018, 4012])).
% 49.23/49.40 tff(4020,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4021,plain,
% 49.23/49.40 (((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34))) <=> (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4022,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4021])).
% 49.23/49.40 tff(4023,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4022, 4020])).
% 49.23/49.40 tff(4024,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s34)) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4025,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 49.23/49.40 tff(4026,plain,
% 49.23/49.40 (m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34))),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4025, 3095, 4011])).
% 49.23/49.40 tff(4027,plain,
% 49.23/49.40 (~m_counter_cell_v_value(c_bit1, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4026, 4019])).
% 49.23/49.40 tff(4028,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4029,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4030,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 49.23/49.40 tff(4031,plain,
% 49.23/49.40 (node3(c_bit1, s33, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4030, 21, 1040])).
% 49.23/49.40 tff(4032,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4033,plain,
% 49.23/49.40 ((node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34)) <=> (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4034,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4033])).
% 49.23/49.40 tff(4035,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4034, 4032])).
% 49.23/49.40 tff(4036,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | m_counter_cell_v_value(c_bit1, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4037,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33) | (~node3(c_bit1, s33, s34))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 49.23/49.40 tff(4038,plain,
% 49.23/49.40 (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4037, 84, 4031])).
% 49.23/49.40 tff(4039,plain,
% 49.23/49.40 (node1(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4038, 4027])).
% 49.23/49.40 tff(4040,assumption,(m_counter_cell_v_carry_in(c_bit1, s33)), introduced(assumption)).
% 49.23/49.40 tff(4041,assumption,(node1(c_bit1, s33)), introduced(assumption)).
% 49.23/49.40 tff(4042,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4043,plain,
% 49.23/49.40 (((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4044,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4043])).
% 49.23/49.40 tff(4045,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4044, 4042])).
% 49.23/49.40 tff(4046,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4047,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 49.23/49.40 tff(4048,plain,
% 49.23/49.40 ($false),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4047, 55, 4010, 4041, 4040])).
% 49.23/49.40 tff(4049,plain,(m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33)) | (~m_counter_cell_v_carry_in(c_bit1, s33))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.40 tff(4050,plain,
% 49.23/49.40 (~m_counter_cell_v_carry_in(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4049, 4039, 4010])).
% 49.23/49.40 tff(4051,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | (~m_counter_cell_v_value(c_bit0, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | (~m_counter_cell_v_value(c_bit0, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4052,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s34)) | (~m_counter_cell_v_value(c_bit0, s34)) | m_counter_cell_v_carry_out(c_bit0, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4053,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | (~m_counter_cell_v_value(c_bit0, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 49.23/49.40 tff(4054,plain,
% 49.23/49.40 ((~m_counter_cell_v_value(c_bit0, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4053, 2906, 1056])).
% 49.23/49.40 tff(4055,plain,
% 49.23/49.40 (~m_counter_cell_v_value(c_bit0, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4054, 4012])).
% 49.23/49.40 tff(4056,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4057,plain,
% 49.23/49.40 ((node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | m_counter_cell_v_value(c_bit0, s34)) <=> (m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4058,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4057])).
% 49.23/49.40 tff(4059,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | m_counter_cell_v_value(c_bit0, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4058, 4056])).
% 49.23/49.40 tff(4060,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s33) | (~node3(c_bit0, s33, s34)) | m_counter_cell_v_value(c_bit0, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4061,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33) | (~node3(c_bit0, s33, s34))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 49.23/49.40 tff(4062,plain,
% 49.23/49.40 (m_counter_cell_v_value(c_bit0, s34) | node1(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4061, 84, 1044])).
% 49.23/49.40 tff(4063,plain,
% 49.23/49.40 (node1(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4062, 4055])).
% 49.23/49.40 tff(4064,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4065,plain,
% 49.23/49.40 (((~node1(c_bit0, s33)) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4066,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s33)) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4065])).
% 49.23/49.40 tff(4067,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s33)) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4066, 4064])).
% 49.23/49.40 tff(4068,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s33)) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4069,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4068, 4067])).
% 49.23/49.40 tff(4070,plain,
% 49.23/49.40 (m_counter_cell_v_value(c_bit0, s33) | (~node1(c_bit0, s33))),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4069, 55, 1028])).
% 49.23/49.40 tff(4071,plain,
% 49.23/49.40 (m_counter_cell_v_value(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4070, 4063])).
% 49.23/49.40 tff(4072,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4073,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4074,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 49.23/49.40 tff(4075,plain,
% 49.23/49.40 ((~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4074, 2906, 1028])).
% 49.23/49.40 tff(4076,plain,
% 49.23/49.40 (m_counter_cell_v_carry_out(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4075, 4071])).
% 49.23/49.40 tff(4077,plain,
% 49.23/49.40 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4078,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4079,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | m_counter_cell_v_carry_in(c_bit1, s33)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4078, 4077])).
% 49.23/49.40 tff(4080,plain,
% 49.23/49.40 ($false),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4079, 2921, 4076, 4050])).
% 49.23/49.40 tff(4081,plain,(m_counter_cell_v_carry_out(c_bit0, s34) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s34))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.40 tff(4082,plain,
% 49.23/49.40 (m_counter_cell_v_carry_out(c_bit0, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4081, 4011, 4010])).
% 49.23/49.40 tff(4083,assumption,(~node4(c_bit0, s34)), introduced(assumption)).
% 49.23/49.40 tff(4084,assumption,(m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 49.23/49.40 tff(4085,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4086,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4087,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4086, 4085])).
% 49.23/49.40 tff(4088,plain,
% 49.23/49.40 ($false),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4087, 2836, 4084, 4083])).
% 49.23/49.40 tff(4089,plain,((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.40 tff(4090,plain,
% 49.23/49.40 (node4(c_bit0, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4089, 4082])).
% 49.23/49.40 tff(4091,plain,
% 49.23/49.40 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | m_counter_cell_v_carry_in(c_bit1, s34))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | m_counter_cell_v_carry_in(c_bit1, s34))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4092,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s34)) | m_counter_cell_v_carry_in(c_bit1, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4093,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | m_counter_cell_v_carry_in(c_bit1, s34)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4092, 4091])).
% 49.23/49.40 tff(4094,plain,
% 49.23/49.40 (m_counter_cell_v_carry_in(c_bit1, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4093, 2921, 4082])).
% 49.23/49.40 tff(4095,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4096,plain,
% 49.23/49.40 (((~node1(c_bit1, s34)) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4097,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s34)) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4096])).
% 49.23/49.40 tff(4098,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s34)) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4097, 4095])).
% 49.23/49.40 tff(4099,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s34)) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4100,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34) | (~node1(c_bit1, s34))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4099, 4098])).
% 49.23/49.40 tff(4101,plain,
% 49.23/49.40 ((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4100, 55, 4011])).
% 49.23/49.40 tff(4102,plain,
% 49.23/49.40 (m_counter_cell_v_value(c_bit1, s34)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4101, 4094])).
% 49.23/49.40 tff(4103,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4104,plain,
% 49.23/49.40 ((node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | (~m_counter_cell_v_value(c_bit1, s34))) <=> ((~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4105,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34))))),
% 49.23/49.40 inference(monotonicity,[status(thm)],[4104])).
% 49.23/49.40 tff(4106,plain,
% 49.23/49.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | (~m_counter_cell_v_value(c_bit1, s34)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)))),
% 49.23/49.40 inference(transitivity,[status(thm)],[4105, 4103])).
% 49.23/49.40 tff(4107,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s33) | (~node3(c_bit1, s33, s34)) | (~m_counter_cell_v_value(c_bit1, s34)))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4108,plain,
% 49.23/49.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33) | (~node3(c_bit1, s33, s34))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 49.23/49.40 tff(4109,plain,
% 49.23/49.40 ((~m_counter_cell_v_value(c_bit1, s34)) | node2(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4108, 130, 4031])).
% 49.23/49.40 tff(4110,plain,
% 49.23/49.40 (node2(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4109, 4102])).
% 49.23/49.40 tff(4111,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s33) | m_counter_cell_v_value(c_bit1, s33) | (~node2(c_bit1, s33)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s33) | m_counter_cell_v_value(c_bit1, s33) | (~node2(c_bit1, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4112,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s33) | m_counter_cell_v_value(c_bit1, s33) | (~node2(c_bit1, s33)))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4113,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s33) | m_counter_cell_v_value(c_bit1, s33) | (~node2(c_bit1, s33))),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4112, 4111])).
% 49.23/49.40 tff(4114,plain,
% 49.23/49.40 (m_counter_cell_v_carry_in(c_bit1, s33) | (~node2(c_bit1, s33))),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4113, 3024, 4010])).
% 49.23/49.40 tff(4115,plain,
% 49.23/49.40 (m_counter_cell_v_carry_in(c_bit1, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4114, 4110])).
% 49.23/49.40 tff(4116,assumption,(~m_counter_cell_v_carry_out(c_bit0, s33)), introduced(assumption)).
% 49.23/49.40 tff(4117,plain,
% 49.23/49.40 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4118,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_carry_out(c_bit0, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4119,plain,
% 49.23/49.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 49.23/49.40 tff(4120,plain,
% 49.23/49.40 ($false),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4119, 2851, 4116, 4040])).
% 49.23/49.40 tff(4121,plain,(m_counter_cell_v_carry_out(c_bit0, s33) | (~m_counter_cell_v_carry_in(c_bit1, s33))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.40 tff(4122,plain,
% 49.23/49.40 (m_counter_cell_v_carry_out(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4121, 4115])).
% 49.23/49.40 tff(4123,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | node4(c_bit0, s33))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | node4(c_bit0, s33))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.40 tff(4124,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s33)) | node4(c_bit0, s33))),
% 49.23/49.40 inference(quant_inst,[status(thm)],[])).
% 49.23/49.40 tff(4125,plain,
% 49.23/49.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s33)) | node4(c_bit0, s33)),
% 49.23/49.40 inference(modus_ponens,[status(thm)],[4124, 4123])).
% 49.23/49.40 tff(4126,plain,
% 49.23/49.40 (node4(c_bit0, s33)),
% 49.23/49.40 inference(unit_resolution,[status(thm)],[4125, 2836, 4122])).
% 49.23/49.40 tff(4127,assumption,(node4(c_bit0, s33)), introduced(assumption)).
% 49.23/49.40 tff(4128,assumption,(~m_counter_cell_v_value(c_bit0, s33)), introduced(assumption)).
% 49.23/49.40 tff(4129,plain,
% 49.23/49.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s33) | (~node4(c_bit0, s33)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s33) | (~node4(c_bit0, s33)))),
% 49.23/49.40 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4130,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s33) | (~node4(c_bit0, s33)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4131,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s33) | (~node4(c_bit0, s33))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4130, 4129])).
% 49.23/49.41 tff(4132,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4131, 2823, 4128, 4127])).
% 49.23/49.41 tff(4133,plain,(m_counter_cell_v_value(c_bit0, s33) | (~node4(c_bit0, s33))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4134,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit0, s33)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4133, 4126])).
% 49.23/49.41 tff(4135,plain,
% 49.23/49.41 (~node2(c_bit0, s33)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[1032, 4134])).
% 49.23/49.41 tff(4136,plain,
% 49.23/49.41 (~m_counter_cell_v_value(c_bit0, s34)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[1051, 4135])).
% 49.23/49.41 tff(4137,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4138,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4139,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s34) | (~node4(c_bit0, s34))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 49.23/49.41 tff(4140,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4139, 2823, 4136, 4090])).
% 49.23/49.41 tff(4141,plain,((~node1(c_bit1, s34)) | m_counter_cell_v_value(c_bit1, s33)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4142,plain,
% 49.23/49.41 (~node1(c_bit1, s34)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4141, 4009])).
% 49.23/49.41 tff(4143,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4144,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4145,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4144, 4143])).
% 49.23/49.41 tff(4146,plain,
% 49.23/49.41 (node3(c_bit1, s34, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4145, 21, 1071])).
% 49.23/49.41 tff(4147,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4148,plain,
% 49.23/49.41 ((node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35)) <=> (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4149,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35))))),
% 49.23/49.41 inference(monotonicity,[status(thm)],[4148])).
% 49.23/49.41 tff(4150,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)))),
% 49.23/49.41 inference(transitivity,[status(thm)],[4149, 4147])).
% 49.23/49.41 tff(4151,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s34) | (~node3(c_bit1, s34, s35)) | m_counter_cell_v_value(c_bit1, s35))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4152,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34) | (~node3(c_bit1, s34, s35))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 49.23/49.41 tff(4153,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4152, 84, 4146])).
% 49.23/49.41 tff(4154,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit1, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4153, 4142])).
% 49.23/49.41 tff(4155,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4156,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4157,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4156, 4155])).
% 49.23/49.41 tff(4158,plain,
% 49.23/49.41 ((~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4157, 2906, 1087])).
% 49.23/49.41 tff(4159,plain,
% 49.23/49.41 (m_counter_cell_v_carry_out(c_bit0, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4158, 1083])).
% 49.23/49.41 tff(4160,plain,
% 49.23/49.41 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4161,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4162,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s35)) | m_counter_cell_v_carry_in(c_bit1, s35)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 49.23/49.41 tff(4163,plain,
% 49.23/49.41 (m_counter_cell_v_carry_in(c_bit1, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4162, 2921, 4159])).
% 49.23/49.41 tff(4164,assumption,(m_counter_cell_v_value(c_bit1, s35)), introduced(assumption)).
% 49.23/49.41 tff(4165,assumption,(node2(c_bit1, s35)), introduced(assumption)).
% 49.23/49.41 tff(4166,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4167,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4168,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4167, 4166])).
% 49.23/49.41 tff(4169,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4168, 104, 4165, 4164, 4163])).
% 49.23/49.41 tff(4170,plain,((~node2(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4171,plain,
% 49.23/49.41 (~node2(c_bit1, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4170, 4154])).
% 49.23/49.41 tff(4172,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4173,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4174,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 49.23/49.41 tff(4175,plain,
% 49.23/49.41 (node3(c_bit1, s35, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4174, 21, 1099])).
% 49.23/49.41 tff(4176,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4177,plain,
% 49.23/49.41 ((node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36))) <=> ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4178,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36))))),
% 49.23/49.41 inference(monotonicity,[status(thm)],[4177])).
% 49.23/49.41 tff(4179,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)))),
% 49.23/49.41 inference(transitivity,[status(thm)],[4178, 4176])).
% 49.23/49.41 tff(4180,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s35) | (~node3(c_bit1, s35, s36)) | (~m_counter_cell_v_value(c_bit1, s36)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4181,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4180, 4179])).
% 49.23/49.41 tff(4182,plain,
% 49.23/49.41 ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4181, 130, 4175])).
% 49.23/49.41 tff(4183,plain,
% 49.23/49.41 (~m_counter_cell_v_value(c_bit1, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4182, 4171])).
% 49.23/49.41 tff(4184,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4185,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4186,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s36) | (~node4(c_bit0, s36))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 49.23/49.41 tff(4187,plain,
% 49.23/49.41 (~node4(c_bit0, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4186, 2823, 1111])).
% 49.23/49.41 tff(4188,assumption,(m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 49.23/49.41 tff(4189,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4190,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4191,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 49.23/49.41 tff(4192,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4191, 2836, 4188, 4187])).
% 49.23/49.41 tff(4193,plain,(~m_counter_cell_v_carry_out(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4194,assumption,(m_counter_cell_v_carry_in(c_bit1, s36)), introduced(assumption)).
% 49.23/49.41 tff(4195,assumption,(~m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 49.23/49.41 tff(4196,plain,
% 49.23/49.41 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4197,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4198,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4197, 4196])).
% 49.23/49.41 tff(4199,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4198, 2851, 4195, 4194])).
% 49.23/49.41 tff(4200,plain,((~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4201,plain,
% 49.23/49.41 (~m_counter_cell_v_carry_in(c_bit1, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4200, 4193])).
% 49.23/49.41 tff(4202,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4203,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4204,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4203, 4202])).
% 49.23/49.41 tff(4205,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4204, 3024, 4201])).
% 49.23/49.41 tff(4206,plain,
% 49.23/49.41 (~node2(c_bit1, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4205, 4183])).
% 49.23/49.41 tff(4207,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4208,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4209,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 49.23/49.41 tff(4210,plain,
% 49.23/49.41 (node3(c_bit1, s36, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4209, 21, 1130])).
% 49.23/49.41 tff(4211,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4212,plain,
% 49.23/49.41 ((node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37))) <=> ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4213,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37))))),
% 49.23/49.41 inference(monotonicity,[status(thm)],[4212])).
% 49.23/49.41 tff(4214,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)))),
% 49.23/49.41 inference(transitivity,[status(thm)],[4213, 4211])).
% 49.23/49.41 tff(4215,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s36) | (~node3(c_bit1, s36, s37)) | (~m_counter_cell_v_value(c_bit1, s37)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4216,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 49.23/49.41 tff(4217,plain,
% 49.23/49.41 ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4216, 130, 4210])).
% 49.23/49.41 tff(4218,plain,
% 49.23/49.41 (~m_counter_cell_v_value(c_bit1, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4217, 4206])).
% 49.23/49.41 tff(4219,assumption,(~m_counter_cell_v_value(c_bit1, s37)), introduced(assumption)).
% 49.23/49.41 tff(4220,assumption,(node1(c_bit1, s37)), introduced(assumption)).
% 49.23/49.41 tff(4221,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4222,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4223,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4222, 4221])).
% 49.23/49.41 tff(4224,plain,
% 49.23/49.41 ((~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4223, 2906, 1146])).
% 49.23/49.41 tff(4225,plain,
% 49.23/49.41 (m_counter_cell_v_carry_out(c_bit0, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4224, 1142])).
% 49.23/49.41 tff(4226,plain,
% 49.23/49.41 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4227,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4228,plain,
% 49.23/49.41 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s37)) | m_counter_cell_v_carry_in(c_bit1, s37)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 49.23/49.41 tff(4229,plain,
% 49.23/49.41 (m_counter_cell_v_carry_in(c_bit1, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4228, 2921, 4225])).
% 49.23/49.41 tff(4230,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4231,plain,
% 49.23/49.41 (((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4232,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))))),
% 49.23/49.41 inference(monotonicity,[status(thm)],[4231])).
% 49.23/49.41 tff(4233,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)))),
% 49.23/49.41 inference(transitivity,[status(thm)],[4232, 4230])).
% 49.23/49.41 tff(4234,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4235,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 49.23/49.41 tff(4236,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4235, 55, 4229, 4220, 4219])).
% 49.23/49.41 tff(4237,plain,((~node1(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4238,plain,
% 49.23/49.41 (~node1(c_bit1, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4237, 4218])).
% 49.23/49.41 tff(4239,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4240,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4241,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38)),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4240, 4239])).
% 49.23/49.41 tff(4242,plain,
% 49.23/49.41 (node3(c_bit1, s37, s38)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4241, 21, 1158])).
% 49.23/49.41 tff(4243,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4244,plain,
% 49.23/49.41 ((node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38)) <=> (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4245,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38))))),
% 49.23/49.41 inference(monotonicity,[status(thm)],[4244])).
% 49.23/49.41 tff(4246,plain,
% 49.23/49.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)))),
% 49.23/49.41 inference(transitivity,[status(thm)],[4245, 4243])).
% 49.23/49.41 tff(4247,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s37) | (~node3(c_bit1, s37, s38)) | m_counter_cell_v_value(c_bit1, s38))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4248,plain,
% 49.23/49.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37) | (~node3(c_bit1, s37, s38))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4247, 4246])).
% 49.23/49.41 tff(4249,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4248, 84, 4242])).
% 49.23/49.41 tff(4250,plain,
% 49.23/49.41 (m_counter_cell_v_value(c_bit1, s38)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4249, 4238])).
% 49.23/49.41 tff(4251,assumption,(m_counter_cell_v_carry_in(c_bit1, s38)), introduced(assumption)).
% 49.23/49.41 tff(4252,assumption,(node4(c_bit0, s38)), introduced(assumption)).
% 49.23/49.41 tff(4253,assumption,(~m_counter_cell_v_value(c_bit0, s38)), introduced(assumption)).
% 49.23/49.41 tff(4254,plain,
% 49.23/49.41 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))),
% 49.23/49.41 inference(rewrite,[status(thm)],[])).
% 49.23/49.41 tff(4255,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38)))),
% 49.23/49.41 inference(quant_inst,[status(thm)],[])).
% 49.23/49.41 tff(4256,plain,
% 49.23/49.41 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38))),
% 49.23/49.41 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 49.23/49.41 tff(4257,plain,
% 49.23/49.41 ($false),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4256, 2823, 4253, 4252])).
% 49.23/49.41 tff(4258,plain,(m_counter_cell_v_value(c_bit0, s38) | (~node4(c_bit0, s38))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.41 tff(4259,plain,
% 49.23/49.41 (~node4(c_bit0, s38)),
% 49.23/49.41 inference(unit_resolution,[status(thm)],[4258, 1170])).
% 49.23/49.41 tff(4260,assumption,(~node4(c_bit0, s38)), introduced(assumption)).
% 49.23/49.42 tff(4261,assumption,(m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 49.23/49.42 tff(4262,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4263,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4264,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4263, 4262])).
% 49.23/49.42 tff(4265,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4264, 2836, 4261, 4260])).
% 49.23/49.42 tff(4266,plain,((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4267,plain,
% 49.23/49.42 (~m_counter_cell_v_carry_out(c_bit0, s38)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4266, 4259])).
% 49.23/49.42 tff(4268,plain,
% 49.23/49.42 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4269,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4270,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4269, 4268])).
% 49.23/49.42 tff(4271,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4270, 2851, 4267, 4251])).
% 49.23/49.42 tff(4272,plain,(~m_counter_cell_v_carry_in(c_bit1, s38)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4273,assumption,(m_counter_cell_v_value(c_bit1, s38)), introduced(assumption)).
% 49.23/49.42 tff(4274,assumption,(node1(c_bit1, s38)), introduced(assumption)).
% 49.23/49.42 tff(4275,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4276,plain,
% 49.23/49.42 (((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38))) <=> (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4277,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4276])).
% 49.23/49.42 tff(4278,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4277, 4275])).
% 49.23/49.42 tff(4279,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s38)) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4280,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 49.23/49.42 tff(4281,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4280, 3095, 4274, 4273, 4272])).
% 49.23/49.42 tff(4282,plain,((~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4283,plain,
% 49.23/49.42 (~node1(c_bit1, s38)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4282, 4250])).
% 49.23/49.42 tff(4284,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4285,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4286,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4285, 4284])).
% 49.23/49.42 tff(4287,plain,
% 49.23/49.42 (node3(c_bit1, s38, s39)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4286, 21, 1189])).
% 49.23/49.42 tff(4288,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4289,plain,
% 49.23/49.42 ((node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39)) <=> (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4290,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4289])).
% 49.23/49.42 tff(4291,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4290, 4288])).
% 49.23/49.42 tff(4292,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s38) | (~node3(c_bit1, s38, s39)) | m_counter_cell_v_value(c_bit1, s39))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4293,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4292, 4291])).
% 49.23/49.42 tff(4294,plain,
% 49.23/49.42 (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4293, 84, 4287])).
% 49.23/49.42 tff(4295,plain,
% 49.23/49.42 (m_counter_cell_v_value(c_bit1, s39)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4294, 4283])).
% 49.23/49.42 tff(4296,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4297,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4298,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4297, 4296])).
% 49.23/49.42 tff(4299,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4298, 104, 4295, 2926, 2925])).
% 49.23/49.42 tff(4300,plain,(~node2(c_bit1, s39)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4301,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4302,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4303,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 49.23/49.42 tff(4304,plain,
% 49.23/49.42 (node3(c_bit1, s39, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4303, 21, 1217])).
% 49.23/49.42 tff(4305,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4306,plain,
% 49.23/49.42 ((node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40))) <=> ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4307,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4306])).
% 49.23/49.42 tff(4308,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4307, 4305])).
% 49.23/49.42 tff(4309,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s39) | (~node3(c_bit1, s39, s40)) | (~m_counter_cell_v_value(c_bit1, s40)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4310,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 49.23/49.42 tff(4311,plain,
% 49.23/49.42 ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4310, 130, 4304])).
% 49.23/49.42 tff(4312,plain,
% 49.23/49.42 (~m_counter_cell_v_value(c_bit1, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4311, 4300])).
% 49.23/49.42 tff(4313,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4314,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4315,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4314, 4313])).
% 49.23/49.42 tff(4316,plain,
% 49.23/49.42 (~node4(c_bit0, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4315, 2823, 1229])).
% 49.23/49.42 tff(4317,assumption,(m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 49.23/49.42 tff(4318,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4319,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4320,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4319, 4318])).
% 49.23/49.42 tff(4321,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4320, 2836, 4317, 4316])).
% 49.23/49.42 tff(4322,plain,(~m_counter_cell_v_carry_out(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4323,assumption,(m_counter_cell_v_carry_in(c_bit1, s40)), introduced(assumption)).
% 49.23/49.42 tff(4324,assumption,(~m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 49.23/49.42 tff(4325,plain,
% 49.23/49.42 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4326,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4327,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 49.23/49.42 tff(4328,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4327, 2851, 4324, 4323])).
% 49.23/49.42 tff(4329,plain,(m_counter_cell_v_carry_out(c_bit0, s40) | (~m_counter_cell_v_carry_in(c_bit1, s40))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4330,plain,
% 49.23/49.42 (~m_counter_cell_v_carry_in(c_bit1, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4329, 4322])).
% 49.23/49.42 tff(4331,assumption,(~m_counter_cell_v_value(c_bit1, s40)), introduced(assumption)).
% 49.23/49.42 tff(4332,assumption,(node2(c_bit1, s40)), introduced(assumption)).
% 49.23/49.42 tff(4333,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4334,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4335,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 49.23/49.42 tff(4336,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4335, 3024, 4332, 4331, 4330])).
% 49.23/49.42 tff(4337,plain,(m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4338,plain,
% 49.23/49.42 (~node2(c_bit1, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4337, 4312])).
% 49.23/49.42 tff(4339,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4340,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4341,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 49.23/49.42 tff(4342,plain,
% 49.23/49.42 (node3(c_bit1, s40, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4341, 21, 1248])).
% 49.23/49.42 tff(4343,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4344,plain,
% 49.23/49.42 ((node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41))) <=> ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4345,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4344])).
% 49.23/49.42 tff(4346,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4345, 4343])).
% 49.23/49.42 tff(4347,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s40) | (~node3(c_bit1, s40, s41)) | (~m_counter_cell_v_value(c_bit1, s41)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4348,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40) | (~node3(c_bit1, s40, s41))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4347, 4346])).
% 49.23/49.42 tff(4349,plain,
% 49.23/49.42 ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4348, 130, 4342])).
% 49.23/49.42 tff(4350,plain,
% 49.23/49.42 (~m_counter_cell_v_value(c_bit1, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4349, 4338])).
% 49.23/49.42 tff(4351,assumption,(node1(c_bit1, s41)), introduced(assumption)).
% 49.23/49.42 tff(4352,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4353,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4354,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4353, 4352])).
% 49.23/49.42 tff(4355,plain,
% 49.23/49.42 ((~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4354, 2906, 1264])).
% 49.23/49.42 tff(4356,plain,
% 49.23/49.42 (m_counter_cell_v_carry_out(c_bit0, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4355, 1260])).
% 49.23/49.42 tff(4357,plain,
% 49.23/49.42 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4358,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4359,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s41)) | m_counter_cell_v_carry_in(c_bit1, s41)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4358, 4357])).
% 49.23/49.42 tff(4360,plain,
% 49.23/49.42 (m_counter_cell_v_carry_in(c_bit1, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4359, 2921, 4356])).
% 49.23/49.42 tff(4361,assumption,(~m_counter_cell_v_value(c_bit1, s41)), introduced(assumption)).
% 49.23/49.42 tff(4362,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4363,plain,
% 49.23/49.42 (((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4364,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4363])).
% 49.23/49.42 tff(4365,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4364, 4362])).
% 49.23/49.42 tff(4366,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s41)) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4367,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 49.23/49.42 tff(4368,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4367, 55, 4361, 4360, 4351])).
% 49.23/49.42 tff(4369,plain,((~node1(c_bit1, s41)) | m_counter_cell_v_value(c_bit1, s41)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4370,plain,
% 49.23/49.42 (~node1(c_bit1, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4369, 4350])).
% 49.23/49.42 tff(4371,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4372,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4373,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 49.23/49.42 tff(4374,plain,
% 49.23/49.42 (node3(c_bit1, s41, s42)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4373, 21, 1276])).
% 49.23/49.42 tff(4375,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4376,plain,
% 49.23/49.42 ((node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42)) <=> (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4377,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42))))),
% 49.23/49.42 inference(monotonicity,[status(thm)],[4376])).
% 49.23/49.42 tff(4378,plain,
% 49.23/49.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)))),
% 49.23/49.42 inference(transitivity,[status(thm)],[4377, 4375])).
% 49.23/49.42 tff(4379,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s41) | (~node3(c_bit1, s41, s42)) | m_counter_cell_v_value(c_bit1, s42))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4380,plain,
% 49.23/49.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4379, 4378])).
% 49.23/49.42 tff(4381,plain,
% 49.23/49.42 (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4380, 84, 4374])).
% 49.23/49.42 tff(4382,plain,
% 49.23/49.42 (m_counter_cell_v_value(c_bit1, s42)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4381, 4370])).
% 49.23/49.42 tff(4383,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4384,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42)))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4385,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s42) | (~node4(c_bit0, s42))),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 49.23/49.42 tff(4386,plain,
% 49.23/49.42 (~node4(c_bit0, s42)),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4385, 2823, 1288])).
% 49.23/49.42 tff(4387,assumption,(m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 49.23/49.42 tff(4388,plain,
% 49.23/49.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4389,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4390,plain,
% 49.23/49.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42)),
% 49.23/49.42 inference(modus_ponens,[status(thm)],[4389, 4388])).
% 49.23/49.42 tff(4391,plain,
% 49.23/49.42 ($false),
% 49.23/49.42 inference(unit_resolution,[status(thm)],[4390, 2836, 4387, 4386])).
% 49.23/49.42 tff(4392,plain,(~m_counter_cell_v_carry_out(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.42 tff(4393,plain,
% 49.23/49.42 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))),
% 49.23/49.42 inference(rewrite,[status(thm)],[])).
% 49.23/49.42 tff(4394,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42))),
% 49.23/49.42 inference(quant_inst,[status(thm)],[])).
% 49.23/49.42 tff(4395,plain,
% 49.23/49.42 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4394, 4393])).
% 49.23/49.43 tff(4396,plain,
% 49.23/49.43 (~m_counter_cell_v_carry_in(c_bit1, s42)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4395, 2851, 4392])).
% 49.23/49.43 tff(4397,assumption,(node1(c_bit1, s42)), introduced(assumption)).
% 49.23/49.43 tff(4398,assumption,(m_counter_cell_v_value(c_bit1, s42)), introduced(assumption)).
% 49.23/49.43 tff(4399,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4400,plain,
% 49.23/49.43 (((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42))) <=> (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4401,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4400])).
% 49.23/49.43 tff(4402,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4401, 4399])).
% 49.23/49.43 tff(4403,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4404,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4403, 4402])).
% 49.23/49.43 tff(4405,plain,
% 49.23/49.43 ($false),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4404, 3095, 4398, 4397, 4396])).
% 49.23/49.43 tff(4406,plain,((~node1(c_bit1, s42)) | (~m_counter_cell_v_value(c_bit1, s42))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.43 tff(4407,plain,
% 49.23/49.43 (~node1(c_bit1, s42)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4406, 4382])).
% 49.23/49.43 tff(4408,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4409,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4410,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4409, 4408])).
% 49.23/49.43 tff(4411,plain,
% 49.23/49.43 (node3(c_bit1, s42, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4410, 21, 1307])).
% 49.23/49.43 tff(4412,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4413,plain,
% 49.23/49.43 ((node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43)) <=> (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4414,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4413])).
% 49.23/49.43 tff(4415,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4414, 4412])).
% 49.23/49.43 tff(4416,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s42) | (~node3(c_bit1, s42, s43)) | m_counter_cell_v_value(c_bit1, s43))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4417,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 49.23/49.43 tff(4418,plain,
% 49.23/49.43 (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4417, 84, 4411])).
% 49.23/49.43 tff(4419,plain,
% 49.23/49.43 (m_counter_cell_v_value(c_bit1, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4418, 4407])).
% 49.23/49.43 tff(4420,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4421,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4422,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4421, 4420])).
% 49.23/49.43 tff(4423,plain,
% 49.23/49.43 ((~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4422, 2906, 1323])).
% 49.23/49.43 tff(4424,plain,
% 49.23/49.43 (m_counter_cell_v_carry_out(c_bit0, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4423, 1319])).
% 49.23/49.43 tff(4425,plain,
% 49.23/49.43 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4426,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4427,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s43)) | m_counter_cell_v_carry_in(c_bit1, s43)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 49.23/49.43 tff(4428,plain,
% 49.23/49.43 (m_counter_cell_v_carry_in(c_bit1, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4427, 2921, 4424])).
% 49.23/49.43 tff(4429,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4430,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4431,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4430, 4429])).
% 49.23/49.43 tff(4432,plain,
% 49.23/49.43 ((~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4431, 104, 4428])).
% 49.23/49.43 tff(4433,plain,
% 49.23/49.43 (~node2(c_bit1, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4432, 4419])).
% 49.23/49.43 tff(4434,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4435,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4436,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 49.23/49.43 tff(4437,plain,
% 49.23/49.43 (node3(c_bit1, s43, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4436, 21, 1335])).
% 49.23/49.43 tff(4438,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4439,plain,
% 49.23/49.43 ((node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44))) <=> ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4440,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4439])).
% 49.23/49.43 tff(4441,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4440, 4438])).
% 49.23/49.43 tff(4442,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4443,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4442, 4441])).
% 49.23/49.43 tff(4444,plain,
% 49.23/49.43 ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4443, 130, 4437])).
% 49.23/49.43 tff(4445,plain,
% 49.23/49.43 (~m_counter_cell_v_value(c_bit1, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4444, 4433])).
% 49.23/49.43 tff(4446,assumption,(node2(c_bit1, s44)), introduced(assumption)).
% 49.23/49.43 tff(4447,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4448,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4449,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s44) | (~node4(c_bit0, s44))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 49.23/49.43 tff(4450,plain,
% 49.23/49.43 (~node4(c_bit0, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4449, 2823, 1347])).
% 49.23/49.43 tff(4451,assumption,(m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 49.23/49.43 tff(4452,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4453,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4454,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4453, 4452])).
% 49.23/49.43 tff(4455,plain,
% 49.23/49.43 ($false),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4454, 2836, 4451, 4450])).
% 49.23/49.43 tff(4456,plain,(~m_counter_cell_v_carry_out(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.43 tff(4457,assumption,(m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 49.23/49.43 tff(4458,assumption,(~m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 49.23/49.43 tff(4459,plain,
% 49.23/49.43 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4460,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4461,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4460, 4459])).
% 49.23/49.43 tff(4462,plain,
% 49.23/49.43 ($false),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4461, 2851, 4458, 4457])).
% 49.23/49.43 tff(4463,plain,(m_counter_cell_v_carry_out(c_bit0, s44) | (~m_counter_cell_v_carry_in(c_bit1, s44))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.43 tff(4464,plain,
% 49.23/49.43 (~m_counter_cell_v_carry_in(c_bit1, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4463, 4456])).
% 49.23/49.43 tff(4465,assumption,(~m_counter_cell_v_value(c_bit1, s44)), introduced(assumption)).
% 49.23/49.43 tff(4466,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4467,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4468,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4467, 4466])).
% 49.23/49.43 tff(4469,plain,
% 49.23/49.43 ($false),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4468, 3024, 4465, 4464, 4446])).
% 49.23/49.43 tff(4470,plain,((~node2(c_bit1, s44)) | m_counter_cell_v_value(c_bit1, s44)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.43 tff(4471,plain,
% 49.23/49.43 (~node2(c_bit1, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4470, 4445])).
% 49.23/49.43 tff(4472,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4473,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4474,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4473, 4472])).
% 49.23/49.43 tff(4475,plain,
% 49.23/49.43 (node3(c_bit1, s44, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4474, 21, 1366])).
% 49.23/49.43 tff(4476,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4477,plain,
% 49.23/49.43 ((node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45))) <=> ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4478,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4477])).
% 49.23/49.43 tff(4479,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4478, 4476])).
% 49.23/49.43 tff(4480,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s44) | (~node3(c_bit1, s44, s45)) | (~m_counter_cell_v_value(c_bit1, s45)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4481,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44) | (~node3(c_bit1, s44, s45))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 49.23/49.43 tff(4482,plain,
% 49.23/49.43 ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4481, 130, 4475])).
% 49.23/49.43 tff(4483,plain,
% 49.23/49.43 (~m_counter_cell_v_value(c_bit1, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4482, 4471])).
% 49.23/49.43 tff(4484,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4485,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4486,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4485, 4484])).
% 49.23/49.43 tff(4487,plain,
% 49.23/49.43 ((~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4486, 2906, 1380])).
% 49.23/49.43 tff(4488,plain,
% 49.23/49.43 (m_counter_cell_v_carry_out(c_bit0, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4487, 1378])).
% 49.23/49.43 tff(4489,plain,
% 49.23/49.43 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4490,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4491,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s45)) | m_counter_cell_v_carry_in(c_bit1, s45)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 49.23/49.43 tff(4492,plain,
% 49.23/49.43 (m_counter_cell_v_carry_in(c_bit1, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4491, 2921, 4488])).
% 49.23/49.43 tff(4493,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4494,plain,
% 49.23/49.43 (((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4495,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4494])).
% 49.23/49.43 tff(4496,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4495, 4493])).
% 49.23/49.43 tff(4497,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s45)) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4498,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s45)) | m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 49.23/49.43 tff(4499,plain,
% 49.23/49.43 (m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4498, 55, 4492])).
% 49.23/49.43 tff(4500,plain,
% 49.23/49.43 (~node1(c_bit1, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4499, 4483])).
% 49.23/49.43 tff(4501,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4502,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4503,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 49.23/49.43 tff(4504,plain,
% 49.23/49.43 (node3(c_bit1, s45, s46)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4503, 21, 1392])).
% 49.23/49.43 tff(4505,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4506,plain,
% 49.23/49.43 ((node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46)) <=> (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4507,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46))))),
% 49.23/49.43 inference(monotonicity,[status(thm)],[4506])).
% 49.23/49.43 tff(4508,plain,
% 49.23/49.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)))),
% 49.23/49.43 inference(transitivity,[status(thm)],[4507, 4505])).
% 49.23/49.43 tff(4509,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s45) | (~node3(c_bit1, s45, s46)) | m_counter_cell_v_value(c_bit1, s46))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4510,plain,
% 49.23/49.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45) | (~node3(c_bit1, s45, s46))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4509, 4508])).
% 49.23/49.43 tff(4511,plain,
% 49.23/49.43 (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4510, 84, 4504])).
% 49.23/49.43 tff(4512,plain,
% 49.23/49.43 (m_counter_cell_v_value(c_bit1, s46)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4511, 4500])).
% 49.23/49.43 tff(4513,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4514,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46)))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4515,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s46) | (~node4(c_bit0, s46))),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 49.23/49.43 tff(4516,plain,
% 49.23/49.43 (~node4(c_bit0, s46)),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4515, 2823, 1404])).
% 49.23/49.43 tff(4517,assumption,(m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 49.23/49.43 tff(4518,plain,
% 49.23/49.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4519,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.43 tff(4520,plain,
% 49.23/49.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46)),
% 49.23/49.43 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 49.23/49.43 tff(4521,plain,
% 49.23/49.43 ($false),
% 49.23/49.43 inference(unit_resolution,[status(thm)],[4520, 2836, 4517, 4516])).
% 49.23/49.43 tff(4522,plain,(~m_counter_cell_v_carry_out(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.43 tff(4523,plain,
% 49.23/49.43 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))),
% 49.23/49.43 inference(rewrite,[status(thm)],[])).
% 49.23/49.43 tff(4524,plain,
% 49.23/49.43 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46))),
% 49.23/49.43 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4525,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 49.23/49.44 tff(4526,plain,
% 49.23/49.44 (~m_counter_cell_v_carry_in(c_bit1, s46)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4525, 2851, 4522])).
% 49.23/49.44 tff(4527,assumption,(node1(c_bit1, s46)), introduced(assumption)).
% 49.23/49.44 tff(4528,assumption,(m_counter_cell_v_value(c_bit1, s46)), introduced(assumption)).
% 49.23/49.44 tff(4529,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4530,plain,
% 49.23/49.44 (((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46))) <=> (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4531,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4530])).
% 49.23/49.44 tff(4532,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4531, 4529])).
% 49.23/49.44 tff(4533,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4534,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4533, 4532])).
% 49.23/49.44 tff(4535,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4534, 3095, 4528, 4527, 4526])).
% 49.23/49.44 tff(4536,plain,((~node1(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4537,plain,
% 49.23/49.44 (~node1(c_bit1, s46)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4536, 4512])).
% 49.23/49.44 tff(4538,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4539,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4540,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4539, 4538])).
% 49.23/49.44 tff(4541,plain,
% 49.23/49.44 (node3(c_bit1, s46, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4540, 21, 1423])).
% 49.23/49.44 tff(4542,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4543,plain,
% 49.23/49.44 ((node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47)) <=> (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4544,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4543])).
% 49.23/49.44 tff(4545,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4544, 4542])).
% 49.23/49.44 tff(4546,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s46) | (~node3(c_bit1, s46, s47)) | m_counter_cell_v_value(c_bit1, s47))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4547,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46) | (~node3(c_bit1, s46, s47))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4546, 4545])).
% 49.23/49.44 tff(4548,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4547, 84, 4541])).
% 49.23/49.44 tff(4549,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4548, 4537])).
% 49.23/49.44 tff(4550,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4551,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4552,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4551, 4550])).
% 49.23/49.44 tff(4553,plain,
% 49.23/49.44 ((~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4552, 2906, 1439])).
% 49.23/49.44 tff(4554,plain,
% 49.23/49.44 (m_counter_cell_v_carry_out(c_bit0, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4553, 1435])).
% 49.23/49.44 tff(4555,plain,
% 49.23/49.44 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4556,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4557,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s47)) | m_counter_cell_v_carry_in(c_bit1, s47)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 49.23/49.44 tff(4558,plain,
% 49.23/49.44 (m_counter_cell_v_carry_in(c_bit1, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4557, 2921, 4554])).
% 49.23/49.44 tff(4559,assumption,(m_counter_cell_v_value(c_bit1, s47)), introduced(assumption)).
% 49.23/49.44 tff(4560,assumption,(node2(c_bit1, s47)), introduced(assumption)).
% 49.23/49.44 tff(4561,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4562,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4563,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4562, 4561])).
% 49.23/49.44 tff(4564,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4563, 104, 4560, 4559, 4558])).
% 49.23/49.44 tff(4565,plain,((~node2(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4566,plain,
% 49.23/49.44 (~node2(c_bit1, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4565, 4549])).
% 49.23/49.44 tff(4567,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4568,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4569,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 49.23/49.44 tff(4570,plain,
% 49.23/49.44 (node3(c_bit1, s47, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4569, 21, 1451])).
% 49.23/49.44 tff(4571,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4572,plain,
% 49.23/49.44 ((node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48))) <=> ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4573,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4572])).
% 49.23/49.44 tff(4574,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4573, 4571])).
% 49.23/49.44 tff(4575,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s47) | (~node3(c_bit1, s47, s48)) | (~m_counter_cell_v_value(c_bit1, s48)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4576,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47) | (~node3(c_bit1, s47, s48))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4575, 4574])).
% 49.23/49.44 tff(4577,plain,
% 49.23/49.44 ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4576, 130, 4570])).
% 49.23/49.44 tff(4578,plain,
% 49.23/49.44 (~m_counter_cell_v_value(c_bit1, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4577, 4566])).
% 49.23/49.44 tff(4579,assumption,(m_counter_cell_v_carry_in(c_bit1, s48)), introduced(assumption)).
% 49.23/49.44 tff(4580,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4581,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4582,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s48) | (~node4(c_bit0, s48))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4581, 4580])).
% 49.23/49.44 tff(4583,plain,
% 49.23/49.44 (~node4(c_bit0, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4582, 2823, 1463])).
% 49.23/49.44 tff(4584,assumption,(~node4(c_bit0, s48)), introduced(assumption)).
% 49.23/49.44 tff(4585,assumption,(m_counter_cell_v_carry_out(c_bit0, s48)), introduced(assumption)).
% 49.23/49.44 tff(4586,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4587,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4588,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 49.23/49.44 tff(4589,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4588, 2836, 4585, 4584])).
% 49.23/49.44 tff(4590,plain,((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4591,plain,
% 49.23/49.44 (~m_counter_cell_v_carry_out(c_bit0, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4590, 4583])).
% 49.23/49.44 tff(4592,plain,
% 49.23/49.44 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4593,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4594,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4593, 4592])).
% 49.23/49.44 tff(4595,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4594, 2851, 4591, 4579])).
% 49.23/49.44 tff(4596,plain,(~m_counter_cell_v_carry_in(c_bit1, s48)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4597,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4598,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4599,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4598, 4597])).
% 49.23/49.44 tff(4600,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4599, 3024, 4596])).
% 49.23/49.44 tff(4601,plain,
% 49.23/49.44 (~node2(c_bit1, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4600, 4578])).
% 49.23/49.44 tff(4602,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4603,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4604,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4603, 4602])).
% 49.23/49.44 tff(4605,plain,
% 49.23/49.44 (node3(c_bit1, s48, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4604, 21, 1482])).
% 49.23/49.44 tff(4606,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4607,plain,
% 49.23/49.44 ((node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49))) <=> ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4608,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4607])).
% 49.23/49.44 tff(4609,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4608, 4606])).
% 49.23/49.44 tff(4610,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s48) | (~node3(c_bit1, s48, s49)) | (~m_counter_cell_v_value(c_bit1, s49)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4611,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48) | (~node3(c_bit1, s48, s49))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 49.23/49.44 tff(4612,plain,
% 49.23/49.44 ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4611, 130, 4605])).
% 49.23/49.44 tff(4613,plain,
% 49.23/49.44 (~m_counter_cell_v_value(c_bit1, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4612, 4601])).
% 49.23/49.44 tff(4614,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4615,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4616,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4615, 4614])).
% 49.23/49.44 tff(4617,plain,
% 49.23/49.44 ((~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4616, 2906, 1498])).
% 49.23/49.44 tff(4618,plain,
% 49.23/49.44 (m_counter_cell_v_carry_out(c_bit0, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4617, 1494])).
% 49.23/49.44 tff(4619,assumption,(~m_counter_cell_v_carry_in(c_bit1, s49)), introduced(assumption)).
% 49.23/49.44 tff(4620,assumption,(m_counter_cell_v_carry_out(c_bit0, s49)), introduced(assumption)).
% 49.23/49.44 tff(4621,plain,
% 49.23/49.44 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4622,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4623,plain,
% 49.23/49.44 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 49.23/49.44 tff(4624,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4623, 2921, 4620, 4619])).
% 49.23/49.44 tff(4625,plain,((~m_counter_cell_v_carry_out(c_bit0, s49)) | m_counter_cell_v_carry_in(c_bit1, s49)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4626,plain,
% 49.23/49.44 (m_counter_cell_v_carry_in(c_bit1, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4625, 4618])).
% 49.23/49.44 tff(4627,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4628,plain,
% 49.23/49.44 (((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4629,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4628])).
% 49.23/49.44 tff(4630,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4629, 4627])).
% 49.23/49.44 tff(4631,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4632,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 49.23/49.44 tff(4633,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4632, 55, 4626])).
% 49.23/49.44 tff(4634,plain,
% 49.23/49.44 (~node1(c_bit1, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4633, 4613])).
% 49.23/49.44 tff(4635,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4636,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4637,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4636, 4635])).
% 49.23/49.44 tff(4638,plain,
% 49.23/49.44 (node3(c_bit1, s49, s50)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4637, 21, 1510])).
% 49.23/49.44 tff(4639,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4640,plain,
% 49.23/49.44 ((node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50)) <=> (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4641,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50))))),
% 49.23/49.44 inference(monotonicity,[status(thm)],[4640])).
% 49.23/49.44 tff(4642,plain,
% 49.23/49.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)))),
% 49.23/49.44 inference(transitivity,[status(thm)],[4641, 4639])).
% 49.23/49.44 tff(4643,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s49) | (~node3(c_bit1, s49, s50)) | m_counter_cell_v_value(c_bit1, s50))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4644,plain,
% 49.23/49.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49) | (~node3(c_bit1, s49, s50))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4643, 4642])).
% 49.23/49.44 tff(4645,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4644, 84, 4638])).
% 49.23/49.44 tff(4646,plain,
% 49.23/49.44 (m_counter_cell_v_value(c_bit1, s50)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4645, 4634])).
% 49.23/49.44 tff(4647,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4648,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50)))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4649,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s50) | (~node4(c_bit0, s50))),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 49.23/49.44 tff(4650,plain,
% 49.23/49.44 (~node4(c_bit0, s50)),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4649, 2823, 1522])).
% 49.23/49.44 tff(4651,assumption,(m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 49.23/49.44 tff(4652,plain,
% 49.23/49.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))),
% 49.23/49.44 inference(rewrite,[status(thm)],[])).
% 49.23/49.44 tff(4653,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50))),
% 49.23/49.44 inference(quant_inst,[status(thm)],[])).
% 49.23/49.44 tff(4654,plain,
% 49.23/49.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)),
% 49.23/49.44 inference(modus_ponens,[status(thm)],[4653, 4652])).
% 49.23/49.44 tff(4655,plain,
% 49.23/49.44 ($false),
% 49.23/49.44 inference(unit_resolution,[status(thm)],[4654, 2836, 4651, 4650])).
% 49.23/49.44 tff(4656,plain,(~m_counter_cell_v_carry_out(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.44 tff(4657,assumption,(m_counter_cell_v_carry_in(c_bit1, s50)), introduced(assumption)).
% 49.23/49.45 tff(4658,assumption,(~m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 49.23/49.45 tff(4659,plain,
% 49.23/49.45 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4660,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4661,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4660, 4659])).
% 49.23/49.45 tff(4662,plain,
% 49.23/49.45 ($false),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4661, 2851, 4658, 4657])).
% 49.23/49.45 tff(4663,plain,((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.45 tff(4664,plain,
% 49.23/49.45 (~m_counter_cell_v_carry_in(c_bit1, s50)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4663, 4656])).
% 49.23/49.45 tff(4665,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4666,plain,
% 49.23/49.45 (((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50))) <=> (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4667,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4666])).
% 49.23/49.45 tff(4668,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4667, 4665])).
% 49.23/49.45 tff(4669,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4670,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4669, 4668])).
% 49.23/49.45 tff(4671,plain,
% 49.23/49.45 ((~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4670, 3095, 4664])).
% 49.23/49.45 tff(4672,plain,
% 49.23/49.45 (~node1(c_bit1, s50)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4671, 4646])).
% 49.23/49.45 tff(4673,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4674,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4675,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 49.23/49.45 tff(4676,plain,
% 49.23/49.45 (node3(c_bit1, s50, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4675, 21, 1541])).
% 49.23/49.45 tff(4677,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4678,plain,
% 49.23/49.45 ((node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51)) <=> (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4679,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4678])).
% 49.23/49.45 tff(4680,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4679, 4677])).
% 49.23/49.45 tff(4681,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s50) | (~node3(c_bit1, s50, s51)) | m_counter_cell_v_value(c_bit1, s51))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4682,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50) | (~node3(c_bit1, s50, s51))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 49.23/49.45 tff(4683,plain,
% 49.23/49.45 (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4682, 84, 4676])).
% 49.23/49.45 tff(4684,plain,
% 49.23/49.45 (m_counter_cell_v_value(c_bit1, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4683, 4672])).
% 49.23/49.45 tff(4685,assumption,(node2(c_bit1, s51)), introduced(assumption)).
% 49.23/49.45 tff(4686,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4687,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4688,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4687, 4686])).
% 49.23/49.45 tff(4689,plain,
% 49.23/49.45 ((~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4688, 2906, 1557])).
% 49.23/49.45 tff(4690,plain,
% 49.23/49.45 (m_counter_cell_v_carry_out(c_bit0, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4689, 1553])).
% 49.23/49.45 tff(4691,plain,
% 49.23/49.45 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4692,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4693,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s51)) | m_counter_cell_v_carry_in(c_bit1, s51)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4692, 4691])).
% 49.23/49.45 tff(4694,plain,
% 49.23/49.45 (m_counter_cell_v_carry_in(c_bit1, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4693, 2921, 4690])).
% 49.23/49.45 tff(4695,assumption,(m_counter_cell_v_value(c_bit1, s51)), introduced(assumption)).
% 49.23/49.45 tff(4696,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4697,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4698,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 49.23/49.45 tff(4699,plain,
% 49.23/49.45 ($false),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4698, 104, 4695, 4694, 4685])).
% 49.23/49.45 tff(4700,plain,((~node2(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.45 tff(4701,plain,
% 49.23/49.45 (~node2(c_bit1, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4700, 4684])).
% 49.23/49.45 tff(4702,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4703,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4704,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4703, 4702])).
% 49.23/49.45 tff(4705,plain,
% 49.23/49.45 (node3(c_bit1, s51, s52)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4704, 21, 1569])).
% 49.23/49.45 tff(4706,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4707,plain,
% 49.23/49.45 ((node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52))) <=> ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4708,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4707])).
% 49.23/49.45 tff(4709,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4708, 4706])).
% 49.23/49.45 tff(4710,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s51) | (~node3(c_bit1, s51, s52)) | (~m_counter_cell_v_value(c_bit1, s52)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4711,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 49.23/49.45 tff(4712,plain,
% 49.23/49.45 ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4711, 130, 4705])).
% 49.23/49.45 tff(4713,plain,
% 49.23/49.45 (~m_counter_cell_v_value(c_bit1, s52)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4712, 4701])).
% 49.23/49.45 tff(4714,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4715,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4716,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4715, 4714])).
% 49.23/49.45 tff(4717,plain,
% 49.23/49.45 ($false),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4716, 3024, 4713, 2896, 2895])).
% 49.23/49.45 tff(4718,plain,(~node2(c_bit1, s52)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.45 tff(4719,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4720,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4721,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4720, 4719])).
% 49.23/49.45 tff(4722,plain,
% 49.23/49.45 (node3(c_bit1, s52, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4721, 21, 1600])).
% 49.23/49.45 tff(4723,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4724,plain,
% 49.23/49.45 ((node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53))) <=> ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4725,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4724])).
% 49.23/49.45 tff(4726,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4725, 4723])).
% 49.23/49.45 tff(4727,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s52) | (~node3(c_bit1, s52, s53)) | (~m_counter_cell_v_value(c_bit1, s53)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4728,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4727, 4726])).
% 49.23/49.45 tff(4729,plain,
% 49.23/49.45 ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4728, 130, 4722])).
% 49.23/49.45 tff(4730,plain,
% 49.23/49.45 (~m_counter_cell_v_value(c_bit1, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4729, 4718])).
% 49.23/49.45 tff(4731,assumption,(~m_counter_cell_v_value(c_bit1, s53)), introduced(assumption)).
% 49.23/49.45 tff(4732,assumption,(node1(c_bit1, s53)), introduced(assumption)).
% 49.23/49.45 tff(4733,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4734,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4735,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 49.23/49.45 tff(4736,plain,
% 49.23/49.45 ((~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4735, 2906, 1616])).
% 49.23/49.45 tff(4737,plain,
% 49.23/49.45 (m_counter_cell_v_carry_out(c_bit0, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4736, 1612])).
% 49.23/49.45 tff(4738,plain,
% 49.23/49.45 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4739,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4740,plain,
% 49.23/49.45 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s53)) | m_counter_cell_v_carry_in(c_bit1, s53)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4739, 4738])).
% 49.23/49.45 tff(4741,plain,
% 49.23/49.45 (m_counter_cell_v_carry_in(c_bit1, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4740, 2921, 4737])).
% 49.23/49.45 tff(4742,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4743,plain,
% 49.23/49.45 (((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4744,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4743])).
% 49.23/49.45 tff(4745,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4744, 4742])).
% 49.23/49.45 tff(4746,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4747,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 49.23/49.45 tff(4748,plain,
% 49.23/49.45 ($false),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4747, 55, 4741, 4732, 4731])).
% 49.23/49.45 tff(4749,plain,(m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))), inference(lemma,lemma(discharge,[]))).
% 49.23/49.45 tff(4750,plain,
% 49.23/49.45 (~node1(c_bit1, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4749, 4730])).
% 49.23/49.45 tff(4751,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4752,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4753,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54)),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4752, 4751])).
% 49.23/49.45 tff(4754,plain,
% 49.23/49.45 (node3(c_bit1, s53, s54)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4753, 21, 1628])).
% 49.23/49.45 tff(4755,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4756,plain,
% 49.23/49.45 ((node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54)) <=> (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4757,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54))))),
% 49.23/49.45 inference(monotonicity,[status(thm)],[4756])).
% 49.23/49.45 tff(4758,plain,
% 49.23/49.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)))),
% 49.23/49.45 inference(transitivity,[status(thm)],[4757, 4755])).
% 49.23/49.45 tff(4759,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s53) | (~node3(c_bit1, s53, s54)) | m_counter_cell_v_value(c_bit1, s54))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4760,plain,
% 49.23/49.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 49.23/49.45 tff(4761,plain,
% 49.23/49.45 (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4760, 84, 4754])).
% 49.23/49.45 tff(4762,plain,
% 49.23/49.45 (m_counter_cell_v_value(c_bit1, s54)),
% 49.23/49.45 inference(unit_resolution,[status(thm)],[4761, 4750])).
% 49.23/49.45 tff(4763,plain,
% 49.23/49.45 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))),
% 49.23/49.45 inference(rewrite,[status(thm)],[])).
% 49.23/49.45 tff(4764,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54)))),
% 49.23/49.45 inference(quant_inst,[status(thm)],[])).
% 49.23/49.45 tff(4765,plain,
% 49.23/49.45 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s54) | (~node4(c_bit0, s54))),
% 49.23/49.45 inference(modus_ponens,[status(thm)],[4764, 4763])).
% 49.23/49.45 tff(4766,plain,
% 49.23/49.45 (~node4(c_bit0, s54)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4765, 2823, 1640])).
% 49.23/49.46 tff(4767,assumption,(m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 49.23/49.46 tff(4768,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4769,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4770,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54)),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4769, 4768])).
% 49.23/49.46 tff(4771,plain,
% 49.23/49.46 ($false),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4770, 2836, 4767, 4766])).
% 49.23/49.46 tff(4772,plain,(~m_counter_cell_v_carry_out(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.46 tff(4773,assumption,(m_counter_cell_v_carry_in(c_bit1, s54)), introduced(assumption)).
% 49.23/49.46 tff(4774,assumption,(~m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 49.23/49.46 tff(4775,plain,
% 49.23/49.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4776,plain,
% 49.23/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4777,plain,
% 49.23/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54)),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4776, 4775])).
% 49.23/49.46 tff(4778,plain,
% 49.23/49.46 ($false),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4777, 2851, 4774, 4773])).
% 49.23/49.46 tff(4779,plain,((~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 49.23/49.46 tff(4780,plain,
% 49.23/49.46 (~m_counter_cell_v_carry_in(c_bit1, s54)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4779, 4772])).
% 49.23/49.46 tff(4781,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4782,plain,
% 49.23/49.46 (((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54))) <=> (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4783,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))))),
% 49.23/49.46 inference(monotonicity,[status(thm)],[4782])).
% 49.23/49.46 tff(4784,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54)))),
% 49.23/49.46 inference(transitivity,[status(thm)],[4783, 4781])).
% 49.23/49.46 tff(4785,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4786,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 49.23/49.46 tff(4787,plain,
% 49.23/49.46 ((~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4786, 3095, 4780])).
% 49.23/49.46 tff(4788,plain,
% 49.23/49.46 (~node1(c_bit1, s54)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4787, 4762])).
% 49.23/49.46 tff(4789,plain,
% 49.23/49.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4790,plain,
% 49.23/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4791,plain,
% 49.23/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55)),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 49.23/49.46 tff(4792,plain,
% 49.23/49.46 (node3(c_bit1, s54, s55)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4791, 21, 1659])).
% 49.23/49.46 tff(4793,plain,
% 49.23/49.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4794,plain,
% 49.23/49.46 ((node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55)) <=> (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4795,plain,
% 49.23/49.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55))))),
% 49.23/49.46 inference(monotonicity,[status(thm)],[4794])).
% 49.23/49.46 tff(4796,plain,
% 49.23/49.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)))),
% 49.23/49.46 inference(transitivity,[status(thm)],[4795, 4793])).
% 49.23/49.46 tff(4797,plain,
% 49.23/49.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s54) | (~node3(c_bit1, s54, s55)) | m_counter_cell_v_value(c_bit1, s55))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4798,plain,
% 49.23/49.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55))),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4797, 4796])).
% 49.23/49.46 tff(4799,plain,
% 49.23/49.46 (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4798, 84, 4792])).
% 49.23/49.46 tff(4800,plain,
% 49.23/49.46 (m_counter_cell_v_value(c_bit1, s55)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4799, 4788])).
% 49.23/49.46 tff(4801,assumption,(node2(c_bit1, s55)), introduced(assumption)).
% 49.23/49.46 tff(4802,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4803,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4804,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 49.23/49.46 tff(4805,plain,
% 49.23/49.46 ((~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4804, 2906, 1675])).
% 49.23/49.46 tff(4806,plain,
% 49.23/49.46 (m_counter_cell_v_carry_out(c_bit0, s55)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4805, 1671])).
% 49.23/49.46 tff(4807,plain,
% 49.23/49.46 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4808,plain,
% 49.23/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4809,plain,
% 49.23/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s55)) | m_counter_cell_v_carry_in(c_bit1, s55)),
% 49.23/49.46 inference(modus_ponens,[status(thm)],[4808, 4807])).
% 49.23/49.46 tff(4810,plain,
% 49.23/49.46 (m_counter_cell_v_carry_in(c_bit1, s55)),
% 49.23/49.46 inference(unit_resolution,[status(thm)],[4809, 2921, 4806])).
% 49.23/49.46 tff(4811,assumption,(m_counter_cell_v_value(c_bit1, s55)), introduced(assumption)).
% 49.23/49.46 tff(4812,plain,
% 49.23/49.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))),
% 49.23/49.46 inference(rewrite,[status(thm)],[])).
% 49.23/49.46 tff(4813,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))),
% 49.23/49.46 inference(quant_inst,[status(thm)],[])).
% 49.23/49.46 tff(4814,plain,
% 49.23/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4813, 4812])).
% 49.30/49.46 tff(4815,plain,
% 49.30/49.46 ($false),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4814, 104, 4811, 4810, 4801])).
% 49.30/49.46 tff(4816,plain,((~node2(c_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.46 tff(4817,plain,
% 49.30/49.46 (~node2(c_bit1, s55)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4816, 4800])).
% 49.30/49.46 tff(4818,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4819,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4820,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4819, 4818])).
% 49.30/49.46 tff(4821,plain,
% 49.30/49.46 (node3(c_bit1, s55, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4820, 21, 1687])).
% 49.30/49.46 tff(4822,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4823,plain,
% 49.30/49.46 ((node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56))) <=> ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4824,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56))))),
% 49.30/49.46 inference(monotonicity,[status(thm)],[4823])).
% 49.30/49.46 tff(4825,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 49.30/49.46 inference(transitivity,[status(thm)],[4824, 4822])).
% 49.30/49.46 tff(4826,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | (~m_counter_cell_v_value(c_bit1, s56)))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4827,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4826, 4825])).
% 49.30/49.46 tff(4828,plain,
% 49.30/49.46 ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4827, 130, 4821])).
% 49.30/49.46 tff(4829,plain,
% 49.30/49.46 (~m_counter_cell_v_value(c_bit1, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4828, 4817])).
% 49.30/49.46 tff(4830,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4831,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56)))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4832,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s56) | (~node4(c_bit0, s56))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4831, 4830])).
% 49.30/49.46 tff(4833,plain,
% 49.30/49.46 (~node4(c_bit0, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4832, 2823, 1699])).
% 49.30/49.46 tff(4834,assumption,(m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 49.30/49.46 tff(4835,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4836,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4837,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4836, 4835])).
% 49.30/49.46 tff(4838,plain,
% 49.30/49.46 ($false),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4837, 2836, 4834, 4833])).
% 49.30/49.46 tff(4839,plain,(~m_counter_cell_v_carry_out(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.46 tff(4840,assumption,(m_counter_cell_v_carry_in(c_bit1, s56)), introduced(assumption)).
% 49.30/49.46 tff(4841,assumption,(~m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 49.30/49.46 tff(4842,plain,
% 49.30/49.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4843,plain,
% 49.30/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4844,plain,
% 49.30/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4843, 4842])).
% 49.30/49.46 tff(4845,plain,
% 49.30/49.46 ($false),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4844, 2851, 4841, 4840])).
% 49.30/49.46 tff(4846,plain,((~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.46 tff(4847,plain,
% 49.30/49.46 (~m_counter_cell_v_carry_in(c_bit1, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4846, 4839])).
% 49.30/49.46 tff(4848,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4849,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4850,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4849, 4848])).
% 49.30/49.46 tff(4851,plain,
% 49.30/49.46 (m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4850, 3024, 4847])).
% 49.30/49.46 tff(4852,plain,
% 49.30/49.46 (~node2(c_bit1, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4851, 4829])).
% 49.30/49.46 tff(4853,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4854,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4855,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 49.30/49.46 tff(4856,plain,
% 49.30/49.46 (node3(c_bit1, s56, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4855, 21, 1718])).
% 49.30/49.46 tff(4857,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4858,plain,
% 49.30/49.46 ((node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57))) <=> ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4859,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57))))),
% 49.30/49.46 inference(monotonicity,[status(thm)],[4858])).
% 49.30/49.46 tff(4860,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)))),
% 49.30/49.46 inference(transitivity,[status(thm)],[4859, 4857])).
% 49.30/49.46 tff(4861,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s56) | (~node3(c_bit1, s56, s57)) | (~m_counter_cell_v_value(c_bit1, s57)))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4862,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4861, 4860])).
% 49.30/49.46 tff(4863,plain,
% 49.30/49.46 ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4862, 130, 4856])).
% 49.30/49.46 tff(4864,plain,
% 49.30/49.46 (~m_counter_cell_v_value(c_bit1, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4863, 4852])).
% 49.30/49.46 tff(4865,assumption,(node1(c_bit1, s57)), introduced(assumption)).
% 49.30/49.46 tff(4866,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4867,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4868,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4867, 4866])).
% 49.30/49.46 tff(4869,plain,
% 49.30/49.46 ((~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4868, 2906, 1734])).
% 49.30/49.46 tff(4870,plain,
% 49.30/49.46 (m_counter_cell_v_carry_out(c_bit0, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4869, 1730])).
% 49.30/49.46 tff(4871,plain,
% 49.30/49.46 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4872,plain,
% 49.30/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4873,plain,
% 49.30/49.46 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s57)) | m_counter_cell_v_carry_in(c_bit1, s57)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 49.30/49.46 tff(4874,plain,
% 49.30/49.46 (m_counter_cell_v_carry_in(c_bit1, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4873, 2921, 4870])).
% 49.30/49.46 tff(4875,assumption,(~m_counter_cell_v_value(c_bit1, s57)), introduced(assumption)).
% 49.30/49.46 tff(4876,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4877,plain,
% 49.30/49.46 (((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4878,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))))),
% 49.30/49.46 inference(monotonicity,[status(thm)],[4877])).
% 49.30/49.46 tff(4879,plain,
% 49.30/49.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57)))),
% 49.30/49.46 inference(transitivity,[status(thm)],[4878, 4876])).
% 49.30/49.46 tff(4880,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4881,plain,
% 49.30/49.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4880, 4879])).
% 49.30/49.46 tff(4882,plain,
% 49.30/49.46 ($false),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4881, 55, 4875, 4874, 4865])).
% 49.30/49.46 tff(4883,plain,(m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.46 tff(4884,plain,
% 49.30/49.46 (~node1(c_bit1, s57)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4883, 4864])).
% 49.30/49.46 tff(4885,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4886,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 49.30/49.46 inference(quant_inst,[status(thm)],[])).
% 49.30/49.46 tff(4887,plain,
% 49.30/49.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58)),
% 49.30/49.46 inference(modus_ponens,[status(thm)],[4886, 4885])).
% 49.30/49.46 tff(4888,plain,
% 49.30/49.46 (node3(c_bit1, s57, s58)),
% 49.30/49.46 inference(unit_resolution,[status(thm)],[4887, 21, 1746])).
% 49.30/49.46 tff(4889,plain,
% 49.30/49.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 49.30/49.46 inference(rewrite,[status(thm)],[])).
% 49.30/49.46 tff(4890,plain,
% 49.30/49.46 ((node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58)) <=> (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4891,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[4890])).
% 49.30/49.47 tff(4892,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)))),
% 49.30/49.47 inference(transitivity,[status(thm)],[4891, 4889])).
% 49.30/49.47 tff(4893,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s57) | (~node3(c_bit1, s57, s58)) | m_counter_cell_v_value(c_bit1, s58))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4894,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4893, 4892])).
% 49.30/49.47 tff(4895,plain,
% 49.30/49.47 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4894, 84, 4888])).
% 49.30/49.47 tff(4896,plain,
% 49.30/49.47 (m_counter_cell_v_value(c_bit1, s58)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4895, 4884])).
% 49.30/49.47 tff(4897,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4898,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4899,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s58) | (~node4(c_bit0, s58))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 49.30/49.47 tff(4900,plain,
% 49.30/49.47 (~node4(c_bit0, s58)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4899, 2823, 1758])).
% 49.30/49.47 tff(4901,assumption,(m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 49.30/49.47 tff(4902,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4903,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4904,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4903, 4902])).
% 49.30/49.47 tff(4905,plain,
% 49.30/49.47 ($false),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4904, 2836, 4901, 4900])).
% 49.30/49.47 tff(4906,plain,(~m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.47 tff(4907,assumption,(m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 49.30/49.47 tff(4908,assumption,(~m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 49.30/49.47 tff(4909,plain,
% 49.30/49.47 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4910,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4911,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4910, 4909])).
% 49.30/49.47 tff(4912,plain,
% 49.30/49.47 ($false),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4911, 2851, 4908, 4907])).
% 49.30/49.47 tff(4913,plain,((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.47 tff(4914,plain,
% 49.30/49.47 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4913, 4906])).
% 49.30/49.47 tff(4915,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4916,plain,
% 49.30/49.47 (((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58))) <=> (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4917,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[4916])).
% 49.30/49.47 tff(4918,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58)))),
% 49.30/49.47 inference(transitivity,[status(thm)],[4917, 4915])).
% 49.30/49.47 tff(4919,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4920,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4919, 4918])).
% 49.30/49.47 tff(4921,plain,
% 49.30/49.47 ((~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4920, 3095, 4914])).
% 49.30/49.47 tff(4922,plain,
% 49.30/49.47 (~node1(c_bit1, s58)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4921, 4896])).
% 49.30/49.47 tff(4923,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4924,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4925,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4924, 4923])).
% 49.30/49.47 tff(4926,plain,
% 49.30/49.47 (node3(c_bit1, s58, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4925, 21, 1777])).
% 49.30/49.47 tff(4927,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4928,plain,
% 49.30/49.47 ((node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59)) <=> (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4929,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[4928])).
% 49.30/49.47 tff(4930,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)))),
% 49.30/49.47 inference(transitivity,[status(thm)],[4929, 4927])).
% 49.30/49.47 tff(4931,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s58) | (~node3(c_bit1, s58, s59)) | m_counter_cell_v_value(c_bit1, s59))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4932,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58) | (~node3(c_bit1, s58, s59))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4931, 4930])).
% 49.30/49.47 tff(4933,plain,
% 49.30/49.47 (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4932, 84, 4926])).
% 49.30/49.47 tff(4934,plain,
% 49.30/49.47 (m_counter_cell_v_value(c_bit1, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4933, 4922])).
% 49.30/49.47 tff(4935,assumption,(node2(c_bit1, s59)), introduced(assumption)).
% 49.30/49.47 tff(4936,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4937,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4938,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 49.30/49.47 tff(4939,plain,
% 49.30/49.47 ((~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4938, 2906, 1793])).
% 49.30/49.47 tff(4940,plain,
% 49.30/49.47 (m_counter_cell_v_carry_out(c_bit0, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4939, 1789])).
% 49.30/49.47 tff(4941,plain,
% 49.30/49.47 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4942,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4943,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s59)) | m_counter_cell_v_carry_in(c_bit1, s59)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 49.30/49.47 tff(4944,plain,
% 49.30/49.47 (m_counter_cell_v_carry_in(c_bit1, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4943, 2921, 4940])).
% 49.30/49.47 tff(4945,assumption,(m_counter_cell_v_value(c_bit1, s59)), introduced(assumption)).
% 49.30/49.47 tff(4946,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4947,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4948,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4947, 4946])).
% 49.30/49.47 tff(4949,plain,
% 49.30/49.47 ($false),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4948, 104, 4945, 4944, 4935])).
% 49.30/49.47 tff(4950,plain,((~node2(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.47 tff(4951,plain,
% 49.30/49.47 (~node2(c_bit1, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4950, 4934])).
% 49.30/49.47 tff(4952,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit1, s59, s60))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit1, s59, s60))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4953,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit1, s59, s60))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4954,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit1, s59, s60)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4953, 4952])).
% 49.30/49.47 tff(4955,plain,
% 49.30/49.47 (node3(c_bit1, s59, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4954, 21, 1805])).
% 49.30/49.47 tff(4956,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4957,plain,
% 49.30/49.47 ((node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60))) <=> ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4958,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[4957])).
% 49.30/49.47 tff(4959,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 49.30/49.47 inference(transitivity,[status(thm)],[4958, 4956])).
% 49.30/49.47 tff(4960,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4961,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4960, 4959])).
% 49.30/49.47 tff(4962,plain,
% 49.30/49.47 ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4961, 130, 4955])).
% 49.30/49.47 tff(4963,plain,
% 49.30/49.47 (~m_counter_cell_v_value(c_bit1, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4962, 4951])).
% 49.30/49.47 tff(4964,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4965,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4966,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4965, 4964])).
% 49.30/49.47 tff(4967,plain,
% 49.30/49.47 (~node4(c_bit0, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4966, 2823, 1817])).
% 49.30/49.47 tff(4968,assumption,(m_counter_cell_v_carry_out(c_bit0, s60)), introduced(assumption)).
% 49.30/49.47 tff(4969,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4970,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4971,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4970, 4969])).
% 49.30/49.47 tff(4972,plain,
% 49.30/49.47 ($false),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4971, 2836, 4968, 4967])).
% 49.30/49.47 tff(4973,plain,(~m_counter_cell_v_carry_out(c_bit0, s60)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.47 tff(4974,plain,
% 49.30/49.47 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4975,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4976,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s60)) | m_counter_cell_v_carry_out(c_bit0, s60)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4975, 4974])).
% 49.30/49.47 tff(4977,plain,
% 49.30/49.47 (~m_counter_cell_v_carry_in(c_bit1, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4976, 2851, 4973])).
% 49.30/49.47 tff(4978,assumption,(node2(c_bit1, s60)), introduced(assumption)).
% 49.30/49.47 tff(4979,assumption,(~m_counter_cell_v_value(c_bit1, s60)), introduced(assumption)).
% 49.30/49.47 tff(4980,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4981,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4982,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4981, 4980])).
% 49.30/49.47 tff(4983,plain,
% 49.30/49.47 ($false),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4982, 3024, 4979, 4978, 4977])).
% 49.30/49.47 tff(4984,plain,((~node2(c_bit1, s60)) | m_counter_cell_v_value(c_bit1, s60)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.47 tff(4985,plain,
% 49.30/49.47 (~node2(c_bit1, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4984, 4963])).
% 49.30/49.47 tff(4986,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit1, s60, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit1, s60, s61))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4987,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit1, s60, s61))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4988,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit1, s60, s61)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 49.30/49.47 tff(4989,plain,
% 49.30/49.47 (node3(c_bit1, s60, s61)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4988, 21, 1836])).
% 49.30/49.47 tff(4990,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4991,plain,
% 49.30/49.47 ((node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61))) <=> ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(4992,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[4991])).
% 49.30/49.47 tff(4993,plain,
% 49.30/49.47 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 49.30/49.47 inference(transitivity,[status(thm)],[4992, 4990])).
% 49.30/49.47 tff(4994,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(4995,plain,
% 49.30/49.47 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61))),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[4994, 4993])).
% 49.30/49.47 tff(4996,plain,
% 49.30/49.47 ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4995, 130, 4989])).
% 49.30/49.47 tff(4997,plain,
% 49.30/49.47 (~m_counter_cell_v_value(c_bit1, s61)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[4996, 4985])).
% 49.30/49.47 tff(4998,assumption,(~m_counter_cell_v_value(c_bit1, s61)), introduced(assumption)).
% 49.30/49.47 tff(4999,assumption,(node1(c_bit1, s61)), introduced(assumption)).
% 49.30/49.47 tff(5000,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(5001,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(5002,plain,
% 49.30/49.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[5001, 5000])).
% 49.30/49.47 tff(5003,plain,
% 49.30/49.47 ((~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[5002, 2906, 1852])).
% 49.30/49.47 tff(5004,plain,
% 49.30/49.47 (m_counter_cell_v_carry_out(c_bit0, s61)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[5003, 1848])).
% 49.30/49.47 tff(5005,plain,
% 49.30/49.47 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(5006,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))),
% 49.30/49.47 inference(quant_inst,[status(thm)],[])).
% 49.30/49.47 tff(5007,plain,
% 49.30/49.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s61)) | m_counter_cell_v_carry_in(c_bit1, s61)),
% 49.30/49.47 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 49.30/49.47 tff(5008,plain,
% 49.30/49.47 (m_counter_cell_v_carry_in(c_bit1, s61)),
% 49.30/49.47 inference(unit_resolution,[status(thm)],[5007, 2921, 5004])).
% 49.30/49.47 tff(5009,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(5010,plain,
% 49.30/49.47 (((~node1(c_bit1, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 49.30/49.47 inference(rewrite,[status(thm)],[])).
% 49.30/49.47 tff(5011,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))))),
% 49.30/49.47 inference(monotonicity,[status(thm)],[5010])).
% 49.30/49.47 tff(5012,plain,
% 49.30/49.47 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5011, 5009])).
% 49.30/49.48 tff(5013,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5014,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5013, 5012])).
% 49.30/49.48 tff(5015,plain,
% 49.30/49.48 ($false),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5014, 55, 5008, 4999, 4998])).
% 49.30/49.48 tff(5016,plain,(m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.48 tff(5017,plain,
% 49.30/49.48 (~node1(c_bit1, s61)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5016, 4997])).
% 49.30/49.48 tff(5018,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit1, s61, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit1, s61, s62))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5019,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit1, s61, s62))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5020,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit1, s61, s62)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 49.30/49.48 tff(5021,plain,
% 49.30/49.48 (node3(c_bit1, s61, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5020, 21, 1864])).
% 49.30/49.48 tff(5022,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5023,plain,
% 49.30/49.48 ((node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62)) <=> (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5024,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5023])).
% 49.30/49.48 tff(5025,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5024, 5022])).
% 49.30/49.48 tff(5026,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5027,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5026, 5025])).
% 49.30/49.48 tff(5028,plain,
% 49.30/49.48 (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5027, 84, 5021])).
% 49.30/49.48 tff(5029,plain,
% 49.30/49.48 (m_counter_cell_v_value(c_bit1, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5028, 5017])).
% 49.30/49.48 tff(5030,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5031,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5032,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5031, 5030])).
% 49.30/49.48 tff(5033,plain,
% 49.30/49.48 (~node4(c_bit0, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5032, 2823, 1876])).
% 49.30/49.48 tff(5034,assumption,(m_counter_cell_v_carry_out(c_bit0, s62)), introduced(assumption)).
% 49.30/49.48 tff(5035,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5036,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5037,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 49.30/49.48 tff(5038,plain,
% 49.30/49.48 ($false),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5037, 2836, 5034, 5033])).
% 49.30/49.48 tff(5039,plain,(~m_counter_cell_v_carry_out(c_bit0, s62)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.48 tff(5040,assumption,(m_counter_cell_v_carry_in(c_bit1, s62)), introduced(assumption)).
% 49.30/49.48 tff(5041,assumption,(~m_counter_cell_v_carry_out(c_bit0, s62)), introduced(assumption)).
% 49.30/49.48 tff(5042,plain,
% 49.30/49.48 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5043,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5044,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit0, s62)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5043, 5042])).
% 49.30/49.48 tff(5045,plain,
% 49.30/49.48 ($false),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5044, 2851, 5041, 5040])).
% 49.30/49.48 tff(5046,plain,((~m_counter_cell_v_carry_in(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit0, s62)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.48 tff(5047,plain,
% 49.30/49.48 (~m_counter_cell_v_carry_in(c_bit1, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5046, 5039])).
% 49.30/49.48 tff(5048,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5049,plain,
% 49.30/49.48 (((~node1(c_bit1, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62))) <=> (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5050,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5049])).
% 49.30/49.48 tff(5051,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5050, 5048])).
% 49.30/49.48 tff(5052,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5053,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 49.30/49.48 tff(5054,plain,
% 49.30/49.48 ((~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62))),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5053, 3095, 5047])).
% 49.30/49.48 tff(5055,plain,
% 49.30/49.48 (~node1(c_bit1, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5054, 5029])).
% 49.30/49.48 tff(5056,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit1, s62, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit1, s62, s63))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5057,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit1, s62, s63))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5058,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit1, s62, s63)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5057, 5056])).
% 49.30/49.48 tff(5059,plain,
% 49.30/49.48 (node3(c_bit1, s62, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5058, 21, 1895])).
% 49.30/49.48 tff(5060,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5061,plain,
% 49.30/49.48 ((node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63)) <=> (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5062,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5061])).
% 49.30/49.48 tff(5063,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5062, 5060])).
% 49.30/49.48 tff(5064,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5065,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5064, 5063])).
% 49.30/49.48 tff(5066,plain,
% 49.30/49.48 (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5065, 84, 5059])).
% 49.30/49.48 tff(5067,plain,
% 49.30/49.48 (m_counter_cell_v_value(c_bit1, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5066, 5055])).
% 49.30/49.48 tff(5068,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5069,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5070,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5069, 5068])).
% 49.30/49.48 tff(5071,plain,
% 49.30/49.48 ((~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5070, 2906, 1911])).
% 49.30/49.48 tff(5072,plain,
% 49.30/49.48 (m_counter_cell_v_carry_out(c_bit0, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5071, 1907])).
% 49.30/49.48 tff(5073,plain,
% 49.30/49.48 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5074,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5075,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5074, 5073])).
% 49.30/49.48 tff(5076,plain,
% 49.30/49.48 (m_counter_cell_v_carry_in(c_bit1, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5075, 2921, 5072])).
% 49.30/49.48 tff(5077,assumption,(m_counter_cell_v_value(c_bit1, s63)), introduced(assumption)).
% 49.30/49.48 tff(5078,assumption,(node2(c_bit1, s63)), introduced(assumption)).
% 49.30/49.48 tff(5079,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5080,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5081,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5080, 5079])).
% 49.30/49.48 tff(5082,plain,
% 49.30/49.48 ($false),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5081, 104, 5078, 5077, 5076])).
% 49.30/49.48 tff(5083,plain,((~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.48 tff(5084,plain,
% 49.30/49.48 (~node2(c_bit1, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5083, 5067])).
% 49.30/49.48 tff(5085,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit1, s63, s64))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit1, s63, s64))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5086,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit1, s63, s64))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5087,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit1, s63, s64)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 49.30/49.48 tff(5088,plain,
% 49.30/49.48 (node3(c_bit1, s63, s64)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5087, 21, 1923])).
% 49.30/49.48 tff(5089,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5090,plain,
% 49.30/49.48 ((node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64))) <=> ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5091,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5090])).
% 49.30/49.48 tff(5092,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5091, 5089])).
% 49.30/49.48 tff(5093,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5094,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5093, 5092])).
% 49.30/49.48 tff(5095,plain,
% 49.30/49.48 ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5094, 130, 5088])).
% 49.30/49.48 tff(5096,plain,
% 49.30/49.48 (~m_counter_cell_v_value(c_bit1, s64)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5095, 5084])).
% 49.30/49.48 tff(5097,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5098,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5099,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5098, 5097])).
% 49.30/49.48 tff(5100,plain,
% 49.30/49.48 (~node2(c_bit1, s64)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5099, 3024, 5096, 2881])).
% 49.30/49.48 tff(5101,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit1, s64, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit1, s64, s65))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5102,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit1, s64, s65))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5103,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit1, s64, s65)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 49.30/49.48 tff(5104,plain,
% 49.30/49.48 (node3(c_bit1, s64, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5103, 21, 1954])).
% 49.30/49.48 tff(5105,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5106,plain,
% 49.30/49.48 ((node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65))) <=> ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5107,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5106])).
% 49.30/49.48 tff(5108,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5107, 5105])).
% 49.30/49.48 tff(5109,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5110,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5109, 5108])).
% 49.30/49.48 tff(5111,plain,
% 49.30/49.48 ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5110, 130, 5104])).
% 49.30/49.48 tff(5112,plain,
% 49.30/49.48 (~m_counter_cell_v_value(c_bit1, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5111, 5100])).
% 49.30/49.48 tff(5113,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5114,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5115,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5114, 5113])).
% 49.30/49.48 tff(5116,plain,
% 49.30/49.48 ((~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5115, 2906, 1970])).
% 49.30/49.48 tff(5117,plain,
% 49.30/49.48 (m_counter_cell_v_carry_out(c_bit0, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5116, 1966])).
% 49.30/49.48 tff(5118,plain,
% 49.30/49.48 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5119,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5120,plain,
% 49.30/49.48 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s65)) | m_counter_cell_v_carry_in(c_bit1, s65)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 49.30/49.48 tff(5121,plain,
% 49.30/49.48 (m_counter_cell_v_carry_in(c_bit1, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5120, 2921, 5117])).
% 49.30/49.48 tff(5122,assumption,(m_counter_cell_v_carry_in(c_bit1, s65)), introduced(assumption)).
% 49.30/49.48 tff(5123,assumption,(~m_counter_cell_v_value(c_bit1, s65)), introduced(assumption)).
% 49.30/49.48 tff(5124,assumption,(node1(c_bit1, s65)), introduced(assumption)).
% 49.30/49.48 tff(5125,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5126,plain,
% 49.30/49.48 (((~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5127,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))))),
% 49.30/49.48 inference(monotonicity,[status(thm)],[5126])).
% 49.30/49.48 tff(5128,plain,
% 49.30/49.48 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 49.30/49.48 inference(transitivity,[status(thm)],[5127, 5125])).
% 49.30/49.48 tff(5129,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5130,plain,
% 49.30/49.48 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5129, 5128])).
% 49.30/49.48 tff(5131,plain,
% 49.30/49.48 ($false),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5130, 55, 5124, 5123, 5122])).
% 49.30/49.48 tff(5132,plain,(m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.48 tff(5133,plain,
% 49.30/49.48 (m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5132, 5121])).
% 49.30/49.48 tff(5134,plain,
% 49.30/49.48 (~node1(c_bit1, s65)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5133, 5112])).
% 49.30/49.48 tff(5135,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit1, s65, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit1, s65, s66))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5136,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit1, s65, s66))),
% 49.30/49.48 inference(quant_inst,[status(thm)],[])).
% 49.30/49.48 tff(5137,plain,
% 49.30/49.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit1, s65, s66)),
% 49.30/49.48 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 49.30/49.48 tff(5138,plain,
% 49.30/49.48 (node3(c_bit1, s65, s66)),
% 49.30/49.48 inference(unit_resolution,[status(thm)],[5137, 21, 1982])).
% 49.30/49.48 tff(5139,plain,
% 49.30/49.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 49.30/49.48 inference(rewrite,[status(thm)],[])).
% 49.30/49.48 tff(5140,plain,
% 49.30/49.48 ((node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66)) <=> (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5141,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5140])).
% 49.30/49.49 tff(5142,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5141, 5139])).
% 49.30/49.49 tff(5143,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5144,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5143, 5142])).
% 49.30/49.49 tff(5145,plain,
% 49.30/49.49 (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5144, 84, 5138])).
% 49.30/49.49 tff(5146,plain,
% 49.30/49.49 (m_counter_cell_v_value(c_bit1, s66)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5145, 5134])).
% 49.30/49.49 tff(5147,assumption,(node1(c_bit1, s66)), introduced(assumption)).
% 49.30/49.49 tff(5148,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5149,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5150,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 49.30/49.49 tff(5151,plain,
% 49.30/49.49 (~node4(c_bit0, s66)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5150, 2823, 1994])).
% 49.30/49.49 tff(5152,assumption,(m_counter_cell_v_carry_out(c_bit0, s66)), introduced(assumption)).
% 49.30/49.49 tff(5153,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5154,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5155,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 49.30/49.49 tff(5156,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5155, 2836, 5152, 5151])).
% 49.30/49.49 tff(5157,plain,(~m_counter_cell_v_carry_out(c_bit0, s66)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5158,assumption,(m_counter_cell_v_carry_in(c_bit1, s66)), introduced(assumption)).
% 49.30/49.49 tff(5159,assumption,(~m_counter_cell_v_carry_out(c_bit0, s66)), introduced(assumption)).
% 49.30/49.49 tff(5160,plain,
% 49.30/49.49 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5161,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5162,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s66)) | m_counter_cell_v_carry_out(c_bit0, s66)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5161, 5160])).
% 49.30/49.49 tff(5163,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5162, 2851, 5159, 5158])).
% 49.30/49.49 tff(5164,plain,(m_counter_cell_v_carry_out(c_bit0, s66) | (~m_counter_cell_v_carry_in(c_bit1, s66))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5165,plain,
% 49.30/49.49 (~m_counter_cell_v_carry_in(c_bit1, s66)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5164, 5157])).
% 49.30/49.49 tff(5166,assumption,(m_counter_cell_v_value(c_bit1, s66)), introduced(assumption)).
% 49.30/49.49 tff(5167,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5168,plain,
% 49.30/49.49 (((~node1(c_bit1, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66))) <=> (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5169,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5168])).
% 49.30/49.49 tff(5170,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5169, 5167])).
% 49.30/49.49 tff(5171,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5172,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5171, 5170])).
% 49.30/49.49 tff(5173,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5172, 3095, 5166, 5165, 5147])).
% 49.30/49.49 tff(5174,plain,((~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5175,plain,
% 49.30/49.49 (~node1(c_bit1, s66)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5174, 5146])).
% 49.30/49.49 tff(5176,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit1, s66, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit1, s66, s67))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5177,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit1, s66, s67))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5178,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit1, s66, s67)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5177, 5176])).
% 49.30/49.49 tff(5179,plain,
% 49.30/49.49 (node3(c_bit1, s66, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5178, 21, 2013])).
% 49.30/49.49 tff(5180,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5181,plain,
% 49.30/49.49 ((node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67)) <=> (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5182,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5181])).
% 49.30/49.49 tff(5183,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5182, 5180])).
% 49.30/49.49 tff(5184,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5185,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5184, 5183])).
% 49.30/49.49 tff(5186,plain,
% 49.30/49.49 (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5185, 84, 5179])).
% 49.30/49.49 tff(5187,plain,
% 49.30/49.49 (m_counter_cell_v_value(c_bit1, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5186, 5175])).
% 49.30/49.49 tff(5188,assumption,(m_counter_cell_v_value(c_bit1, s67)), introduced(assumption)).
% 49.30/49.49 tff(5189,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5190,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5191,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 49.30/49.49 tff(5192,plain,
% 49.30/49.49 ((~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5191, 2906, 2029])).
% 49.30/49.49 tff(5193,plain,
% 49.30/49.49 (m_counter_cell_v_carry_out(c_bit0, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5192, 2025])).
% 49.30/49.49 tff(5194,plain,
% 49.30/49.49 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5195,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5196,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s67)) | m_counter_cell_v_carry_in(c_bit1, s67)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 49.30/49.49 tff(5197,plain,
% 49.30/49.49 (m_counter_cell_v_carry_in(c_bit1, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5196, 2921, 5193])).
% 49.30/49.49 tff(5198,assumption,(node2(c_bit1, s67)), introduced(assumption)).
% 49.30/49.49 tff(5199,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5200,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5201,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 49.30/49.49 tff(5202,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5201, 104, 5198, 5197, 5188])).
% 49.30/49.49 tff(5203,plain,((~node2(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5204,plain,
% 49.30/49.49 (~node2(c_bit1, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5203, 5187])).
% 49.30/49.49 tff(5205,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit1, s67, s68))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit1, s67, s68))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5206,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit1, s67, s68))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5207,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit1, s67, s68)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5206, 5205])).
% 49.30/49.49 tff(5208,plain,
% 49.30/49.49 (node3(c_bit1, s67, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5207, 21, 2041])).
% 49.30/49.49 tff(5209,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5210,plain,
% 49.30/49.49 ((node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68))) <=> ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5211,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5210])).
% 49.30/49.49 tff(5212,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5211, 5209])).
% 49.30/49.49 tff(5213,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5214,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5213, 5212])).
% 49.30/49.49 tff(5215,plain,
% 49.30/49.49 ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5214, 130, 5208])).
% 49.30/49.49 tff(5216,plain,
% 49.30/49.49 (~m_counter_cell_v_value(c_bit1, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5215, 5204])).
% 49.30/49.49 tff(5217,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5218,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5219,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5218, 5217])).
% 49.30/49.49 tff(5220,plain,
% 49.30/49.49 (~node4(c_bit0, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5219, 2823, 2053])).
% 49.30/49.49 tff(5221,assumption,(m_counter_cell_v_carry_out(c_bit0, s68)), introduced(assumption)).
% 49.30/49.49 tff(5222,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5223,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5224,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 49.30/49.49 tff(5225,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5224, 2836, 5221, 5220])).
% 49.30/49.49 tff(5226,plain,(~m_counter_cell_v_carry_out(c_bit0, s68)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5227,assumption,(m_counter_cell_v_carry_in(c_bit1, s68)), introduced(assumption)).
% 49.30/49.49 tff(5228,assumption,(~m_counter_cell_v_carry_out(c_bit0, s68)), introduced(assumption)).
% 49.30/49.49 tff(5229,plain,
% 49.30/49.49 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5230,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5231,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s68)) | m_counter_cell_v_carry_out(c_bit0, s68)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5230, 5229])).
% 49.30/49.49 tff(5232,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5231, 2851, 5228, 5227])).
% 49.30/49.49 tff(5233,plain,(m_counter_cell_v_carry_out(c_bit0, s68) | (~m_counter_cell_v_carry_in(c_bit1, s68))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5234,plain,
% 49.30/49.49 (~m_counter_cell_v_carry_in(c_bit1, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5233, 5226])).
% 49.30/49.49 tff(5235,assumption,(~m_counter_cell_v_value(c_bit1, s68)), introduced(assumption)).
% 49.30/49.49 tff(5236,assumption,(node2(c_bit1, s68)), introduced(assumption)).
% 49.30/49.49 tff(5237,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5238,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5239,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5238, 5237])).
% 49.30/49.49 tff(5240,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5239, 3024, 5236, 5235, 5234])).
% 49.30/49.49 tff(5241,plain,(m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5242,plain,
% 49.30/49.49 (~node2(c_bit1, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5241, 5216])).
% 49.30/49.49 tff(5243,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit1, s68, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit1, s68, s69))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5244,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit1, s68, s69))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5245,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit1, s68, s69)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5244, 5243])).
% 49.30/49.49 tff(5246,plain,
% 49.30/49.49 (node3(c_bit1, s68, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5245, 21, 2072])).
% 49.30/49.49 tff(5247,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5248,plain,
% 49.30/49.49 ((node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69))) <=> ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5249,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5248])).
% 49.30/49.49 tff(5250,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5249, 5247])).
% 49.30/49.49 tff(5251,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5252,plain,
% 49.30/49.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5251, 5250])).
% 49.30/49.49 tff(5253,plain,
% 49.30/49.49 ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5252, 130, 5246])).
% 49.30/49.49 tff(5254,plain,
% 49.30/49.49 (~m_counter_cell_v_value(c_bit1, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5253, 5242])).
% 49.30/49.49 tff(5255,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5256,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5257,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5256, 5255])).
% 49.30/49.49 tff(5258,plain,
% 49.30/49.49 ((~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5257, 2906, 2088])).
% 49.30/49.49 tff(5259,plain,
% 49.30/49.49 (m_counter_cell_v_carry_out(c_bit0, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5258, 2084])).
% 49.30/49.49 tff(5260,plain,
% 49.30/49.49 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5261,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5262,plain,
% 49.30/49.49 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s69)) | m_counter_cell_v_carry_in(c_bit1, s69)),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 49.30/49.49 tff(5263,plain,
% 49.30/49.49 (m_counter_cell_v_carry_in(c_bit1, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5262, 2921, 5259])).
% 49.30/49.49 tff(5264,assumption,(m_counter_cell_v_carry_in(c_bit1, s69)), introduced(assumption)).
% 49.30/49.49 tff(5265,assumption,(node1(c_bit1, s69)), introduced(assumption)).
% 49.30/49.49 tff(5266,assumption,(~m_counter_cell_v_value(c_bit1, s69)), introduced(assumption)).
% 49.30/49.49 tff(5267,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5268,plain,
% 49.30/49.49 (((~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 49.30/49.49 inference(rewrite,[status(thm)],[])).
% 49.30/49.49 tff(5269,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))))),
% 49.30/49.49 inference(monotonicity,[status(thm)],[5268])).
% 49.30/49.49 tff(5270,plain,
% 49.30/49.49 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 49.30/49.49 inference(transitivity,[status(thm)],[5269, 5267])).
% 49.30/49.49 tff(5271,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))),
% 49.30/49.49 inference(quant_inst,[status(thm)],[])).
% 49.30/49.49 tff(5272,plain,
% 49.30/49.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))),
% 49.30/49.49 inference(modus_ponens,[status(thm)],[5271, 5270])).
% 49.30/49.49 tff(5273,plain,
% 49.30/49.49 ($false),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5272, 55, 5266, 5265, 5264])).
% 49.30/49.49 tff(5274,plain,(m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69))), inference(lemma,lemma(discharge,[]))).
% 49.30/49.49 tff(5275,plain,
% 49.30/49.49 (m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5274, 5263])).
% 49.30/49.49 tff(5276,plain,
% 49.30/49.49 (~node1(c_bit1, s69)),
% 49.30/49.49 inference(unit_resolution,[status(thm)],[5275, 5254])).
% 49.30/49.49 tff(5277,plain,
% 49.30/49.49 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit1, s69, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit1, s69, s70))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5278,plain,
% 49.30/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit1, s69, s70))),
% 49.30/49.50 inference(quant_inst,[status(thm)],[])).
% 49.30/49.50 tff(5279,plain,
% 49.30/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit1, s69, s70)),
% 49.30/49.50 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 49.30/49.50 tff(5280,plain,
% 49.30/49.50 (node3(c_bit1, s69, s70)),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5279, 21, 2100])).
% 49.30/49.50 tff(5281,plain,
% 49.30/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5282,plain,
% 49.30/49.50 ((node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70)) <=> (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5283,plain,
% 49.30/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70))))),
% 49.30/49.50 inference(monotonicity,[status(thm)],[5282])).
% 49.30/49.50 tff(5284,plain,
% 49.30/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 49.30/49.50 inference(transitivity,[status(thm)],[5283, 5281])).
% 49.30/49.50 tff(5285,plain,
% 49.30/49.50 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))),
% 49.30/49.50 inference(quant_inst,[status(thm)],[])).
% 49.30/49.50 tff(5286,plain,
% 49.30/49.50 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70))),
% 49.30/49.50 inference(modus_ponens,[status(thm)],[5285, 5284])).
% 49.30/49.50 tff(5287,plain,
% 49.30/49.50 (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69)),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5286, 84, 5280])).
% 49.30/49.50 tff(5288,plain,
% 49.30/49.50 (m_counter_cell_v_value(c_bit1, s70)),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5287, 5276])).
% 49.30/49.50 tff(5289,plain,
% 49.30/49.50 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5290,plain,
% 49.30/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))),
% 49.30/49.50 inference(quant_inst,[status(thm)],[])).
% 49.30/49.50 tff(5291,plain,
% 49.30/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70))),
% 49.30/49.50 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 49.30/49.50 tff(5292,plain,
% 49.30/49.50 (~node4(c_bit0, s70)),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5291, 2823, 2112])).
% 49.30/49.50 tff(5293,assumption,(m_counter_cell_v_carry_out(c_bit0, s70)), introduced(assumption)).
% 49.30/49.50 tff(5294,plain,
% 49.30/49.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5295,plain,
% 49.30/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))),
% 49.30/49.50 inference(quant_inst,[status(thm)],[])).
% 49.30/49.50 tff(5296,plain,
% 49.30/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70)),
% 49.30/49.50 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 49.30/49.50 tff(5297,plain,
% 49.30/49.50 ($false),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5296, 2836, 5293, 5292])).
% 49.30/49.50 tff(5298,plain,(~m_counter_cell_v_carry_out(c_bit0, s70)), inference(lemma,lemma(discharge,[]))).
% 49.30/49.50 tff(5299,plain,
% 49.30/49.50 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5300,plain,
% 49.30/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))),
% 49.30/49.50 inference(quant_inst,[status(thm)],[])).
% 49.30/49.50 tff(5301,plain,
% 49.30/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70)),
% 49.30/49.50 inference(modus_ponens,[status(thm)],[5300, 5299])).
% 49.30/49.50 tff(5302,plain,
% 49.30/49.50 (~m_counter_cell_v_carry_in(c_bit1, s70)),
% 49.30/49.50 inference(unit_resolution,[status(thm)],[5301, 2851, 5298])).
% 49.30/49.50 tff(5303,assumption,(node1(c_bit1, s70)), introduced(assumption)).
% 49.30/49.50 tff(5304,assumption,(m_counter_cell_v_value(c_bit1, s70)), introduced(assumption)).
% 49.30/49.50 tff(5305,plain,
% 49.30/49.50 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5306,plain,
% 49.30/49.50 (((~node1(c_bit1, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70))) <=> (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 49.30/49.50 inference(rewrite,[status(thm)],[])).
% 49.30/49.50 tff(5307,plain,
% 49.30/49.50 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70))))),
% 49.30/49.50 inference(monotonicity,[status(thm)],[5306])).
% 49.30/49.50 tff(5308,plain,
% 49.30/49.50 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 49.30/49.50 inference(transitivity,[status(thm)],[5307, 5305])).
% 49.30/49.50 tff(5309,plain,
% 49.30/49.50 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5310,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5309, 5308])).
% 49.34/49.50 tff(5311,plain,
% 49.34/49.50 ($false),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5310, 3095, 5304, 5303, 5302])).
% 49.34/49.50 tff(5312,plain,((~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.50 tff(5313,plain,
% 49.34/49.50 (~node1(c_bit1, s70)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5312, 5288])).
% 49.34/49.50 tff(5314,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit1, s70, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit1, s70, s71))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5315,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit1, s70, s71))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5316,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit1, s70, s71)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5315, 5314])).
% 49.34/49.50 tff(5317,plain,
% 49.34/49.50 (node3(c_bit1, s70, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5316, 21, 2131])).
% 49.34/49.50 tff(5318,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5319,plain,
% 49.34/49.50 ((node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71)) <=> (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5320,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71))))),
% 49.34/49.50 inference(monotonicity,[status(thm)],[5319])).
% 49.34/49.50 tff(5321,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 49.34/49.50 inference(transitivity,[status(thm)],[5320, 5318])).
% 49.34/49.50 tff(5322,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5323,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5322, 5321])).
% 49.34/49.50 tff(5324,plain,
% 49.34/49.50 (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5323, 84, 5317])).
% 49.34/49.50 tff(5325,plain,
% 49.34/49.50 (m_counter_cell_v_value(c_bit1, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5324, 5313])).
% 49.34/49.50 tff(5326,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5327,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5328,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5327, 5326])).
% 49.34/49.50 tff(5329,plain,
% 49.34/49.50 ((~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5328, 2906, 2147])).
% 49.34/49.50 tff(5330,plain,
% 49.34/49.50 (m_counter_cell_v_carry_out(c_bit0, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5329, 2143])).
% 49.34/49.50 tff(5331,plain,
% 49.34/49.50 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5332,plain,
% 49.34/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5333,plain,
% 49.34/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s71)) | m_counter_cell_v_carry_in(c_bit1, s71)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 49.34/49.50 tff(5334,plain,
% 49.34/49.50 (m_counter_cell_v_carry_in(c_bit1, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5333, 2921, 5330])).
% 49.34/49.50 tff(5335,assumption,(m_counter_cell_v_value(c_bit1, s71)), introduced(assumption)).
% 49.34/49.50 tff(5336,assumption,(node2(c_bit1, s71)), introduced(assumption)).
% 49.34/49.50 tff(5337,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5338,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5339,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 49.34/49.50 tff(5340,plain,
% 49.34/49.50 ($false),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5339, 104, 5336, 5335, 5334])).
% 49.34/49.50 tff(5341,plain,((~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.50 tff(5342,plain,
% 49.34/49.50 (~node2(c_bit1, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5341, 5325])).
% 49.34/49.50 tff(5343,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit1, s71, s72))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit1, s71, s72))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5344,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit1, s71, s72))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5345,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit1, s71, s72)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5344, 5343])).
% 49.34/49.50 tff(5346,plain,
% 49.34/49.50 (node3(c_bit1, s71, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5345, 21, 2159])).
% 49.34/49.50 tff(5347,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5348,plain,
% 49.34/49.50 ((node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72))) <=> ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5349,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72))))),
% 49.34/49.50 inference(monotonicity,[status(thm)],[5348])).
% 49.34/49.50 tff(5350,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 49.34/49.50 inference(transitivity,[status(thm)],[5349, 5347])).
% 49.34/49.50 tff(5351,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5352,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5351, 5350])).
% 49.34/49.50 tff(5353,plain,
% 49.34/49.50 ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5352, 130, 5346])).
% 49.34/49.50 tff(5354,plain,
% 49.34/49.50 (~m_counter_cell_v_value(c_bit1, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5353, 5342])).
% 49.34/49.50 tff(5355,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5356,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5357,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5356, 5355])).
% 49.34/49.50 tff(5358,plain,
% 49.34/49.50 (~node4(c_bit0, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5357, 2823, 2171])).
% 49.34/49.50 tff(5359,assumption,(m_counter_cell_v_carry_out(c_bit0, s72)), introduced(assumption)).
% 49.34/49.50 tff(5360,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5361,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5362,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5361, 5360])).
% 49.34/49.50 tff(5363,plain,
% 49.34/49.50 ($false),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5362, 2836, 5359, 5358])).
% 49.34/49.50 tff(5364,plain,(~m_counter_cell_v_carry_out(c_bit0, s72)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.50 tff(5365,assumption,(m_counter_cell_v_carry_in(c_bit1, s72)), introduced(assumption)).
% 49.34/49.50 tff(5366,assumption,(~m_counter_cell_v_carry_out(c_bit0, s72)), introduced(assumption)).
% 49.34/49.50 tff(5367,plain,
% 49.34/49.50 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5368,plain,
% 49.34/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5369,plain,
% 49.34/49.50 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 49.34/49.50 tff(5370,plain,
% 49.34/49.50 ($false),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5369, 2851, 5366, 5365])).
% 49.34/49.50 tff(5371,plain,((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.50 tff(5372,plain,
% 49.34/49.50 (~m_counter_cell_v_carry_in(c_bit1, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5371, 5364])).
% 49.34/49.50 tff(5373,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5374,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5375,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 49.34/49.50 tff(5376,plain,
% 49.34/49.50 (m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72))),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5375, 3024, 5372])).
% 49.34/49.50 tff(5377,plain,
% 49.34/49.50 (~node2(c_bit1, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5376, 5354])).
% 49.34/49.50 tff(5378,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit1, s72, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit1, s72, s73))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5379,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit1, s72, s73))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5380,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit1, s72, s73)),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5379, 5378])).
% 49.34/49.50 tff(5381,plain,
% 49.34/49.50 (node3(c_bit1, s72, s73)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5380, 21, 2190])).
% 49.34/49.50 tff(5382,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5383,plain,
% 49.34/49.50 ((node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73))) <=> ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5384,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73))))),
% 49.34/49.50 inference(monotonicity,[status(thm)],[5383])).
% 49.34/49.50 tff(5385,plain,
% 49.34/49.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 49.34/49.50 inference(transitivity,[status(thm)],[5384, 5382])).
% 49.34/49.50 tff(5386,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5387,plain,
% 49.34/49.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73))),
% 49.34/49.50 inference(modus_ponens,[status(thm)],[5386, 5385])).
% 49.34/49.50 tff(5388,plain,
% 49.34/49.50 ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5387, 130, 5381])).
% 49.34/49.50 tff(5389,plain,
% 49.34/49.50 (~m_counter_cell_v_value(c_bit1, s73)),
% 49.34/49.50 inference(unit_resolution,[status(thm)],[5388, 5377])).
% 49.34/49.50 tff(5390,assumption,(node1(c_bit1, s73)), introduced(assumption)).
% 49.34/49.50 tff(5391,plain,
% 49.34/49.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 49.34/49.50 inference(rewrite,[status(thm)],[])).
% 49.34/49.50 tff(5392,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 49.34/49.50 inference(quant_inst,[status(thm)],[])).
% 49.34/49.50 tff(5393,plain,
% 49.34/49.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5392, 5391])).
% 49.34/49.51 tff(5394,plain,
% 49.34/49.51 ((~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5393, 2906, 2206])).
% 49.34/49.51 tff(5395,plain,
% 49.34/49.51 (m_counter_cell_v_carry_out(c_bit0, s73)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5394, 2202])).
% 49.34/49.51 tff(5396,plain,
% 49.34/49.51 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5397,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5398,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s73)) | m_counter_cell_v_carry_in(c_bit1, s73)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5397, 5396])).
% 49.34/49.51 tff(5399,plain,
% 49.34/49.51 (m_counter_cell_v_carry_in(c_bit1, s73)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5398, 2921, 5395])).
% 49.34/49.51 tff(5400,assumption,(~m_counter_cell_v_value(c_bit1, s73)), introduced(assumption)).
% 49.34/49.51 tff(5401,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5402,plain,
% 49.34/49.51 (((~node1(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5403,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5402])).
% 49.34/49.51 tff(5404,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5403, 5401])).
% 49.34/49.51 tff(5405,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5406,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5405, 5404])).
% 49.34/49.51 tff(5407,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5406, 55, 5400, 5399, 5390])).
% 49.34/49.51 tff(5408,plain,((~node1(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5409,plain,
% 49.34/49.51 (~node1(c_bit1, s73)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5408, 5389])).
% 49.34/49.51 tff(5410,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit1, s73, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit1, s73, s74))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5411,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit1, s73, s74))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5412,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit1, s73, s74)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5411, 5410])).
% 49.34/49.51 tff(5413,plain,
% 49.34/49.51 (node3(c_bit1, s73, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5412, 21, 2218])).
% 49.34/49.51 tff(5414,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5415,plain,
% 49.34/49.51 ((node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74)) <=> (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5416,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5415])).
% 49.34/49.51 tff(5417,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5416, 5414])).
% 49.34/49.51 tff(5418,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5419,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 49.34/49.51 tff(5420,plain,
% 49.34/49.51 (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5419, 84, 5413])).
% 49.34/49.51 tff(5421,plain,
% 49.34/49.51 (m_counter_cell_v_value(c_bit1, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5420, 5409])).
% 49.34/49.51 tff(5422,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5423,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5424,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 49.34/49.51 tff(5425,plain,
% 49.34/49.51 (~node4(c_bit0, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5424, 2823, 2230])).
% 49.34/49.51 tff(5426,assumption,(m_counter_cell_v_carry_out(c_bit0, s74)), introduced(assumption)).
% 49.34/49.51 tff(5427,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5428,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5429,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 49.34/49.51 tff(5430,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5429, 2836, 5426, 5425])).
% 49.34/49.51 tff(5431,plain,(~m_counter_cell_v_carry_out(c_bit0, s74)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5432,assumption,(m_counter_cell_v_carry_in(c_bit1, s74)), introduced(assumption)).
% 49.34/49.51 tff(5433,assumption,(~m_counter_cell_v_carry_out(c_bit0, s74)), introduced(assumption)).
% 49.34/49.51 tff(5434,plain,
% 49.34/49.51 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5435,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5436,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit0, s74)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5435, 5434])).
% 49.34/49.51 tff(5437,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5436, 2851, 5433, 5432])).
% 49.34/49.51 tff(5438,plain,((~m_counter_cell_v_carry_in(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit0, s74)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5439,plain,
% 49.34/49.51 (~m_counter_cell_v_carry_in(c_bit1, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5438, 5431])).
% 49.34/49.51 tff(5440,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5441,plain,
% 49.34/49.51 (((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74))) <=> (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5442,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5441])).
% 49.34/49.51 tff(5443,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5442, 5440])).
% 49.34/49.51 tff(5444,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5445,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 49.34/49.51 tff(5446,plain,
% 49.34/49.51 ((~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74))),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5445, 3095, 5439])).
% 49.34/49.51 tff(5447,plain,
% 49.34/49.51 (~node1(c_bit1, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5446, 5421])).
% 49.34/49.51 tff(5448,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit1, s74, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit1, s74, s75))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5449,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit1, s74, s75))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5450,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit1, s74, s75)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 49.34/49.51 tff(5451,plain,
% 49.34/49.51 (node3(c_bit1, s74, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5450, 21, 2249])).
% 49.34/49.51 tff(5452,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5453,plain,
% 49.34/49.51 ((node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75)) <=> (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5454,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5453])).
% 49.34/49.51 tff(5455,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5454, 5452])).
% 49.34/49.51 tff(5456,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5457,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 49.34/49.51 tff(5458,plain,
% 49.34/49.51 (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5457, 84, 5451])).
% 49.34/49.51 tff(5459,plain,
% 49.34/49.51 (m_counter_cell_v_value(c_bit1, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5458, 5447])).
% 49.34/49.51 tff(5460,assumption,(node2(c_bit1, s75)), introduced(assumption)).
% 49.34/49.51 tff(5461,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5462,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5463,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5462, 5461])).
% 49.34/49.51 tff(5464,plain,
% 49.34/49.51 ((~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5463, 2906, 2265])).
% 49.34/49.51 tff(5465,plain,
% 49.34/49.51 (m_counter_cell_v_carry_out(c_bit0, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5464, 2261])).
% 49.34/49.51 tff(5466,plain,
% 49.34/49.51 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5467,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5468,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 49.34/49.51 tff(5469,plain,
% 49.34/49.51 (m_counter_cell_v_carry_in(c_bit1, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5468, 2921, 5465])).
% 49.34/49.51 tff(5470,assumption,(m_counter_cell_v_value(c_bit1, s75)), introduced(assumption)).
% 49.34/49.51 tff(5471,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5472,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5473,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5472, 5471])).
% 49.34/49.51 tff(5474,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5473, 104, 5470, 5469, 5460])).
% 49.34/49.51 tff(5475,plain,((~node2(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5476,plain,
% 49.34/49.51 (~node2(c_bit1, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5475, 5459])).
% 49.34/49.51 tff(5477,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit1, s75, s76))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit1, s75, s76))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5478,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit1, s75, s76))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5479,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit1, s75, s76)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 49.34/49.51 tff(5480,plain,
% 49.34/49.51 (node3(c_bit1, s75, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5479, 21, 2277])).
% 49.34/49.51 tff(5481,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5482,plain,
% 49.34/49.51 ((node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76))) <=> ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5483,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5482])).
% 49.34/49.51 tff(5484,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5483, 5481])).
% 49.34/49.51 tff(5485,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5486,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5485, 5484])).
% 49.34/49.51 tff(5487,plain,
% 49.34/49.51 ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5486, 130, 5480])).
% 49.34/49.51 tff(5488,plain,
% 49.34/49.51 (~m_counter_cell_v_value(c_bit1, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5487, 5476])).
% 49.34/49.51 tff(5489,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5490,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5491,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5490, 5489])).
% 49.34/49.51 tff(5492,plain,
% 49.34/49.51 (~node4(c_bit0, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5491, 2823, 2289])).
% 49.34/49.51 tff(5493,assumption,(m_counter_cell_v_carry_out(c_bit0, s76)), introduced(assumption)).
% 49.34/49.51 tff(5494,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5495,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5496,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5495, 5494])).
% 49.34/49.51 tff(5497,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5496, 2836, 5493, 5492])).
% 49.34/49.51 tff(5498,plain,(~m_counter_cell_v_carry_out(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5499,assumption,(m_counter_cell_v_carry_in(c_bit1, s76)), introduced(assumption)).
% 49.34/49.51 tff(5500,assumption,(~m_counter_cell_v_carry_out(c_bit0, s76)), introduced(assumption)).
% 49.34/49.51 tff(5501,plain,
% 49.34/49.51 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5502,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5503,plain,
% 49.34/49.51 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 49.34/49.51 tff(5504,plain,
% 49.34/49.51 ($false),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5503, 2851, 5500, 5499])).
% 49.34/49.51 tff(5505,plain,((~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.51 tff(5506,plain,
% 49.34/49.51 (~m_counter_cell_v_carry_in(c_bit1, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5505, 5498])).
% 49.34/49.51 tff(5507,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5508,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5509,plain,
% 49.34/49.51 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 49.34/49.51 tff(5510,plain,
% 49.34/49.51 (m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76))),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5509, 3024, 5506])).
% 49.34/49.51 tff(5511,plain,
% 49.34/49.51 (~node2(c_bit1, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5510, 5488])).
% 49.34/49.51 tff(5512,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit1, s76, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit1, s76, s77))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5513,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit1, s76, s77))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5514,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit1, s76, s77)),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 49.34/49.51 tff(5515,plain,
% 49.34/49.51 (node3(c_bit1, s76, s77)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5514, 21, 2308])).
% 49.34/49.51 tff(5516,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5517,plain,
% 49.34/49.51 ((node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77))) <=> ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 49.34/49.51 inference(rewrite,[status(thm)],[])).
% 49.34/49.51 tff(5518,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77))))),
% 49.34/49.51 inference(monotonicity,[status(thm)],[5517])).
% 49.34/49.51 tff(5519,plain,
% 49.34/49.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 49.34/49.51 inference(transitivity,[status(thm)],[5518, 5516])).
% 49.34/49.51 tff(5520,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))),
% 49.34/49.51 inference(quant_inst,[status(thm)],[])).
% 49.34/49.51 tff(5521,plain,
% 49.34/49.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77))),
% 49.34/49.51 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 49.34/49.51 tff(5522,plain,
% 49.34/49.51 ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5521, 130, 5515])).
% 49.34/49.51 tff(5523,plain,
% 49.34/49.51 (~m_counter_cell_v_value(c_bit1, s77)),
% 49.34/49.51 inference(unit_resolution,[status(thm)],[5522, 5511])).
% 49.34/49.51 tff(5524,assumption,(~m_counter_cell_v_value(c_bit1, s77)), introduced(assumption)).
% 49.34/49.51 tff(5525,assumption,(node1(c_bit1, s77)), introduced(assumption)).
% 49.34/49.51 tff(5526,plain,
% 49.34/49.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5527,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5528,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5527, 5526])).
% 49.34/49.52 tff(5529,plain,
% 49.34/49.52 ((~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5528, 2906, 2324])).
% 49.34/49.52 tff(5530,plain,
% 49.34/49.52 (m_counter_cell_v_carry_out(c_bit0, s77)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5529, 2320])).
% 49.34/49.52 tff(5531,plain,
% 49.34/49.52 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5532,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5533,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s77)) | m_counter_cell_v_carry_in(c_bit1, s77)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 49.34/49.52 tff(5534,plain,
% 49.34/49.52 (m_counter_cell_v_carry_in(c_bit1, s77)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5533, 2921, 5530])).
% 49.34/49.52 tff(5535,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5536,plain,
% 49.34/49.52 (((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5537,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5536])).
% 49.34/49.52 tff(5538,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5537, 5535])).
% 49.34/49.52 tff(5539,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5540,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5539, 5538])).
% 49.34/49.52 tff(5541,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5540, 55, 5534, 5525, 5524])).
% 49.34/49.52 tff(5542,plain,(m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5543,plain,
% 49.34/49.52 (~node1(c_bit1, s77)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5542, 5523])).
% 49.34/49.52 tff(5544,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit1, s77, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit1, s77, s78))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5545,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit1, s77, s78))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5546,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit1, s77, s78)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 49.34/49.52 tff(5547,plain,
% 49.34/49.52 (node3(c_bit1, s77, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5546, 21, 2336])).
% 49.34/49.52 tff(5548,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5549,plain,
% 49.34/49.52 ((node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78)) <=> (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5550,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5549])).
% 49.34/49.52 tff(5551,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5550, 5548])).
% 49.34/49.52 tff(5552,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5553,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5552, 5551])).
% 49.34/49.52 tff(5554,plain,
% 49.34/49.52 (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5553, 84, 5547])).
% 49.34/49.52 tff(5555,plain,
% 49.34/49.52 (m_counter_cell_v_value(c_bit1, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5554, 5543])).
% 49.34/49.52 tff(5556,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5557,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5558,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5557, 5556])).
% 49.34/49.52 tff(5559,plain,
% 49.34/49.52 (~node4(c_bit0, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5558, 2823, 2348])).
% 49.34/49.52 tff(5560,assumption,(m_counter_cell_v_carry_out(c_bit0, s78)), introduced(assumption)).
% 49.34/49.52 tff(5561,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5562,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5563,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 49.34/49.52 tff(5564,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5563, 2836, 5560, 5559])).
% 49.34/49.52 tff(5565,plain,(~m_counter_cell_v_carry_out(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5566,assumption,(m_counter_cell_v_carry_in(c_bit1, s78)), introduced(assumption)).
% 49.34/49.52 tff(5567,assumption,(~m_counter_cell_v_carry_out(c_bit0, s78)), introduced(assumption)).
% 49.34/49.52 tff(5568,plain,
% 49.34/49.52 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5569,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5570,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 49.34/49.52 tff(5571,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5570, 2851, 5567, 5566])).
% 49.34/49.52 tff(5572,plain,((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5573,plain,
% 49.34/49.52 (~m_counter_cell_v_carry_in(c_bit1, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5572, 5565])).
% 49.34/49.52 tff(5574,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5575,plain,
% 49.34/49.52 (((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78))) <=> (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5576,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5575])).
% 49.34/49.52 tff(5577,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5576, 5574])).
% 49.34/49.52 tff(5578,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5579,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 49.34/49.52 tff(5580,plain,
% 49.34/49.52 ((~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78))),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5579, 3095, 5573])).
% 49.34/49.52 tff(5581,plain,
% 49.34/49.52 (~node1(c_bit1, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5580, 5555])).
% 49.34/49.52 tff(5582,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit1, s78, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit1, s78, s79))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5583,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit1, s78, s79))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5584,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit1, s78, s79)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5583, 5582])).
% 49.34/49.52 tff(5585,plain,
% 49.34/49.52 (node3(c_bit1, s78, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5584, 21, 2367])).
% 49.34/49.52 tff(5586,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5587,plain,
% 49.34/49.52 ((node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79)) <=> (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5588,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5587])).
% 49.34/49.52 tff(5589,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5588, 5586])).
% 49.34/49.52 tff(5590,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5591,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5590, 5589])).
% 49.34/49.52 tff(5592,plain,
% 49.34/49.52 (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5591, 84, 5585])).
% 49.34/49.52 tff(5593,plain,
% 49.34/49.52 (m_counter_cell_v_value(c_bit1, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5592, 5581])).
% 49.34/49.52 tff(5594,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5595,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5596,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5595, 5594])).
% 49.34/49.52 tff(5597,plain,
% 49.34/49.52 ((~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5596, 2906, 2383])).
% 49.34/49.52 tff(5598,plain,
% 49.34/49.52 (m_counter_cell_v_carry_out(c_bit0, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5597, 2379])).
% 49.34/49.52 tff(5599,plain,
% 49.34/49.52 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5600,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5601,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s79)) | m_counter_cell_v_carry_in(c_bit1, s79)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5600, 5599])).
% 49.34/49.52 tff(5602,plain,
% 49.34/49.52 (m_counter_cell_v_carry_in(c_bit1, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5601, 2921, 5598])).
% 49.34/49.52 tff(5603,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5604,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5605,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5604, 5603])).
% 49.34/49.52 tff(5606,plain,
% 49.34/49.52 ((~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79))),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5605, 104, 5602])).
% 49.34/49.52 tff(5607,plain,
% 49.34/49.52 (~node2(c_bit1, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5606, 5593])).
% 49.34/49.52 tff(5608,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit1, s79, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit1, s79, s80))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5609,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit1, s79, s80))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5610,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit1, s79, s80)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5609, 5608])).
% 49.34/49.52 tff(5611,plain,
% 49.34/49.52 (node3(c_bit1, s79, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5610, 21, 2395])).
% 49.34/49.52 tff(5612,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5613,plain,
% 49.34/49.52 ((node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80))) <=> ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5614,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5613])).
% 49.34/49.52 tff(5615,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5614, 5612])).
% 49.34/49.52 tff(5616,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5617,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5616, 5615])).
% 49.34/49.52 tff(5618,plain,
% 49.34/49.52 ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5617, 130, 5611])).
% 49.34/49.52 tff(5619,plain,
% 49.34/49.52 (~m_counter_cell_v_value(c_bit1, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5618, 5607])).
% 49.34/49.52 tff(5620,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5621,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5622,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 49.34/49.52 tff(5623,plain,
% 49.34/49.52 (~node4(c_bit0, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5622, 2823, 2407])).
% 49.34/49.52 tff(5624,assumption,(~node4(c_bit0, s80)), introduced(assumption)).
% 49.34/49.52 tff(5625,assumption,(m_counter_cell_v_carry_out(c_bit0, s80)), introduced(assumption)).
% 49.34/49.52 tff(5626,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5627,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5628,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5627, 5626])).
% 49.34/49.52 tff(5629,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5628, 2836, 5625, 5624])).
% 49.34/49.52 tff(5630,plain,((~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5631,plain,
% 49.34/49.52 (~m_counter_cell_v_carry_out(c_bit0, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5630, 5623])).
% 49.34/49.52 tff(5632,assumption,(m_counter_cell_v_carry_in(c_bit1, s80)), introduced(assumption)).
% 49.34/49.52 tff(5633,assumption,(~m_counter_cell_v_carry_out(c_bit0, s80)), introduced(assumption)).
% 49.34/49.52 tff(5634,plain,
% 49.34/49.52 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5635,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5636,plain,
% 49.34/49.52 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5635, 5634])).
% 49.34/49.52 tff(5637,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5636, 2851, 5633, 5632])).
% 49.34/49.52 tff(5638,plain,(m_counter_cell_v_carry_out(c_bit0, s80) | (~m_counter_cell_v_carry_in(c_bit1, s80))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5639,plain,
% 49.34/49.52 (~m_counter_cell_v_carry_in(c_bit1, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5638, 5631])).
% 49.34/49.52 tff(5640,assumption,(~m_counter_cell_v_value(c_bit1, s80)), introduced(assumption)).
% 49.34/49.52 tff(5641,assumption,(node2(c_bit1, s80)), introduced(assumption)).
% 49.34/49.52 tff(5642,plain,
% 49.34/49.52 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5643,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5644,plain,
% 49.34/49.52 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80))),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5643, 5642])).
% 49.34/49.52 tff(5645,plain,
% 49.34/49.52 ($false),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5644, 3024, 5641, 5640, 5639])).
% 49.34/49.52 tff(5646,plain,(m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80))), inference(lemma,lemma(discharge,[]))).
% 49.34/49.52 tff(5647,plain,
% 49.34/49.52 (~node2(c_bit1, s80)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5646, 5619])).
% 49.34/49.52 tff(5648,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit1, s80, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit1, s80, s81))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5649,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit1, s80, s81))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5650,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit1, s80, s81)),
% 49.34/49.52 inference(modus_ponens,[status(thm)],[5649, 5648])).
% 49.34/49.52 tff(5651,plain,
% 49.34/49.52 (node3(c_bit1, s80, s81)),
% 49.34/49.52 inference(unit_resolution,[status(thm)],[5650, 21, 2426])).
% 49.34/49.52 tff(5652,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5653,plain,
% 49.34/49.52 ((node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81))) <=> ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 49.34/49.52 inference(rewrite,[status(thm)],[])).
% 49.34/49.52 tff(5654,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81))))),
% 49.34/49.52 inference(monotonicity,[status(thm)],[5653])).
% 49.34/49.52 tff(5655,plain,
% 49.34/49.52 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 49.34/49.52 inference(transitivity,[status(thm)],[5654, 5652])).
% 49.34/49.52 tff(5656,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))),
% 49.34/49.52 inference(quant_inst,[status(thm)],[])).
% 49.34/49.52 tff(5657,plain,
% 49.34/49.52 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5656, 5655])).
% 49.34/49.53 tff(5658,plain,
% 49.34/49.53 ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5657, 130, 5651])).
% 49.34/49.53 tff(5659,plain,
% 49.34/49.53 (~m_counter_cell_v_value(c_bit1, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5658, 5647])).
% 49.34/49.53 tff(5660,assumption,(node1(c_bit1, s81)), introduced(assumption)).
% 49.34/49.53 tff(5661,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5662,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5663,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5662, 5661])).
% 49.34/49.53 tff(5664,plain,
% 49.34/49.53 ((~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5663, 2906, 2442])).
% 49.34/49.53 tff(5665,plain,
% 49.34/49.53 (m_counter_cell_v_carry_out(c_bit0, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5664, 2438])).
% 49.34/49.53 tff(5666,plain,
% 49.34/49.53 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5667,plain,
% 49.34/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5668,plain,
% 49.34/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 49.34/49.53 tff(5669,plain,
% 49.34/49.53 (m_counter_cell_v_carry_in(c_bit1, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5668, 2921, 5665])).
% 49.34/49.53 tff(5670,assumption,(~m_counter_cell_v_value(c_bit1, s81)), introduced(assumption)).
% 49.34/49.53 tff(5671,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5672,plain,
% 49.34/49.53 (((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5673,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81))))),
% 49.34/49.53 inference(monotonicity,[status(thm)],[5672])).
% 49.34/49.53 tff(5674,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 49.34/49.53 inference(transitivity,[status(thm)],[5673, 5671])).
% 49.34/49.53 tff(5675,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5676,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5675, 5674])).
% 49.34/49.53 tff(5677,plain,
% 49.34/49.53 ($false),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5676, 55, 5670, 5669, 5660])).
% 49.34/49.53 tff(5678,plain,((~node1(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.53 tff(5679,plain,
% 49.34/49.53 (~node1(c_bit1, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5678, 5659])).
% 49.34/49.53 tff(5680,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit1, s81, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit1, s81, s82))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5681,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit1, s81, s82))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5682,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit1, s81, s82)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5681, 5680])).
% 49.34/49.53 tff(5683,plain,
% 49.34/49.53 (node3(c_bit1, s81, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5682, 21, 2454])).
% 49.34/49.53 tff(5684,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5685,plain,
% 49.34/49.53 ((node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82)) <=> (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5686,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82))))),
% 49.34/49.53 inference(monotonicity,[status(thm)],[5685])).
% 49.34/49.53 tff(5687,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 49.34/49.53 inference(transitivity,[status(thm)],[5686, 5684])).
% 49.34/49.53 tff(5688,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5689,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 49.34/49.53 tff(5690,plain,
% 49.34/49.53 (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5689, 84, 5683])).
% 49.34/49.53 tff(5691,plain,
% 49.34/49.53 (m_counter_cell_v_value(c_bit1, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5690, 5679])).
% 49.34/49.53 tff(5692,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5693,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5694,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5693, 5692])).
% 49.34/49.53 tff(5695,plain,
% 49.34/49.53 (~node4(c_bit0, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5694, 2823, 2466])).
% 49.34/49.53 tff(5696,assumption,(m_counter_cell_v_carry_out(c_bit0, s82)), introduced(assumption)).
% 49.34/49.53 tff(5697,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5698,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5699,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 49.34/49.53 tff(5700,plain,
% 49.34/49.53 ($false),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5699, 2836, 5696, 5695])).
% 49.34/49.53 tff(5701,plain,(~m_counter_cell_v_carry_out(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.53 tff(5702,assumption,(m_counter_cell_v_carry_in(c_bit1, s82)), introduced(assumption)).
% 49.34/49.53 tff(5703,assumption,(~m_counter_cell_v_carry_out(c_bit0, s82)), introduced(assumption)).
% 49.34/49.53 tff(5704,plain,
% 49.34/49.53 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5705,plain,
% 49.34/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5706,plain,
% 49.34/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 49.34/49.53 tff(5707,plain,
% 49.34/49.53 ($false),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5706, 2851, 5703, 5702])).
% 49.34/49.53 tff(5708,plain,((~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 49.34/49.53 tff(5709,plain,
% 49.34/49.53 (~m_counter_cell_v_carry_in(c_bit1, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5708, 5701])).
% 49.34/49.53 tff(5710,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5711,plain,
% 49.34/49.53 (((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82))) <=> (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5712,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))))),
% 49.34/49.53 inference(monotonicity,[status(thm)],[5711])).
% 49.34/49.53 tff(5713,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 49.34/49.53 inference(transitivity,[status(thm)],[5712, 5710])).
% 49.34/49.53 tff(5714,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5715,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 49.34/49.53 tff(5716,plain,
% 49.34/49.53 ((~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5715, 3095, 5709])).
% 49.34/49.53 tff(5717,plain,
% 49.34/49.53 (~node1(c_bit1, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5716, 5691])).
% 49.34/49.53 tff(5718,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit1, s82, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit1, s82, s83))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5719,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit1, s82, s83))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5720,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit1, s82, s83)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5719, 5718])).
% 49.34/49.53 tff(5721,plain,
% 49.34/49.53 (node3(c_bit1, s82, s83)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5720, 21, 2485])).
% 49.34/49.53 tff(5722,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5723,plain,
% 49.34/49.53 ((node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83)) <=> (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5724,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83))))),
% 49.34/49.53 inference(monotonicity,[status(thm)],[5723])).
% 49.34/49.53 tff(5725,plain,
% 49.34/49.53 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 49.34/49.53 inference(transitivity,[status(thm)],[5724, 5722])).
% 49.34/49.53 tff(5726,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5727,plain,
% 49.34/49.53 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83))),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5726, 5725])).
% 49.34/49.53 tff(5728,plain,
% 49.34/49.53 (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5727, 84, 5721])).
% 49.34/49.53 tff(5729,plain,
% 49.34/49.53 (m_counter_cell_v_value(c_bit1, s83)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5728, 5717])).
% 49.34/49.53 tff(5730,assumption,(node2(c_bit1, s83)), introduced(assumption)).
% 49.34/49.53 tff(5731,plain,
% 49.34/49.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.34/49.53 tff(5732,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))),
% 49.34/49.53 inference(quant_inst,[status(thm)],[])).
% 49.34/49.53 tff(5733,plain,
% 49.34/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83)),
% 49.34/49.53 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 49.34/49.53 tff(5734,plain,
% 49.34/49.53 ((~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5733, 2906, 2501])).
% 49.34/49.53 tff(5735,plain,
% 49.34/49.53 (m_counter_cell_v_carry_out(c_bit0, s83)),
% 49.34/49.53 inference(unit_resolution,[status(thm)],[5734, 2497])).
% 49.34/49.53 tff(5736,plain,
% 49.34/49.53 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))),
% 49.34/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5737,plain,
% 49.37/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5738,plain,
% 49.37/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s83)) | m_counter_cell_v_carry_in(c_bit1, s83)),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5737, 5736])).
% 49.37/49.53 tff(5739,plain,
% 49.37/49.53 (m_counter_cell_v_carry_in(c_bit1, s83)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5738, 2921, 5735])).
% 49.37/49.53 tff(5740,assumption,(m_counter_cell_v_value(c_bit1, s83)), introduced(assumption)).
% 49.37/49.53 tff(5741,plain,
% 49.37/49.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5742,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5743,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83))),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5742, 5741])).
% 49.37/49.53 tff(5744,plain,
% 49.37/49.53 ($false),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5743, 104, 5740, 5739, 5730])).
% 49.37/49.53 tff(5745,plain,((~node2(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.53 tff(5746,plain,
% 49.37/49.53 (~node2(c_bit1, s83)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5745, 5729])).
% 49.37/49.53 tff(5747,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit1, s83, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit1, s83, s84))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5748,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit1, s83, s84))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5749,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit1, s83, s84)),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 49.37/49.53 tff(5750,plain,
% 49.37/49.53 (node3(c_bit1, s83, s84)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5749, 21, 2513])).
% 49.37/49.53 tff(5751,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5752,plain,
% 49.37/49.53 ((node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84))) <=> ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5753,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84))))),
% 49.37/49.53 inference(monotonicity,[status(thm)],[5752])).
% 49.37/49.53 tff(5754,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 49.37/49.53 inference(transitivity,[status(thm)],[5753, 5751])).
% 49.37/49.53 tff(5755,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5756,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84))),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 49.37/49.53 tff(5757,plain,
% 49.37/49.53 ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5756, 130, 5750])).
% 49.37/49.53 tff(5758,plain,
% 49.37/49.53 (~m_counter_cell_v_value(c_bit1, s84)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5757, 5746])).
% 49.37/49.53 tff(5759,plain,
% 49.37/49.53 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5760,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5761,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84))),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5760, 5759])).
% 49.37/49.53 tff(5762,plain,
% 49.37/49.53 (~node4(c_bit0, s84)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5761, 2823, 2525])).
% 49.37/49.53 tff(5763,assumption,(m_counter_cell_v_carry_out(c_bit0, s84)), introduced(assumption)).
% 49.37/49.53 tff(5764,plain,
% 49.37/49.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5765,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5766,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84)),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5765, 5764])).
% 49.37/49.53 tff(5767,plain,
% 49.37/49.53 ($false),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5766, 2836, 5763, 5762])).
% 49.37/49.53 tff(5768,plain,(~m_counter_cell_v_carry_out(c_bit0, s84)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.53 tff(5769,plain,
% 49.37/49.53 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5770,plain,
% 49.37/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5771,plain,
% 49.37/49.53 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84)),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5770, 5769])).
% 49.37/49.53 tff(5772,plain,
% 49.37/49.53 (~m_counter_cell_v_carry_in(c_bit1, s84)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5771, 2851, 5768])).
% 49.37/49.53 tff(5773,assumption,(~m_counter_cell_v_value(c_bit1, s84)), introduced(assumption)).
% 49.37/49.53 tff(5774,assumption,(node2(c_bit1, s84)), introduced(assumption)).
% 49.37/49.53 tff(5775,plain,
% 49.37/49.53 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5776,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5777,plain,
% 49.37/49.53 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84))),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5776, 5775])).
% 49.37/49.53 tff(5778,plain,
% 49.37/49.53 ($false),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5777, 3024, 5774, 5773, 5772])).
% 49.37/49.53 tff(5779,plain,(m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.53 tff(5780,plain,
% 49.37/49.53 (~node2(c_bit1, s84)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5779, 5758])).
% 49.37/49.53 tff(5781,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit1, s84, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit1, s84, s85))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5782,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit1, s84, s85))),
% 49.37/49.53 inference(quant_inst,[status(thm)],[])).
% 49.37/49.53 tff(5783,plain,
% 49.37/49.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit1, s84, s85)),
% 49.37/49.53 inference(modus_ponens,[status(thm)],[5782, 5781])).
% 49.37/49.53 tff(5784,plain,
% 49.37/49.53 (node3(c_bit1, s84, s85)),
% 49.37/49.53 inference(unit_resolution,[status(thm)],[5783, 21, 2544])).
% 49.37/49.53 tff(5785,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5786,plain,
% 49.37/49.53 ((node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85))) <=> ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 49.37/49.53 inference(rewrite,[status(thm)],[])).
% 49.37/49.53 tff(5787,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85))))),
% 49.37/49.53 inference(monotonicity,[status(thm)],[5786])).
% 49.37/49.53 tff(5788,plain,
% 49.37/49.53 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5787, 5785])).
% 49.37/49.54 tff(5789,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5790,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 49.37/49.54 tff(5791,plain,
% 49.37/49.54 ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5790, 130, 5784])).
% 49.37/49.54 tff(5792,plain,
% 49.37/49.54 (~m_counter_cell_v_value(c_bit1, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5791, 5780])).
% 49.37/49.54 tff(5793,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5794,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5795,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5794, 5793])).
% 49.37/49.54 tff(5796,plain,
% 49.37/49.54 ((~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5795, 2906, 2560])).
% 49.37/49.54 tff(5797,plain,
% 49.37/49.54 (m_counter_cell_v_carry_out(c_bit0, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5796, 2556])).
% 49.37/49.54 tff(5798,plain,
% 49.37/49.54 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5799,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5800,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s85)) | m_counter_cell_v_carry_in(c_bit1, s85)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5799, 5798])).
% 49.37/49.54 tff(5801,plain,
% 49.37/49.54 (m_counter_cell_v_carry_in(c_bit1, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5800, 2921, 5797])).
% 49.37/49.54 tff(5802,assumption,(~m_counter_cell_v_value(c_bit1, s85)), introduced(assumption)).
% 49.37/49.54 tff(5803,assumption,(m_counter_cell_v_carry_in(c_bit1, s85)), introduced(assumption)).
% 49.37/49.54 tff(5804,assumption,(node1(c_bit1, s85)), introduced(assumption)).
% 49.37/49.54 tff(5805,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5806,plain,
% 49.37/49.54 (((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5807,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))))),
% 49.37/49.54 inference(monotonicity,[status(thm)],[5806])).
% 49.37/49.54 tff(5808,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5807, 5805])).
% 49.37/49.54 tff(5809,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5810,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5809, 5808])).
% 49.37/49.54 tff(5811,plain,
% 49.37/49.54 ($false),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5810, 55, 5804, 5803, 5802])).
% 49.37/49.54 tff(5812,plain,(m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.54 tff(5813,plain,
% 49.37/49.54 (m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5812, 5801])).
% 49.37/49.54 tff(5814,plain,
% 49.37/49.54 (~node1(c_bit1, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5813, 5792])).
% 49.37/49.54 tff(5815,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit1, s85, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit1, s85, s86))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5816,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit1, s85, s86))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5817,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit1, s85, s86)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5816, 5815])).
% 49.37/49.54 tff(5818,plain,
% 49.37/49.54 (node3(c_bit1, s85, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5817, 21, 2572])).
% 49.37/49.54 tff(5819,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5820,plain,
% 49.37/49.54 ((node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86)) <=> (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5821,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86))))),
% 49.37/49.54 inference(monotonicity,[status(thm)],[5820])).
% 49.37/49.54 tff(5822,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5821, 5819])).
% 49.37/49.54 tff(5823,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5824,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 49.37/49.54 tff(5825,plain,
% 49.37/49.54 (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5824, 84, 5818])).
% 49.37/49.54 tff(5826,plain,
% 49.37/49.54 (m_counter_cell_v_value(c_bit1, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5825, 5814])).
% 49.37/49.54 tff(5827,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5828,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5829,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 49.37/49.54 tff(5830,plain,
% 49.37/49.54 (~node4(c_bit0, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5829, 2823, 2584])).
% 49.37/49.54 tff(5831,assumption,(~node4(c_bit0, s86)), introduced(assumption)).
% 49.37/49.54 tff(5832,assumption,(m_counter_cell_v_carry_out(c_bit0, s86)), introduced(assumption)).
% 49.37/49.54 tff(5833,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5834,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5835,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 49.37/49.54 tff(5836,plain,
% 49.37/49.54 ($false),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5835, 2836, 5832, 5831])).
% 49.37/49.54 tff(5837,plain,((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.54 tff(5838,plain,
% 49.37/49.54 (~m_counter_cell_v_carry_out(c_bit0, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5837, 5830])).
% 49.37/49.54 tff(5839,assumption,(m_counter_cell_v_carry_in(c_bit1, s86)), introduced(assumption)).
% 49.37/49.54 tff(5840,assumption,(~m_counter_cell_v_carry_out(c_bit0, s86)), introduced(assumption)).
% 49.37/49.54 tff(5841,plain,
% 49.37/49.54 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5842,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5843,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5842, 5841])).
% 49.37/49.54 tff(5844,plain,
% 49.37/49.54 ($false),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5843, 2851, 5840, 5839])).
% 49.37/49.54 tff(5845,plain,((~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.54 tff(5846,plain,
% 49.37/49.54 (~m_counter_cell_v_carry_in(c_bit1, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5845, 5838])).
% 49.37/49.54 tff(5847,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5848,plain,
% 49.37/49.54 (((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86))) <=> (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5849,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86))))),
% 49.37/49.54 inference(monotonicity,[status(thm)],[5848])).
% 49.37/49.54 tff(5850,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5849, 5847])).
% 49.37/49.54 tff(5851,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5852,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5851, 5850])).
% 49.37/49.54 tff(5853,plain,
% 49.37/49.54 (~node1(c_bit1, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5852, 3095, 5846, 5826])).
% 49.37/49.54 tff(5854,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit1, s86, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit1, s86, s87))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5855,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit1, s86, s87))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5856,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit1, s86, s87)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5855, 5854])).
% 49.37/49.54 tff(5857,plain,
% 49.37/49.54 (node3(c_bit1, s86, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5856, 21, 2603])).
% 49.37/49.54 tff(5858,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5859,plain,
% 49.37/49.54 ((node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87)) <=> (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5860,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87))))),
% 49.37/49.54 inference(monotonicity,[status(thm)],[5859])).
% 49.37/49.54 tff(5861,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5860, 5858])).
% 49.37/49.54 tff(5862,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5863,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5862, 5861])).
% 49.37/49.54 tff(5864,plain,
% 49.37/49.54 (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5863, 84, 5857])).
% 49.37/49.54 tff(5865,plain,
% 49.37/49.54 (m_counter_cell_v_value(c_bit1, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5864, 5853])).
% 49.37/49.54 tff(5866,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5867,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5868,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5867, 5866])).
% 49.37/49.54 tff(5869,plain,
% 49.37/49.54 ((~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5868, 2906, 2619])).
% 49.37/49.54 tff(5870,plain,
% 49.37/49.54 (m_counter_cell_v_carry_out(c_bit0, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5869, 2615])).
% 49.37/49.54 tff(5871,assumption,(~m_counter_cell_v_carry_in(c_bit1, s87)), introduced(assumption)).
% 49.37/49.54 tff(5872,assumption,(m_counter_cell_v_carry_out(c_bit0, s87)), introduced(assumption)).
% 49.37/49.54 tff(5873,plain,
% 49.37/49.54 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5874,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5875,plain,
% 49.37/49.54 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s87)) | m_counter_cell_v_carry_in(c_bit1, s87)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5874, 5873])).
% 49.37/49.54 tff(5876,plain,
% 49.37/49.54 ($false),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5875, 2921, 5872, 5871])).
% 49.37/49.54 tff(5877,plain,((~m_counter_cell_v_carry_out(c_bit0, s87)) | m_counter_cell_v_carry_in(c_bit1, s87)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.54 tff(5878,plain,
% 49.37/49.54 (m_counter_cell_v_carry_in(c_bit1, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5877, 5870])).
% 49.37/49.54 tff(5879,assumption,(node2(c_bit1, s87)), introduced(assumption)).
% 49.37/49.54 tff(5880,assumption,(m_counter_cell_v_carry_in(c_bit1, s87)), introduced(assumption)).
% 49.37/49.54 tff(5881,assumption,(m_counter_cell_v_value(c_bit1, s87)), introduced(assumption)).
% 49.37/49.54 tff(5882,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5883,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5884,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5883, 5882])).
% 49.37/49.54 tff(5885,plain,
% 49.37/49.54 ($false),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5884, 104, 5881, 5880, 5879])).
% 49.37/49.54 tff(5886,plain,((~node2(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~m_counter_cell_v_carry_in(c_bit1, s87))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.54 tff(5887,plain,
% 49.37/49.54 ((~node2(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87))),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5886, 5878])).
% 49.37/49.54 tff(5888,plain,
% 49.37/49.54 (~node2(c_bit1, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5887, 5865])).
% 49.37/49.54 tff(5889,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit1, s87, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit1, s87, s88))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5890,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit1, s87, s88))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5891,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit1, s87, s88)),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 49.37/49.54 tff(5892,plain,
% 49.37/49.54 (node3(c_bit1, s87, s88)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5891, 21, 2631])).
% 49.37/49.54 tff(5893,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5894,plain,
% 49.37/49.54 ((node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88))) <=> ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5895,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88))))),
% 49.37/49.54 inference(monotonicity,[status(thm)],[5894])).
% 49.37/49.54 tff(5896,plain,
% 49.37/49.54 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 49.37/49.54 inference(transitivity,[status(thm)],[5895, 5893])).
% 49.37/49.54 tff(5897,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5898,plain,
% 49.37/49.54 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5897, 5896])).
% 49.37/49.54 tff(5899,plain,
% 49.37/49.54 ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5898, 130, 5892])).
% 49.37/49.54 tff(5900,plain,
% 49.37/49.54 (~m_counter_cell_v_value(c_bit1, s88)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5899, 5888])).
% 49.37/49.54 tff(5901,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))),
% 49.37/49.54 inference(rewrite,[status(thm)],[])).
% 49.37/49.54 tff(5902,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))),
% 49.37/49.54 inference(quant_inst,[status(thm)],[])).
% 49.37/49.54 tff(5903,plain,
% 49.37/49.54 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88))),
% 49.37/49.54 inference(modus_ponens,[status(thm)],[5902, 5901])).
% 49.37/49.54 tff(5904,plain,
% 49.37/49.54 (~node4(c_bit0, s88)),
% 49.37/49.54 inference(unit_resolution,[status(thm)],[5903, 2823, 2643])).
% 49.37/49.54 tff(5905,assumption,(m_counter_cell_v_carry_out(c_bit0, s88)), introduced(assumption)).
% 49.37/49.54 tff(5906,plain,
% 49.37/49.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5907,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5908,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5907, 5906])).
% 49.37/49.55 tff(5909,plain,
% 49.37/49.55 ($false),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5908, 2836, 5905, 5904])).
% 49.37/49.55 tff(5910,plain,(~m_counter_cell_v_carry_out(c_bit0, s88)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.55 tff(5911,plain,
% 49.37/49.55 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5912,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5913,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s88)) | m_counter_cell_v_carry_out(c_bit0, s88)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5912, 5911])).
% 49.37/49.55 tff(5914,plain,
% 49.37/49.55 (~m_counter_cell_v_carry_in(c_bit1, s88)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5913, 2851, 5910])).
% 49.37/49.55 tff(5915,assumption,(~m_counter_cell_v_value(c_bit1, s88)), introduced(assumption)).
% 49.37/49.55 tff(5916,assumption,(node2(c_bit1, s88)), introduced(assumption)).
% 49.37/49.55 tff(5917,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5918,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5919,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5918, 5917])).
% 49.37/49.55 tff(5920,plain,
% 49.37/49.55 ($false),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5919, 3024, 5916, 5915, 5914])).
% 49.37/49.55 tff(5921,plain,((~node2(c_bit1, s88)) | m_counter_cell_v_value(c_bit1, s88)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.55 tff(5922,plain,
% 49.37/49.55 (~node2(c_bit1, s88)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5921, 5900])).
% 49.37/49.55 tff(5923,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit1, s88, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit1, s88, s89))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5924,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit1, s88, s89))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5925,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit1, s88, s89)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5924, 5923])).
% 49.37/49.55 tff(5926,plain,
% 49.37/49.55 (node3(c_bit1, s88, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5925, 21, 2662])).
% 49.37/49.55 tff(5927,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5928,plain,
% 49.37/49.55 ((node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89))) <=> ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5929,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[5928])).
% 49.37/49.55 tff(5930,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[5929, 5927])).
% 49.37/49.55 tff(5931,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5932,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5931, 5930])).
% 49.37/49.55 tff(5933,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5932, 130, 5926])).
% 49.37/49.55 tff(5934,plain,
% 49.37/49.55 (~m_counter_cell_v_value(c_bit1, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5933, 5922])).
% 49.37/49.55 tff(5935,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5936,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5937,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 49.37/49.55 tff(5938,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5937, 2906, 2678])).
% 49.37/49.55 tff(5939,plain,
% 49.37/49.55 (m_counter_cell_v_carry_out(c_bit0, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5938, 2674])).
% 49.37/49.55 tff(5940,plain,
% 49.37/49.55 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5941,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5942,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5941, 5940])).
% 49.37/49.55 tff(5943,plain,
% 49.37/49.55 (m_counter_cell_v_carry_in(c_bit1, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5942, 2921, 5939])).
% 49.37/49.55 tff(5944,assumption,(m_counter_cell_v_carry_in(c_bit1, s89)), introduced(assumption)).
% 49.37/49.55 tff(5945,assumption,(node1(c_bit1, s89)), introduced(assumption)).
% 49.37/49.55 tff(5946,assumption,(~m_counter_cell_v_value(c_bit1, s89)), introduced(assumption)).
% 49.37/49.55 tff(5947,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5948,plain,
% 49.37/49.55 (((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5949,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[5948])).
% 49.37/49.55 tff(5950,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[5949, 5947])).
% 49.37/49.55 tff(5951,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5952,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5951, 5950])).
% 49.37/49.55 tff(5953,plain,
% 49.37/49.55 ($false),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5952, 55, 5946, 5945, 5944])).
% 49.37/49.55 tff(5954,plain,(m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.55 tff(5955,plain,
% 49.37/49.55 (m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5954, 5943])).
% 49.37/49.55 tff(5956,plain,
% 49.37/49.55 (~node1(c_bit1, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5955, 5934])).
% 49.37/49.55 tff(5957,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit1, s89, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit1, s89, s90))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5958,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit1, s89, s90))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5959,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit1, s89, s90)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5958, 5957])).
% 49.37/49.55 tff(5960,plain,
% 49.37/49.55 (node3(c_bit1, s89, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5959, 21, 2690])).
% 49.37/49.55 tff(5961,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5962,plain,
% 49.37/49.55 ((node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90)) <=> (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5963,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[5962])).
% 49.37/49.55 tff(5964,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[5963, 5961])).
% 49.37/49.55 tff(5965,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5966,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 49.37/49.55 tff(5967,plain,
% 49.37/49.55 (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5966, 84, 5960])).
% 49.37/49.55 tff(5968,plain,
% 49.37/49.55 (m_counter_cell_v_value(c_bit1, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5967, 5956])).
% 49.37/49.55 tff(5969,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5970,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5971,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5970, 5969])).
% 49.37/49.55 tff(5972,plain,
% 49.37/49.55 (~node4(c_bit0, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5971, 2823, 2702])).
% 49.37/49.55 tff(5973,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5974,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5975,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5974, 5973])).
% 49.37/49.55 tff(5976,plain,
% 49.37/49.55 (~m_counter_cell_v_carry_out(c_bit0, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5975, 2836, 5972])).
% 49.37/49.55 tff(5977,plain,
% 49.37/49.55 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5978,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5979,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s90)) | m_counter_cell_v_carry_out(c_bit0, s90)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 49.37/49.55 tff(5980,plain,
% 49.37/49.55 (~m_counter_cell_v_carry_in(c_bit1, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5979, 2851, 5976])).
% 49.37/49.55 tff(5981,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5982,plain,
% 49.37/49.55 (((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90))) <=> (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5983,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[5982])).
% 49.37/49.55 tff(5984,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[5983, 5981])).
% 49.37/49.55 tff(5985,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5986,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5985, 5984])).
% 49.37/49.55 tff(5987,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5986, 3095, 5980])).
% 49.37/49.55 tff(5988,plain,
% 49.37/49.55 (~node1(c_bit1, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5987, 5968])).
% 49.37/49.55 tff(5989,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit1, s90, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit1, s90, s91))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5990,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit1, s90, s91))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5991,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit1, s90, s91)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 49.37/49.55 tff(5992,plain,
% 49.37/49.55 (node3(c_bit1, s90, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5991, 21, 2719])).
% 49.37/49.55 tff(5993,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5994,plain,
% 49.37/49.55 ((node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91)) <=> (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(5995,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[5994])).
% 49.37/49.55 tff(5996,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[5995, 5993])).
% 49.37/49.55 tff(5997,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(5998,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[5997, 5996])).
% 49.37/49.55 tff(5999,plain,
% 49.37/49.55 (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5998, 84, 5992])).
% 49.37/49.55 tff(6000,plain,
% 49.37/49.55 (m_counter_cell_v_value(c_bit1, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[5999, 5988])).
% 49.37/49.55 tff(6001,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6002,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6003,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 49.37/49.55 tff(6004,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6003, 2906, 2733])).
% 49.37/49.55 tff(6005,plain,
% 49.37/49.55 (m_counter_cell_v_carry_out(c_bit0, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6004, 2731])).
% 49.37/49.55 tff(6006,plain,
% 49.37/49.55 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6007,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6008,plain,
% 49.37/49.55 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s91)) | m_counter_cell_v_carry_in(c_bit1, s91)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6007, 6006])).
% 49.37/49.55 tff(6009,plain,
% 49.37/49.55 (m_counter_cell_v_carry_in(c_bit1, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6008, 2921, 6005])).
% 49.37/49.55 tff(6010,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6011,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6012,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6011, 6010])).
% 49.37/49.55 tff(6013,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91))),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6012, 104, 6009])).
% 49.37/49.55 tff(6014,plain,
% 49.37/49.55 (~node2(c_bit1, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6013, 6000])).
% 49.37/49.55 tff(6015,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit1, s91, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit1, s91, s92))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6016,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit1, s91, s92))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6017,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit1, s91, s92)),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 49.37/49.55 tff(6018,plain,
% 49.37/49.55 (node3(c_bit1, s91, s92)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6017, 21, 2745])).
% 49.37/49.55 tff(6019,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6020,plain,
% 49.37/49.55 ((node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92))) <=> ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6021,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92))))),
% 49.37/49.55 inference(monotonicity,[status(thm)],[6020])).
% 49.37/49.55 tff(6022,plain,
% 49.37/49.55 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 49.37/49.55 inference(transitivity,[status(thm)],[6021, 6019])).
% 49.37/49.55 tff(6023,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6024,plain,
% 49.37/49.55 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6023, 6022])).
% 49.37/49.55 tff(6025,plain,
% 49.37/49.55 ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6024, 130, 6018])).
% 49.37/49.55 tff(6026,plain,
% 49.37/49.55 (~m_counter_cell_v_value(c_bit1, s92)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6025, 6014])).
% 49.37/49.55 tff(6027,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6028,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))),
% 49.37/49.55 inference(quant_inst,[status(thm)],[])).
% 49.37/49.55 tff(6029,plain,
% 49.37/49.55 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92))),
% 49.37/49.55 inference(modus_ponens,[status(thm)],[6028, 6027])).
% 49.37/49.55 tff(6030,plain,
% 49.37/49.55 (~node4(c_bit0, s92)),
% 49.37/49.55 inference(unit_resolution,[status(thm)],[6029, 2823, 2757])).
% 49.37/49.55 tff(6031,assumption,(m_counter_cell_v_carry_out(c_bit0, s92)), introduced(assumption)).
% 49.37/49.55 tff(6032,plain,
% 49.37/49.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))),
% 49.37/49.55 inference(rewrite,[status(thm)],[])).
% 49.37/49.55 tff(6033,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6034,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6033, 6032])).
% 49.37/49.56 tff(6035,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6034, 2836, 6031, 6030])).
% 49.37/49.56 tff(6036,plain,(~m_counter_cell_v_carry_out(c_bit0, s92)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6037,assumption,(m_counter_cell_v_carry_in(c_bit1, s92)), introduced(assumption)).
% 49.37/49.56 tff(6038,assumption,(~m_counter_cell_v_carry_out(c_bit0, s92)), introduced(assumption)).
% 49.37/49.56 tff(6039,plain,
% 49.37/49.56 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6040,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6041,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_carry_out(c_bit0, s92)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6040, 6039])).
% 49.37/49.56 tff(6042,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6041, 2851, 6038, 6037])).
% 49.37/49.56 tff(6043,plain,(m_counter_cell_v_carry_out(c_bit0, s92) | (~m_counter_cell_v_carry_in(c_bit1, s92))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6044,plain,
% 49.37/49.56 (~m_counter_cell_v_carry_in(c_bit1, s92)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6043, 6036])).
% 49.37/49.56 tff(6045,assumption,(~m_counter_cell_v_carry_in(c_bit1, s92)), introduced(assumption)).
% 49.37/49.56 tff(6046,assumption,(~m_counter_cell_v_value(c_bit1, s92)), introduced(assumption)).
% 49.37/49.56 tff(6047,assumption,(node2(c_bit1, s92)), introduced(assumption)).
% 49.37/49.56 tff(6048,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6049,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6050,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 49.37/49.56 tff(6051,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6050, 3024, 6047, 6046, 6045])).
% 49.37/49.56 tff(6052,plain,(m_counter_cell_v_carry_in(c_bit1, s92) | (~node2(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6053,plain,
% 49.37/49.56 ((~node2(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6052, 6044])).
% 49.37/49.56 tff(6054,plain,
% 49.37/49.56 (~node2(c_bit1, s92)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6053, 6026])).
% 49.37/49.56 tff(6055,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit1, s92, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit1, s92, s93))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6056,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit1, s92, s93))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6057,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit1, s92, s93)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6056, 6055])).
% 49.37/49.56 tff(6058,plain,
% 49.37/49.56 (node3(c_bit1, s92, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6057, 21, 2776])).
% 49.37/49.56 tff(6059,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6060,plain,
% 49.37/49.56 ((node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93))) <=> ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6061,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6060])).
% 49.37/49.56 tff(6062,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6061, 6059])).
% 49.37/49.56 tff(6063,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6064,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6063, 6062])).
% 49.37/49.56 tff(6065,plain,
% 49.37/49.56 ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6064, 130, 6058])).
% 49.37/49.56 tff(6066,plain,
% 49.37/49.56 (~m_counter_cell_v_value(c_bit1, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6065, 6054])).
% 49.37/49.56 tff(6067,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6068,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6069,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6068, 6067])).
% 49.37/49.56 tff(6070,plain,
% 49.37/49.56 ((~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6069, 2906, 2792])).
% 49.37/49.56 tff(6071,plain,
% 49.37/49.56 (m_counter_cell_v_carry_out(c_bit0, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6070, 2788])).
% 49.37/49.56 tff(6072,plain,
% 49.37/49.56 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6073,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6074,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s93)) | m_counter_cell_v_carry_in(c_bit1, s93)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6073, 6072])).
% 49.37/49.56 tff(6075,plain,
% 49.37/49.56 (m_counter_cell_v_carry_in(c_bit1, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6074, 2921, 6071])).
% 49.37/49.56 tff(6076,assumption,(m_counter_cell_v_carry_in(c_bit1, s93)), introduced(assumption)).
% 49.37/49.56 tff(6077,assumption,(~m_counter_cell_v_value(c_bit1, s93)), introduced(assumption)).
% 49.37/49.56 tff(6078,assumption,(node1(c_bit1, s93)), introduced(assumption)).
% 49.37/49.56 tff(6079,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6080,plain,
% 49.37/49.56 (((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6081,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6080])).
% 49.37/49.56 tff(6082,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6081, 6079])).
% 49.37/49.56 tff(6083,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6084,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6083, 6082])).
% 49.37/49.56 tff(6085,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6084, 55, 6078, 6077, 6076])).
% 49.37/49.56 tff(6086,plain,((~node1(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~m_counter_cell_v_carry_in(c_bit1, s93))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6087,plain,
% 49.37/49.56 ((~node1(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6086, 6075])).
% 49.37/49.56 tff(6088,plain,
% 49.37/49.56 (~node1(c_bit1, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6087, 6066])).
% 49.37/49.56 tff(6089,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit1, s93, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit1, s93, s94))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6090,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit1, s93, s94))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6091,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit1, s93, s94)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6090, 6089])).
% 49.37/49.56 tff(6092,plain,
% 49.37/49.56 (node3(c_bit1, s93, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6091, 21, 2804])).
% 49.37/49.56 tff(6093,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6094,plain,
% 49.37/49.56 ((node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94)) <=> (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6095,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6094])).
% 49.37/49.56 tff(6096,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6095, 6093])).
% 49.37/49.56 tff(6097,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6098,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6097, 6096])).
% 49.37/49.56 tff(6099,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6098, 84, 6092])).
% 49.37/49.56 tff(6100,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit1, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6099, 6088])).
% 49.37/49.56 tff(6101,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6102,plain,
% 49.37/49.56 (((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94))) <=> (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6103,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6102])).
% 49.37/49.56 tff(6104,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6103, 6101])).
% 49.37/49.56 tff(6105,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6106,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6105, 6104])).
% 49.37/49.56 tff(6107,plain,
% 49.37/49.56 (~node1(c_bit1, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6106, 3095, 6100, 2857])).
% 49.37/49.56 tff(6108,plain,
% 49.37/49.56 (succ(s94, s95) <=> succ(s94, s95)),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6109,axiom,(succ(s94, s95)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound95')).
% 49.37/49.56 tff(6110,plain,
% 49.37/49.56 (succ(s94, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 49.37/49.56 tff(6111,plain,
% 49.37/49.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6112,plain,
% 49.37/49.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6113,plain,
% 49.37/49.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6112, 6111])).
% 49.37/49.56 tff(6114,plain,
% 49.37/49.56 (trans(s94, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6113, 6110, 7])).
% 49.37/49.56 tff(6115,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit1, s94, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit1, s94, s95))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6116,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit1, s94, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6117,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit1, s94, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6116, 6115])).
% 49.37/49.56 tff(6118,plain,
% 49.37/49.56 (node3(c_bit1, s94, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6117, 21, 6114])).
% 49.37/49.56 tff(6119,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6120,plain,
% 49.37/49.56 ((node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95)) <=> (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6121,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6120])).
% 49.37/49.56 tff(6122,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6121, 6119])).
% 49.37/49.56 tff(6123,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6124,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6123, 6122])).
% 49.37/49.56 tff(6125,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6124, 84, 6118])).
% 49.37/49.56 tff(6126,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit1, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6125, 6107])).
% 49.37/49.56 tff(6127,assumption,(~m_counter_cell_v_carry_out(c_bit1, s95)), introduced(assumption)).
% 49.37/49.56 tff(6128,assumption,(~m_counter_cell_v_carry_in(c_bit0, s94)), introduced(assumption)).
% 49.37/49.56 tff(6129,plain,
% 49.37/49.56 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s94)),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6130,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6129, 43, 6128])).
% 49.37/49.56 tff(6131,plain,(m_counter_cell_v_carry_in(c_bit0, s94)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6132,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6133,plain,
% 49.37/49.56 (((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6134,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6133])).
% 49.37/49.56 tff(6135,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6134, 6132])).
% 49.37/49.56 tff(6136,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6137,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6136, 6135])).
% 49.37/49.56 tff(6138,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6137, 55, 6131])).
% 49.37/49.56 tff(6139,plain,
% 49.37/49.56 (~node1(c_bit0, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6138, 2816])).
% 49.37/49.56 tff(6140,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit0, s94, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit0, s94, s95))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6141,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit0, s94, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6142,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit0, s94, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 49.37/49.56 tff(6143,plain,
% 49.37/49.56 (node3(c_bit0, s94, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6142, 21, 6114])).
% 49.37/49.56 tff(6144,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6145,plain,
% 49.37/49.56 ((node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95)) <=> (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6146,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95))))),
% 49.37/49.56 inference(monotonicity,[status(thm)],[6145])).
% 49.37/49.56 tff(6147,plain,
% 49.37/49.56 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 49.37/49.56 inference(transitivity,[status(thm)],[6146, 6144])).
% 49.37/49.56 tff(6148,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6149,plain,
% 49.37/49.56 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95))),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6148, 6147])).
% 49.37/49.56 tff(6150,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6149, 84, 6143])).
% 49.37/49.56 tff(6151,plain,
% 49.37/49.56 (m_counter_cell_v_value(c_bit0, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6150, 6139])).
% 49.37/49.56 tff(6152,assumption,(~m_counter_cell_v_carry_in(c_bit0, s95)), introduced(assumption)).
% 49.37/49.56 tff(6153,plain,
% 49.37/49.56 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s95)),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6154,plain,
% 49.37/49.56 ($false),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6153, 43, 6152])).
% 49.37/49.56 tff(6155,plain,(m_counter_cell_v_carry_in(c_bit0, s95)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.56 tff(6156,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6157,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6158,plain,
% 49.37/49.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 49.37/49.56 tff(6159,plain,
% 49.37/49.56 ((~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6158, 2906, 6155])).
% 49.37/49.56 tff(6160,plain,
% 49.37/49.56 (m_counter_cell_v_carry_out(c_bit0, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6159, 6151])).
% 49.37/49.56 tff(6161,plain,
% 49.37/49.56 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))),
% 49.37/49.56 inference(rewrite,[status(thm)],[])).
% 49.37/49.56 tff(6162,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))),
% 49.37/49.56 inference(quant_inst,[status(thm)],[])).
% 49.37/49.56 tff(6163,plain,
% 49.37/49.56 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s95)) | m_counter_cell_v_carry_in(c_bit1, s95)),
% 49.37/49.56 inference(modus_ponens,[status(thm)],[6162, 6161])).
% 49.37/49.56 tff(6164,plain,
% 49.37/49.56 (m_counter_cell_v_carry_in(c_bit1, s95)),
% 49.37/49.56 inference(unit_resolution,[status(thm)],[6163, 2921, 6160])).
% 49.37/49.56 tff(6165,assumption,(m_counter_cell_v_value(c_bit1, s95)), introduced(assumption)).
% 49.37/49.56 tff(6166,plain,
% 49.37/49.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6167,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6168,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6167, 6166])).
% 49.37/49.57 tff(6169,plain,
% 49.37/49.57 ($false),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6168, 2906, 6165, 6164, 6127])).
% 49.37/49.57 tff(6170,plain,(m_counter_cell_v_carry_out(c_bit1, s95) | (~m_counter_cell_v_value(c_bit1, s95))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.57 tff(6171,plain,
% 49.37/49.57 (m_counter_cell_v_carry_out(c_bit1, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6170, 6126])).
% 49.37/49.57 tff(6172,assumption,(~m_counter_cell_v_carry_in(c_bit2, s95)), introduced(assumption)).
% 49.37/49.57 tff(6173,assumption,(m_counter_cell_v_carry_out(c_bit1, s95)), introduced(assumption)).
% 49.37/49.57 tff(6174,plain,
% 49.37/49.57 (^[X: $i] : refl(((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6175,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6174])).
% 49.37/49.57 tff(6176,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6177,plain,
% 49.37/49.57 (^[X: $i] : rewrite((m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X))) <=> ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X)))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6178,plain,
% 49.37/49.57 (![X: $i] : (m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X))) <=> ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6177])).
% 49.37/49.57 tff(6179,axiom,(![X: $i] : (m_counter_cell_v_carry_in(c_bit2, X) | (~m_counter_cell_v_carry_out(c_bit1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_4')).
% 49.37/49.57 tff(6180,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6179, 6178])).
% 49.37/49.57 tff(6181,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6180, 6176])).
% 49.37/49.57 tff(6182,plain,(
% 49.37/49.57 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(skolemize,[status(sab)],[6181])).
% 49.37/49.57 tff(6183,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6182, 6175])).
% 49.37/49.57 tff(6184,plain,
% 49.37/49.57 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6185,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6186,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 49.37/49.57 tff(6187,plain,
% 49.37/49.57 ($false),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6186, 6183, 6173, 6172])).
% 49.37/49.57 tff(6188,plain,(m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_carry_out(c_bit1, s95))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.57 tff(6189,plain,
% 49.37/49.57 (m_counter_cell_v_carry_in(c_bit2, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6188, 6171])).
% 49.37/49.57 tff(6190,assumption,(always5(s95)), introduced(assumption)).
% 49.37/49.57 tff(6191,plain,
% 49.37/49.57 (^[X: $i] : refl(((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6192,plain,
% 49.37/49.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6191])).
% 49.37/49.57 tff(6193,plain,
% 49.37/49.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6194,plain,
% 49.37/49.57 (^[X: $i] : rewrite(((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X))) <=> ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X))))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6195,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X))) <=> ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6194])).
% 49.37/49.57 tff(6196,axiom,(![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty1')).
% 49.37/49.57 tff(6197,plain,
% 49.37/49.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6196, 6195])).
% 49.37/49.57 tff(6198,plain,
% 49.37/49.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6197, 6193])).
% 49.37/49.57 tff(6199,plain,(
% 49.37/49.57 ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(skolemize,[status(sab)],[6198])).
% 49.37/49.57 tff(6200,plain,
% 49.37/49.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6199, 6192])).
% 49.37/49.57 tff(6201,plain,
% 49.37/49.57 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6202,plain,
% 49.37/49.57 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6203,plain,
% 49.37/49.57 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6202, 6201])).
% 49.37/49.57 tff(6204,plain,
% 49.37/49.57 (~m_counter_cell_v_carry_out(c_bit2, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6203, 6200, 6190])).
% 49.37/49.57 tff(6205,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6206,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6207,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6206, 6205])).
% 49.37/49.57 tff(6208,plain,
% 49.37/49.57 (~m_counter_cell_v_value(c_bit2, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6207, 2906, 6189, 6204])).
% 49.37/49.57 tff(6209,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6210,plain,
% 49.37/49.57 (((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6211,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95))))),
% 49.37/49.57 inference(monotonicity,[status(thm)],[6210])).
% 49.37/49.57 tff(6212,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 49.37/49.57 inference(transitivity,[status(thm)],[6211, 6209])).
% 49.37/49.57 tff(6213,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6214,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6213, 6212])).
% 49.37/49.57 tff(6215,plain,
% 49.37/49.57 (~node1(c_bit2, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6214, 55, 6208, 6189])).
% 49.37/49.57 tff(6216,plain,
% 49.37/49.57 (succ(s95, s96) <=> succ(s95, s96)),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6217,axiom,(succ(s95, s96)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound96')).
% 49.37/49.57 tff(6218,plain,
% 49.37/49.57 (succ(s95, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6217, 6216])).
% 49.37/49.57 tff(6219,plain,
% 49.37/49.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6220,plain,
% 49.37/49.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6221,plain,
% 49.37/49.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6220, 6219])).
% 49.37/49.57 tff(6222,plain,
% 49.37/49.57 (trans(s95, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6221, 6218, 7])).
% 49.37/49.57 tff(6223,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit2, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit2, s95, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6224,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit2, s95, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6225,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit2, s95, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 49.37/49.57 tff(6226,plain,
% 49.37/49.57 (node3(c_bit2, s95, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6225, 21, 6222])).
% 49.37/49.57 tff(6227,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6228,plain,
% 49.37/49.57 ((node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96)) <=> (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6229,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96))))),
% 49.37/49.57 inference(monotonicity,[status(thm)],[6228])).
% 49.37/49.57 tff(6230,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 49.37/49.57 inference(transitivity,[status(thm)],[6229, 6227])).
% 49.37/49.57 tff(6231,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6232,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6231, 6230])).
% 49.37/49.57 tff(6233,plain,
% 49.37/49.57 (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6232, 84, 6226])).
% 49.37/49.57 tff(6234,plain,
% 49.37/49.57 (m_counter_cell_v_value(c_bit2, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6233, 6215])).
% 49.37/49.57 tff(6235,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6236,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6237,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6236, 6235])).
% 49.37/49.57 tff(6238,plain,
% 49.37/49.57 ((~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95))),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6237, 104, 6155])).
% 49.37/49.57 tff(6239,plain,
% 49.37/49.57 (~node2(c_bit0, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6238, 6151])).
% 49.37/49.57 tff(6240,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit0, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit0, s95, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6241,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit0, s95, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6242,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit0, s95, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6241, 6240])).
% 49.37/49.57 tff(6243,plain,
% 49.37/49.57 (node3(c_bit0, s95, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6242, 21, 6222])).
% 49.37/49.57 tff(6244,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6245,plain,
% 49.37/49.57 ((node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96))) <=> ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6246,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96))))),
% 49.37/49.57 inference(monotonicity,[status(thm)],[6245])).
% 49.37/49.57 tff(6247,plain,
% 49.37/49.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 49.37/49.57 inference(transitivity,[status(thm)],[6246, 6244])).
% 49.37/49.57 tff(6248,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6249,plain,
% 49.37/49.57 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6248, 6247])).
% 49.37/49.57 tff(6250,plain,
% 49.37/49.57 ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6249, 130, 6243])).
% 49.37/49.57 tff(6251,plain,
% 49.37/49.57 (~m_counter_cell_v_value(c_bit0, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6250, 6239])).
% 49.37/49.57 tff(6252,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s96) | (~node4(c_bit0, s96)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s96) | (~node4(c_bit0, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6253,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s96) | (~node4(c_bit0, s96)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6254,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s96) | (~node4(c_bit0, s96))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6253, 6252])).
% 49.37/49.57 tff(6255,plain,
% 49.37/49.57 (~node4(c_bit0, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6254, 2823, 6251])).
% 49.37/49.57 tff(6256,assumption,(m_counter_cell_v_carry_out(c_bit0, s96)), introduced(assumption)).
% 49.37/49.57 tff(6257,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s96)) | node4(c_bit0, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s96)) | node4(c_bit0, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6258,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s96)) | node4(c_bit0, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6259,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s96)) | node4(c_bit0, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 49.37/49.57 tff(6260,plain,
% 49.37/49.57 ($false),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6259, 2836, 6256, 6255])).
% 49.37/49.57 tff(6261,plain,(~m_counter_cell_v_carry_out(c_bit0, s96)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.57 tff(6262,assumption,(m_counter_cell_v_carry_in(c_bit1, s96)), introduced(assumption)).
% 49.37/49.57 tff(6263,assumption,(~m_counter_cell_v_carry_out(c_bit0, s96)), introduced(assumption)).
% 49.37/49.57 tff(6264,plain,
% 49.37/49.57 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit0, s96))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit0, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6265,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit0, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6266,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit0, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6265, 6264])).
% 49.37/49.57 tff(6267,plain,
% 49.37/49.57 ($false),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6266, 2851, 6263, 6262])).
% 49.37/49.57 tff(6268,plain,((~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit0, s96)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.57 tff(6269,plain,
% 49.37/49.57 (~m_counter_cell_v_carry_in(c_bit1, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6268, 6261])).
% 49.37/49.57 tff(6270,plain,
% 49.37/49.57 (^[I0: $i, X: $i] : refl((m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6271,plain,
% 49.37/49.57 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6270])).
% 49.37/49.57 tff(6272,plain,
% 49.37/49.57 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X))) <=> ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6273,axiom,(![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_counter_cell_10')).
% 49.37/49.57 tff(6274,plain,
% 49.37/49.57 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6273, 6272])).
% 49.37/49.57 tff(6275,plain,(
% 49.37/49.57 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 49.37/49.57 inference(skolemize,[status(sab)],[6274])).
% 49.37/49.57 tff(6276,plain,
% 49.37/49.57 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6275, 6271])).
% 49.37/49.57 tff(6277,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | (~node4(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | (~node4(c_bit1, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6278,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | (~node4(c_bit1, s96)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6279,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | (~node4(c_bit1, s96))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6278, 6277])).
% 49.37/49.57 tff(6280,plain,
% 49.37/49.57 (~node4(c_bit1, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6279, 6276, 6269])).
% 49.37/49.57 tff(6281,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6282,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6283,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6282, 6281])).
% 49.37/49.57 tff(6284,plain,
% 49.37/49.57 (~m_counter_cell_v_carry_out(c_bit1, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6283, 2836, 6280])).
% 49.37/49.57 tff(6285,plain,
% 49.37/49.57 (^[X: $i] : refl(((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)))),
% 49.37/49.57 inference(bind,[status(th)],[])).
% 49.37/49.57 tff(6286,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 49.37/49.57 inference(quant_intro,[status(thm)],[6285])).
% 49.37/49.57 tff(6287,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X)) <=> ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6288,axiom,(![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_5')).
% 49.37/49.57 tff(6289,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 49.37/49.57 tff(6290,plain,(
% 49.37/49.57 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 49.37/49.57 inference(skolemize,[status(sab)],[6289])).
% 49.37/49.57 tff(6291,plain,
% 49.37/49.57 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6290, 6286])).
% 49.37/49.57 tff(6292,plain,
% 49.37/49.57 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6293,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6294,plain,
% 49.37/49.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6293, 6292])).
% 49.37/49.57 tff(6295,plain,
% 49.37/49.57 (~m_counter_cell_v_carry_in(c_bit2, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6294, 6291, 6284])).
% 49.37/49.57 tff(6296,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6297,plain,
% 49.37/49.57 (((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96))) <=> (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6298,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))))),
% 49.37/49.57 inference(monotonicity,[status(thm)],[6297])).
% 49.37/49.57 tff(6299,plain,
% 49.37/49.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 49.37/49.57 inference(transitivity,[status(thm)],[6298, 6296])).
% 49.37/49.57 tff(6300,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6301,plain,
% 49.37/49.57 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6300, 6299])).
% 49.37/49.57 tff(6302,plain,
% 49.37/49.57 ((~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6301, 3095, 6295])).
% 49.37/49.57 tff(6303,plain,
% 49.37/49.57 (~node1(c_bit2, s96)),
% 49.37/49.57 inference(unit_resolution,[status(thm)],[6302, 6234])).
% 49.37/49.57 tff(6304,plain,
% 49.37/49.57 (succ(s96, s97) <=> succ(s96, s97)),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6305,axiom,(succ(s96, s97)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound97')).
% 49.37/49.57 tff(6306,plain,
% 49.37/49.57 (succ(s96, s97)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6305, 6304])).
% 49.37/49.57 tff(6307,plain,
% 49.37/49.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97))),
% 49.37/49.57 inference(rewrite,[status(thm)],[])).
% 49.37/49.57 tff(6308,plain,
% 49.37/49.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))),
% 49.37/49.57 inference(quant_inst,[status(thm)],[])).
% 49.37/49.57 tff(6309,plain,
% 49.37/49.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97)),
% 49.37/49.57 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 49.37/49.58 tff(6310,plain,
% 49.37/49.58 (trans(s96, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6309, 6306, 7])).
% 49.37/49.58 tff(6311,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit2, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit2, s96, s97))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6312,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit2, s96, s97))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6313,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit2, s96, s97)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 49.37/49.58 tff(6314,plain,
% 49.37/49.58 (node3(c_bit2, s96, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6313, 21, 6310])).
% 49.37/49.58 tff(6315,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6316,plain,
% 49.37/49.58 ((node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97)) <=> (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6317,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97))))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6316])).
% 49.37/49.58 tff(6318,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6317, 6315])).
% 49.37/49.58 tff(6319,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6320,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6319, 6318])).
% 49.37/49.58 tff(6321,plain,
% 49.37/49.58 (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6320, 84, 6314])).
% 49.37/49.58 tff(6322,plain,
% 49.37/49.58 (m_counter_cell_v_value(c_bit2, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6321, 6303])).
% 49.37/49.58 tff(6323,plain,
% 49.37/49.58 (^[Y: $i, X: $i] : refl(((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 49.37/49.58 inference(bind,[status(th)],[])).
% 49.37/49.58 tff(6324,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(quant_intro,[status(thm)],[6323])).
% 49.37/49.58 tff(6325,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6326,plain,
% 49.37/49.58 (^[Y: $i, X: $i] : rewrite(((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 49.37/49.58 inference(bind,[status(th)],[])).
% 49.37/49.58 tff(6327,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(quant_intro,[status(thm)],[6326])).
% 49.37/49.58 tff(6328,axiom,(![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty2')).
% 49.37/49.58 tff(6329,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6328, 6327])).
% 49.37/49.58 tff(6330,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6329, 6325])).
% 49.37/49.58 tff(6331,plain,(
% 49.37/49.58 ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(skolemize,[status(sab)],[6330])).
% 49.37/49.58 tff(6332,plain,
% 49.37/49.58 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6331, 6324])).
% 49.37/49.58 tff(6333,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s95, s96)) | (~always5(s95)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6334,plain,
% 49.37/49.58 (((~always5(s95)) | (~trans(s95, s96)) | always5(s96)) <=> ((~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6335,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s95, s96)) | (~always5(s95)) | always5(s96)))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6334])).
% 49.37/49.58 tff(6336,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6335, 6333])).
% 49.37/49.58 tff(6337,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6338,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6337, 6336])).
% 49.37/49.58 tff(6339,plain,
% 49.37/49.58 ((~always5(s95)) | always5(s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6338, 6332, 6222])).
% 49.37/49.58 tff(6340,plain,
% 49.37/49.58 (always5(s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6339, 6190])).
% 49.37/49.58 tff(6341,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s96, s97)) | (~always5(s96)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6342,plain,
% 49.37/49.58 (((~always5(s96)) | (~trans(s96, s97)) | always5(s97)) <=> ((~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6343,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s96, s97)) | (~always5(s96)) | always5(s97)))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6342])).
% 49.37/49.58 tff(6344,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6343, 6341])).
% 49.37/49.58 tff(6345,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6346,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6345, 6344])).
% 49.37/49.58 tff(6347,plain,
% 49.37/49.58 ((~always5(s96)) | always5(s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6346, 6332, 6310])).
% 49.37/49.58 tff(6348,plain,
% 49.37/49.58 (always5(s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6347, 6340])).
% 49.37/49.58 tff(6349,plain,
% 49.37/49.58 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6350,plain,
% 49.37/49.58 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6351,plain,
% 49.37/49.58 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6350, 6349])).
% 49.37/49.58 tff(6352,plain,
% 49.37/49.58 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6351, 6200, 6348])).
% 49.37/49.58 tff(6353,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6354,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6355,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6354, 6353])).
% 49.37/49.58 tff(6356,plain,
% 49.37/49.58 ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97))),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6355, 2906, 6352])).
% 49.37/49.58 tff(6357,plain,
% 49.37/49.58 (~m_counter_cell_v_carry_in(c_bit2, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6356, 6322])).
% 49.37/49.58 tff(6358,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6359,plain,
% 49.37/49.58 (((~node1(c_bit2, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97))) <=> (m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6360,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97))))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6359])).
% 49.37/49.58 tff(6361,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6360, 6358])).
% 49.37/49.58 tff(6362,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6363,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6362, 6361])).
% 49.37/49.58 tff(6364,plain,
% 49.37/49.58 (~node1(c_bit2, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6363, 3095, 6322, 6357])).
% 49.37/49.58 tff(6365,plain,
% 49.37/49.58 (succ(s97, s98) <=> succ(s97, s98)),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6366,axiom,(succ(s97, s98)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound98')).
% 49.37/49.58 tff(6367,plain,
% 49.37/49.58 (succ(s97, s98)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6366, 6365])).
% 49.37/49.58 tff(6368,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6369,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6370,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6369, 6368])).
% 49.37/49.58 tff(6371,plain,
% 49.37/49.58 (trans(s97, s98)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6370, 6367, 7])).
% 49.37/49.58 tff(6372,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit2, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit2, s97, s98))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6373,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit2, s97, s98))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6374,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit2, s97, s98)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6373, 6372])).
% 49.37/49.58 tff(6375,plain,
% 49.37/49.58 (node3(c_bit2, s97, s98)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6374, 21, 6371])).
% 49.37/49.58 tff(6376,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6377,plain,
% 49.37/49.58 ((node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98)) <=> (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6378,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98))))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6377])).
% 49.37/49.58 tff(6379,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6378, 6376])).
% 49.37/49.58 tff(6380,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6381,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6380, 6379])).
% 49.37/49.58 tff(6382,plain,
% 49.37/49.58 (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6381, 84, 6375])).
% 49.37/49.58 tff(6383,plain,
% 49.37/49.58 (m_counter_cell_v_value(c_bit2, s98)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6382, 6364])).
% 49.37/49.58 tff(6384,plain,
% 49.37/49.58 (succ(s98, s99) <=> succ(s98, s99)),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6385,axiom,(succ(s98, s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound99')).
% 49.37/49.58 tff(6386,plain,
% 49.37/49.58 (succ(s98, s99)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6385, 6384])).
% 49.37/49.58 tff(6387,plain,
% 49.37/49.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6388,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6389,plain,
% 49.37/49.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6388, 6387])).
% 49.37/49.58 tff(6390,plain,
% 49.37/49.58 (trans(s98, s99)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6389, 6386, 7])).
% 49.37/49.58 tff(6391,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit2, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit2, s98, s99))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6392,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit2, s98, s99))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6393,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit2, s98, s99)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 49.37/49.58 tff(6394,plain,
% 49.37/49.58 (node3(c_bit2, s98, s99)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6393, 21, 6390])).
% 49.37/49.58 tff(6395,assumption,(node2(c_bit1, s95)), introduced(assumption)).
% 49.37/49.58 tff(6396,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6397,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6398,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 49.37/49.58 tff(6399,plain,
% 49.37/49.58 ($false),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6398, 104, 6165, 6164, 6395])).
% 49.37/49.58 tff(6400,plain,((~node2(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.58 tff(6401,plain,
% 49.37/49.58 (~node2(c_bit1, s95)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6400, 6126])).
% 49.37/49.58 tff(6402,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit1, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit1, s95, s96))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6403,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit1, s95, s96))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6404,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit1, s95, s96)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6403, 6402])).
% 49.37/49.58 tff(6405,plain,
% 49.37/49.58 (node3(c_bit1, s95, s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6404, 21, 6222])).
% 49.37/49.58 tff(6406,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6407,plain,
% 49.37/49.58 ((node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96))) <=> ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6408,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96))))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6407])).
% 49.37/49.58 tff(6409,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6408, 6406])).
% 49.37/49.58 tff(6410,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6411,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6410, 6409])).
% 49.37/49.58 tff(6412,plain,
% 49.37/49.58 ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6411, 130, 6405])).
% 49.37/49.58 tff(6413,plain,
% 49.37/49.58 (~m_counter_cell_v_value(c_bit1, s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6412, 6401])).
% 49.37/49.58 tff(6414,plain,
% 49.37/49.58 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | m_counter_cell_v_value(c_bit1, s96) | (~node2(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | m_counter_cell_v_value(c_bit1, s96) | (~node2(c_bit1, s96)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6415,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | m_counter_cell_v_value(c_bit1, s96) | (~node2(c_bit1, s96)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6416,plain,
% 49.37/49.58 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | m_counter_cell_v_value(c_bit1, s96) | (~node2(c_bit1, s96))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6415, 6414])).
% 49.37/49.58 tff(6417,plain,
% 49.37/49.58 (m_counter_cell_v_value(c_bit1, s96) | (~node2(c_bit1, s96))),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6416, 3024, 6269])).
% 49.37/49.58 tff(6418,plain,
% 49.37/49.58 (~node2(c_bit1, s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6417, 6413])).
% 49.37/49.58 tff(6419,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit1, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit1, s96, s97))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6420,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit1, s96, s97))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6421,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit1, s96, s97)),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6420, 6419])).
% 49.37/49.58 tff(6422,plain,
% 49.37/49.58 (node3(c_bit1, s96, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6421, 21, 6310])).
% 49.37/49.58 tff(6423,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6424,plain,
% 49.37/49.58 ((node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | (~m_counter_cell_v_value(c_bit1, s97))) <=> ((~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 49.37/49.58 inference(rewrite,[status(thm)],[])).
% 49.37/49.58 tff(6425,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | (~m_counter_cell_v_value(c_bit1, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97))))),
% 49.37/49.58 inference(monotonicity,[status(thm)],[6424])).
% 49.37/49.58 tff(6426,plain,
% 49.37/49.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | (~m_counter_cell_v_value(c_bit1, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 49.37/49.58 inference(transitivity,[status(thm)],[6425, 6423])).
% 49.37/49.58 tff(6427,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | (~m_counter_cell_v_value(c_bit1, s97)))),
% 49.37/49.58 inference(quant_inst,[status(thm)],[])).
% 49.37/49.58 tff(6428,plain,
% 49.37/49.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96) | (~node3(c_bit1, s96, s97))),
% 49.37/49.58 inference(modus_ponens,[status(thm)],[6427, 6426])).
% 49.37/49.58 tff(6429,plain,
% 49.37/49.58 ((~m_counter_cell_v_value(c_bit1, s97)) | node2(c_bit1, s96)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6428, 130, 6422])).
% 49.37/49.58 tff(6430,plain,
% 49.37/49.58 (~m_counter_cell_v_value(c_bit1, s97)),
% 49.37/49.58 inference(unit_resolution,[status(thm)],[6429, 6418])).
% 49.37/49.59 tff(6431,assumption,(node1(c_bit1, s97)), introduced(assumption)).
% 49.37/49.59 tff(6432,assumption,(~m_counter_cell_v_carry_in(c_bit0, s96)), introduced(assumption)).
% 49.37/49.59 tff(6433,plain,
% 49.37/49.59 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s96)),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6434,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6433, 43, 6432])).
% 49.37/49.59 tff(6435,plain,(m_counter_cell_v_carry_in(c_bit0, s96)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6436,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6437,plain,
% 49.37/49.59 (((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6438,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6437])).
% 49.37/49.59 tff(6439,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6438, 6436])).
% 49.37/49.59 tff(6440,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6441,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6440, 6439])).
% 49.37/49.59 tff(6442,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6441, 55, 6435])).
% 49.37/49.59 tff(6443,plain,
% 49.37/49.59 (~node1(c_bit0, s96)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6442, 6251])).
% 49.37/49.59 tff(6444,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit0, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit0, s96, s97))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6445,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit0, s96, s97))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6446,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit0, s96, s97)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6445, 6444])).
% 49.37/49.59 tff(6447,plain,
% 49.37/49.59 (node3(c_bit0, s96, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6446, 21, 6310])).
% 49.37/49.59 tff(6448,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6449,plain,
% 49.37/49.59 ((node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97)) <=> (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6450,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6449])).
% 49.37/49.59 tff(6451,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6450, 6448])).
% 49.37/49.59 tff(6452,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6453,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6452, 6451])).
% 49.37/49.59 tff(6454,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6453, 84, 6447])).
% 49.37/49.59 tff(6455,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit0, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6454, 6443])).
% 49.37/49.59 tff(6456,assumption,(~m_counter_cell_v_carry_in(c_bit0, s97)), introduced(assumption)).
% 49.37/49.59 tff(6457,plain,
% 49.37/49.59 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s97)),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6458,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6457, 43, 6456])).
% 49.37/49.59 tff(6459,plain,(m_counter_cell_v_carry_in(c_bit0, s97)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6460,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6461,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6462,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6461, 6460])).
% 49.37/49.59 tff(6463,plain,
% 49.37/49.59 ((~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6462, 2906, 6459])).
% 49.37/49.59 tff(6464,plain,
% 49.37/49.59 (m_counter_cell_v_carry_out(c_bit0, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6463, 6455])).
% 49.37/49.59 tff(6465,plain,
% 49.37/49.59 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6466,plain,
% 49.37/49.59 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6467,plain,
% 49.37/49.59 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s97)) | m_counter_cell_v_carry_in(c_bit1, s97)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6466, 6465])).
% 49.37/49.59 tff(6468,plain,
% 49.37/49.59 (m_counter_cell_v_carry_in(c_bit1, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6467, 2921, 6464])).
% 49.37/49.59 tff(6469,assumption,(~m_counter_cell_v_value(c_bit1, s97)), introduced(assumption)).
% 49.37/49.59 tff(6470,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6471,plain,
% 49.37/49.59 (((~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6472,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6471])).
% 49.37/49.59 tff(6473,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6472, 6470])).
% 49.37/49.59 tff(6474,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6475,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6474, 6473])).
% 49.37/49.59 tff(6476,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6475, 55, 6469, 6468, 6431])).
% 49.37/49.59 tff(6477,plain,((~node1(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6478,plain,
% 49.37/49.59 (~node1(c_bit1, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6477, 6430])).
% 49.37/49.59 tff(6479,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit1, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit1, s97, s98))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6480,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit1, s97, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6481,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit1, s97, s98)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6480, 6479])).
% 49.37/49.59 tff(6482,plain,
% 49.37/49.59 (node3(c_bit1, s97, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6481, 21, 6371])).
% 49.37/49.59 tff(6483,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6484,plain,
% 49.37/49.59 ((node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98)) <=> (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6485,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6484])).
% 49.37/49.59 tff(6486,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6485, 6483])).
% 49.37/49.59 tff(6487,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6488,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6487, 6486])).
% 49.37/49.59 tff(6489,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6488, 84, 6482])).
% 49.37/49.59 tff(6490,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit1, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6489, 6478])).
% 49.37/49.59 tff(6491,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6492,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6493,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 49.37/49.59 tff(6494,plain,
% 49.37/49.59 ((~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97))),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6493, 104, 6459])).
% 49.37/49.59 tff(6495,plain,
% 49.37/49.59 (~node2(c_bit0, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6494, 6455])).
% 49.37/49.59 tff(6496,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit0, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit0, s97, s98))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6497,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit0, s97, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6498,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit0, s97, s98)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6497, 6496])).
% 49.37/49.59 tff(6499,plain,
% 49.37/49.59 (node3(c_bit0, s97, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6498, 21, 6371])).
% 49.37/49.59 tff(6500,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6501,plain,
% 49.37/49.59 ((node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98))) <=> ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6502,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6501])).
% 49.37/49.59 tff(6503,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6502, 6500])).
% 49.37/49.59 tff(6504,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6505,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6504, 6503])).
% 49.37/49.59 tff(6506,plain,
% 49.37/49.59 ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6505, 130, 6499])).
% 49.37/49.59 tff(6507,plain,
% 49.37/49.59 (~m_counter_cell_v_value(c_bit0, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6506, 6495])).
% 49.37/49.59 tff(6508,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6509,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6510,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 49.37/49.59 tff(6511,plain,
% 49.37/49.59 (~node4(c_bit0, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6510, 2823, 6507])).
% 49.37/49.59 tff(6512,assumption,(m_counter_cell_v_carry_out(c_bit0, s98)), introduced(assumption)).
% 49.37/49.59 tff(6513,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6514,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6515,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6514, 6513])).
% 49.37/49.59 tff(6516,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6515, 2836, 6512, 6511])).
% 49.37/49.59 tff(6517,plain,(~m_counter_cell_v_carry_out(c_bit0, s98)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6518,plain,
% 49.37/49.59 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6519,plain,
% 49.37/49.59 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6520,plain,
% 49.37/49.59 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6519, 6518])).
% 49.37/49.59 tff(6521,plain,
% 49.37/49.59 (~m_counter_cell_v_carry_in(c_bit1, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6520, 2851, 6517])).
% 49.37/49.59 tff(6522,assumption,(m_counter_cell_v_value(c_bit1, s98)), introduced(assumption)).
% 49.37/49.59 tff(6523,assumption,(node1(c_bit1, s98)), introduced(assumption)).
% 49.37/49.59 tff(6524,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6525,plain,
% 49.37/49.59 (((~node1(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98))) <=> (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6526,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6525])).
% 49.37/49.59 tff(6527,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6526, 6524])).
% 49.37/49.59 tff(6528,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6529,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 49.37/49.59 tff(6530,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6529, 3095, 6523, 6522, 6521])).
% 49.37/49.59 tff(6531,plain,((~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6532,plain,
% 49.37/49.59 (~node1(c_bit1, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6531, 6490])).
% 49.37/49.59 tff(6533,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit1, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit1, s98, s99))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6534,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit1, s98, s99))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6535,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit1, s98, s99)),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6534, 6533])).
% 49.37/49.59 tff(6536,plain,
% 49.37/49.59 (node3(c_bit1, s98, s99)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6535, 21, 6390])).
% 49.37/49.59 tff(6537,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6538,plain,
% 49.37/49.59 ((node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99)) <=> (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6539,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6538])).
% 49.37/49.59 tff(6540,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6539, 6537])).
% 49.37/49.59 tff(6541,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6542,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6541, 6540])).
% 49.37/49.59 tff(6543,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6542, 84, 6536])).
% 49.37/49.59 tff(6544,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit1, s99)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6543, 6532])).
% 49.37/49.59 tff(6545,assumption,(~m_counter_cell_v_carry_in(c_bit0, s98)), introduced(assumption)).
% 49.37/49.59 tff(6546,plain,
% 49.37/49.59 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s98)),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6547,plain,
% 49.37/49.59 ($false),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6546, 43, 6545])).
% 49.37/49.59 tff(6548,plain,(m_counter_cell_v_carry_in(c_bit0, s98)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.59 tff(6549,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6550,plain,
% 49.37/49.59 (((~node1(c_bit0, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6551,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))))),
% 49.37/49.59 inference(monotonicity,[status(thm)],[6550])).
% 49.37/49.59 tff(6552,plain,
% 49.37/49.59 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 49.37/49.59 inference(transitivity,[status(thm)],[6551, 6549])).
% 49.37/49.59 tff(6553,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6554,plain,
% 49.37/49.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))),
% 49.37/49.59 inference(modus_ponens,[status(thm)],[6553, 6552])).
% 49.37/49.59 tff(6555,plain,
% 49.37/49.59 (m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6554, 55, 6548])).
% 49.37/49.59 tff(6556,plain,
% 49.37/49.59 (~node1(c_bit0, s98)),
% 49.37/49.59 inference(unit_resolution,[status(thm)],[6555, 6507])).
% 49.37/49.59 tff(6557,plain,
% 49.37/49.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit0, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit0, s98, s99))),
% 49.37/49.59 inference(rewrite,[status(thm)],[])).
% 49.37/49.59 tff(6558,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit0, s98, s99))),
% 49.37/49.59 inference(quant_inst,[status(thm)],[])).
% 49.37/49.59 tff(6559,plain,
% 49.37/49.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit0, s98, s99)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6558, 6557])).
% 49.37/49.60 tff(6560,plain,
% 49.37/49.60 (node3(c_bit0, s98, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6559, 21, 6390])).
% 49.37/49.60 tff(6561,plain,
% 49.37/49.60 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6562,plain,
% 49.37/49.60 ((node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6563,plain,
% 49.37/49.60 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99))))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6562])).
% 49.37/49.60 tff(6564,plain,
% 49.37/49.60 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6563, 6561])).
% 49.37/49.60 tff(6565,plain,
% 49.37/49.60 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6566,plain,
% 49.37/49.60 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99))),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6565, 6564])).
% 49.37/49.60 tff(6567,plain,
% 49.37/49.60 (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6566, 84, 6560])).
% 49.37/49.60 tff(6568,plain,
% 49.37/49.60 (m_counter_cell_v_value(c_bit0, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6567, 6556])).
% 49.37/49.60 tff(6569,assumption,(~m_counter_cell_v_carry_in(c_bit0, s99)), introduced(assumption)).
% 49.37/49.60 tff(6570,plain,
% 49.37/49.60 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s99)),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6571,plain,
% 49.37/49.60 ($false),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6570, 43, 6569])).
% 49.37/49.60 tff(6572,plain,(m_counter_cell_v_carry_in(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 49.37/49.60 tff(6573,plain,
% 49.37/49.60 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6574,plain,
% 49.37/49.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6575,plain,
% 49.37/49.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6574, 6573])).
% 49.37/49.60 tff(6576,plain,
% 49.37/49.60 ((~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6575, 2906, 6572])).
% 49.37/49.60 tff(6577,plain,
% 49.37/49.60 (m_counter_cell_v_carry_out(c_bit0, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6576, 6568])).
% 49.37/49.60 tff(6578,plain,
% 49.37/49.60 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6579,plain,
% 49.37/49.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6580,plain,
% 49.37/49.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s99)) | m_counter_cell_v_carry_in(c_bit1, s99)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6579, 6578])).
% 49.37/49.60 tff(6581,plain,
% 49.37/49.60 (m_counter_cell_v_carry_in(c_bit1, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6580, 2921, 6577])).
% 49.37/49.60 tff(6582,plain,
% 49.37/49.60 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6583,plain,
% 49.37/49.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6584,plain,
% 49.37/49.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6583, 6582])).
% 49.37/49.60 tff(6585,plain,
% 49.37/49.60 ((~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6584, 2906, 6581])).
% 49.37/49.60 tff(6586,plain,
% 49.37/49.60 (m_counter_cell_v_carry_out(c_bit1, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6585, 6544])).
% 49.37/49.60 tff(6587,assumption,(m_counter_cell_v_carry_out(c_bit1, s99)), introduced(assumption)).
% 49.37/49.60 tff(6588,assumption,(~m_counter_cell_v_carry_in(c_bit2, s99)), introduced(assumption)).
% 49.37/49.60 tff(6589,plain,
% 49.37/49.60 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6590,plain,
% 49.37/49.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6591,plain,
% 49.37/49.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit2, s99)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6590, 6589])).
% 49.37/49.60 tff(6592,plain,
% 49.37/49.60 ($false),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6591, 6183, 6588, 6587])).
% 49.37/49.60 tff(6593,plain,(m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_carry_out(c_bit1, s99))), inference(lemma,lemma(discharge,[]))).
% 49.37/49.60 tff(6594,plain,
% 49.37/49.60 (m_counter_cell_v_carry_in(c_bit2, s99)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6593, 6586])).
% 49.37/49.60 tff(6595,assumption,(~always5(s99)), introduced(assumption)).
% 49.37/49.60 tff(6596,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s99) | (~trans(s98, s99)) | (~always5(s98)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6597,plain,
% 49.37/49.60 (((~always5(s98)) | (~trans(s98, s99)) | always5(s99)) <=> (always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6598,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s99) | (~trans(s98, s99)) | (~always5(s98))))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6597])).
% 49.37/49.60 tff(6599,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6598, 6596])).
% 49.37/49.60 tff(6600,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6601,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98))),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6600, 6599])).
% 49.37/49.60 tff(6602,plain,
% 49.37/49.60 (always5(s99) | (~always5(s98))),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6601, 6332, 6390])).
% 49.37/49.60 tff(6603,plain,
% 49.37/49.60 (~always5(s98)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6602, 6595])).
% 49.37/49.60 tff(6604,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s97, s98)) | (~always5(s97)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6605,plain,
% 49.37/49.60 (((~always5(s97)) | (~trans(s97, s98)) | always5(s98)) <=> ((~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6606,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s97, s98)) | (~always5(s97)) | always5(s98)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6605])).
% 49.37/49.60 tff(6607,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6606, 6604])).
% 49.37/49.60 tff(6608,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6609,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6608, 6607])).
% 49.37/49.60 tff(6610,plain,
% 49.37/49.60 ((~always5(s97)) | always5(s98)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6609, 6332, 6371])).
% 49.37/49.60 tff(6611,plain,
% 49.37/49.60 (~always5(s97)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6610, 6603])).
% 49.37/49.60 tff(6612,plain,
% 49.37/49.60 (~always5(s96)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6347, 6611])).
% 49.37/49.60 tff(6613,plain,
% 49.37/49.60 (~always5(s95)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6339, 6612])).
% 49.37/49.60 tff(6614,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s94, s95)) | (~always5(s94)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6615,plain,
% 49.37/49.60 (((~always5(s94)) | (~trans(s94, s95)) | always5(s95)) <=> ((~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6616,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s94, s95)) | (~always5(s94)) | always5(s95)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6615])).
% 49.37/49.60 tff(6617,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6616, 6614])).
% 49.37/49.60 tff(6618,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6619,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6618, 6617])).
% 49.37/49.60 tff(6620,plain,
% 49.37/49.60 ((~always5(s94)) | always5(s95)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6619, 6332, 6114])).
% 49.37/49.60 tff(6621,plain,
% 49.37/49.60 (~always5(s94)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6620, 6613])).
% 49.37/49.60 tff(6622,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s93, s94)) | (~always5(s93)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6623,plain,
% 49.37/49.60 (((~always5(s93)) | (~trans(s93, s94)) | always5(s94)) <=> ((~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6624,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s93, s94)) | (~always5(s93)) | always5(s94)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6623])).
% 49.37/49.60 tff(6625,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6624, 6622])).
% 49.37/49.60 tff(6626,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6627,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6626, 6625])).
% 49.37/49.60 tff(6628,plain,
% 49.37/49.60 ((~always5(s93)) | always5(s94)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6627, 6332, 2804])).
% 49.37/49.60 tff(6629,plain,
% 49.37/49.60 (~always5(s93)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6628, 6621])).
% 49.37/49.60 tff(6630,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s92, s93)) | (~always5(s92)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6631,plain,
% 49.37/49.60 (((~always5(s92)) | (~trans(s92, s93)) | always5(s93)) <=> ((~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6632,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s92, s93)) | (~always5(s92)) | always5(s93)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6631])).
% 49.37/49.60 tff(6633,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6632, 6630])).
% 49.37/49.60 tff(6634,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6635,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6634, 6633])).
% 49.37/49.60 tff(6636,plain,
% 49.37/49.60 ((~always5(s92)) | always5(s93)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6635, 6332, 2776])).
% 49.37/49.60 tff(6637,plain,
% 49.37/49.60 (~always5(s92)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6636, 6629])).
% 49.37/49.60 tff(6638,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s91, s92)) | (~always5(s91)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6639,plain,
% 49.37/49.60 (((~always5(s91)) | (~trans(s91, s92)) | always5(s92)) <=> ((~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6640,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s91, s92)) | (~always5(s91)) | always5(s92)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6639])).
% 49.37/49.60 tff(6641,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6640, 6638])).
% 49.37/49.60 tff(6642,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6643,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6642, 6641])).
% 49.37/49.60 tff(6644,plain,
% 49.37/49.60 ((~always5(s91)) | always5(s92)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6643, 6332, 2745])).
% 49.37/49.60 tff(6645,plain,
% 49.37/49.60 (~always5(s91)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6644, 6637])).
% 49.37/49.60 tff(6646,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s90, s91)) | (~always5(s90)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6647,plain,
% 49.37/49.60 (((~always5(s90)) | (~trans(s90, s91)) | always5(s91)) <=> ((~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6648,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s90, s91)) | (~always5(s90)) | always5(s91)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6647])).
% 49.37/49.60 tff(6649,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6648, 6646])).
% 49.37/49.60 tff(6650,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6651,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6650, 6649])).
% 49.37/49.60 tff(6652,plain,
% 49.37/49.60 ((~always5(s90)) | always5(s91)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6651, 6332, 2719])).
% 49.37/49.60 tff(6653,plain,
% 49.37/49.60 (~always5(s90)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6652, 6645])).
% 49.37/49.60 tff(6654,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s89, s90)) | (~always5(s89)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6655,plain,
% 49.37/49.60 (((~always5(s89)) | (~trans(s89, s90)) | always5(s90)) <=> ((~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6656,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s89, s90)) | (~always5(s89)) | always5(s90)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6655])).
% 49.37/49.60 tff(6657,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6656, 6654])).
% 49.37/49.60 tff(6658,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6659,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6658, 6657])).
% 49.37/49.60 tff(6660,plain,
% 49.37/49.60 ((~always5(s89)) | always5(s90)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6659, 6332, 2690])).
% 49.37/49.60 tff(6661,plain,
% 49.37/49.60 (~always5(s89)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6660, 6653])).
% 49.37/49.60 tff(6662,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s88, s89)) | (~always5(s88)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6663,plain,
% 49.37/49.60 (((~always5(s88)) | (~trans(s88, s89)) | always5(s89)) <=> ((~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6664,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s88, s89)) | (~always5(s88)) | always5(s89)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6663])).
% 49.37/49.60 tff(6665,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6664, 6662])).
% 49.37/49.60 tff(6666,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6667,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6666, 6665])).
% 49.37/49.60 tff(6668,plain,
% 49.37/49.60 ((~always5(s88)) | always5(s89)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6667, 6332, 2662])).
% 49.37/49.60 tff(6669,plain,
% 49.37/49.60 (~always5(s88)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6668, 6661])).
% 49.37/49.60 tff(6670,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s87, s88)) | (~always5(s87)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6671,plain,
% 49.37/49.60 (((~always5(s87)) | (~trans(s87, s88)) | always5(s88)) <=> ((~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6672,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s87, s88)) | (~always5(s87)) | always5(s88)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6671])).
% 49.37/49.60 tff(6673,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6672, 6670])).
% 49.37/49.60 tff(6674,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6675,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 49.37/49.60 tff(6676,plain,
% 49.37/49.60 ((~always5(s87)) | always5(s88)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6675, 6332, 2631])).
% 49.37/49.60 tff(6677,plain,
% 49.37/49.60 (~always5(s87)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6676, 6669])).
% 49.37/49.60 tff(6678,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s86, s87)) | (~always5(s86)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6679,plain,
% 49.37/49.60 (((~always5(s86)) | (~trans(s86, s87)) | always5(s87)) <=> ((~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.60 tff(6680,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s86, s87)) | (~always5(s86)) | always5(s87)))),
% 49.37/49.60 inference(monotonicity,[status(thm)],[6679])).
% 49.37/49.60 tff(6681,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 49.37/49.60 inference(transitivity,[status(thm)],[6680, 6678])).
% 49.37/49.60 tff(6682,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))),
% 49.37/49.60 inference(quant_inst,[status(thm)],[])).
% 49.37/49.60 tff(6683,plain,
% 49.37/49.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87)),
% 49.37/49.60 inference(modus_ponens,[status(thm)],[6682, 6681])).
% 49.37/49.60 tff(6684,plain,
% 49.37/49.60 ((~always5(s86)) | always5(s87)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6683, 6332, 2603])).
% 49.37/49.60 tff(6685,plain,
% 49.37/49.60 (~always5(s86)),
% 49.37/49.60 inference(unit_resolution,[status(thm)],[6684, 6677])).
% 49.37/49.60 tff(6686,plain,
% 49.37/49.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s85, s86)) | (~always5(s85)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 49.37/49.60 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6687,plain,
% 49.37/49.61 (((~always5(s85)) | (~trans(s85, s86)) | always5(s86)) <=> ((~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6688,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s85, s86)) | (~always5(s85)) | always5(s86)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6687])).
% 49.37/49.61 tff(6689,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6688, 6686])).
% 49.37/49.61 tff(6690,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6691,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 49.37/49.61 tff(6692,plain,
% 49.37/49.61 ((~always5(s85)) | always5(s86)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6691, 6332, 2572])).
% 49.37/49.61 tff(6693,plain,
% 49.37/49.61 (~always5(s85)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6692, 6685])).
% 49.37/49.61 tff(6694,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s84, s85)) | (~always5(s84)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6695,plain,
% 49.37/49.61 (((~always5(s84)) | (~trans(s84, s85)) | always5(s85)) <=> ((~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6696,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s84, s85)) | (~always5(s84)) | always5(s85)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6695])).
% 49.37/49.61 tff(6697,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6696, 6694])).
% 49.37/49.61 tff(6698,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6699,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 49.37/49.61 tff(6700,plain,
% 49.37/49.61 ((~always5(s84)) | always5(s85)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6699, 6332, 2544])).
% 49.37/49.61 tff(6701,plain,
% 49.37/49.61 (~always5(s84)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6700, 6693])).
% 49.37/49.61 tff(6702,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s83, s84)) | (~always5(s83)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6703,plain,
% 49.37/49.61 (((~always5(s83)) | (~trans(s83, s84)) | always5(s84)) <=> ((~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6704,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s83, s84)) | (~always5(s83)) | always5(s84)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6703])).
% 49.37/49.61 tff(6705,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6704, 6702])).
% 49.37/49.61 tff(6706,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6707,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6706, 6705])).
% 49.37/49.61 tff(6708,plain,
% 49.37/49.61 ((~always5(s83)) | always5(s84)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6707, 6332, 2513])).
% 49.37/49.61 tff(6709,plain,
% 49.37/49.61 (~always5(s83)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6708, 6701])).
% 49.37/49.61 tff(6710,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s82, s83)) | (~always5(s82)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6711,plain,
% 49.37/49.61 (((~always5(s82)) | (~trans(s82, s83)) | always5(s83)) <=> ((~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6712,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s82, s83)) | (~always5(s82)) | always5(s83)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6711])).
% 49.37/49.61 tff(6713,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6712, 6710])).
% 49.37/49.61 tff(6714,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6715,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 49.37/49.61 tff(6716,plain,
% 49.37/49.61 ((~always5(s82)) | always5(s83)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6715, 6332, 2485])).
% 49.37/49.61 tff(6717,plain,
% 49.37/49.61 (~always5(s82)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6716, 6709])).
% 49.37/49.61 tff(6718,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s81, s82)) | (~always5(s81)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6719,plain,
% 49.37/49.61 (((~always5(s81)) | (~trans(s81, s82)) | always5(s82)) <=> ((~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6720,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s81, s82)) | (~always5(s81)) | always5(s82)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6719])).
% 49.37/49.61 tff(6721,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6720, 6718])).
% 49.37/49.61 tff(6722,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6723,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6722, 6721])).
% 49.37/49.61 tff(6724,plain,
% 49.37/49.61 ((~always5(s81)) | always5(s82)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6723, 6332, 2454])).
% 49.37/49.61 tff(6725,plain,
% 49.37/49.61 (~always5(s81)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6724, 6717])).
% 49.37/49.61 tff(6726,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s80, s81)) | (~always5(s80)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6727,plain,
% 49.37/49.61 (((~always5(s80)) | (~trans(s80, s81)) | always5(s81)) <=> ((~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6728,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s80, s81)) | (~always5(s80)) | always5(s81)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6727])).
% 49.37/49.61 tff(6729,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6728, 6726])).
% 49.37/49.61 tff(6730,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6731,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6730, 6729])).
% 49.37/49.61 tff(6732,plain,
% 49.37/49.61 ((~always5(s80)) | always5(s81)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6731, 6332, 2426])).
% 49.37/49.61 tff(6733,plain,
% 49.37/49.61 (~always5(s80)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6732, 6725])).
% 49.37/49.61 tff(6734,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s79, s80)) | (~always5(s79)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6735,plain,
% 49.37/49.61 (((~always5(s79)) | (~trans(s79, s80)) | always5(s80)) <=> ((~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6736,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s79, s80)) | (~always5(s79)) | always5(s80)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6735])).
% 49.37/49.61 tff(6737,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6736, 6734])).
% 49.37/49.61 tff(6738,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6739,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6738, 6737])).
% 49.37/49.61 tff(6740,plain,
% 49.37/49.61 ((~always5(s79)) | always5(s80)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6739, 6332, 2395])).
% 49.37/49.61 tff(6741,plain,
% 49.37/49.61 (~always5(s79)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6740, 6733])).
% 49.37/49.61 tff(6742,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s78, s79)) | (~always5(s78)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6743,plain,
% 49.37/49.61 (((~always5(s78)) | (~trans(s78, s79)) | always5(s79)) <=> ((~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6744,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s78, s79)) | (~always5(s78)) | always5(s79)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6743])).
% 49.37/49.61 tff(6745,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6744, 6742])).
% 49.37/49.61 tff(6746,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6747,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 49.37/49.61 tff(6748,plain,
% 49.37/49.61 ((~always5(s78)) | always5(s79)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6747, 6332, 2367])).
% 49.37/49.61 tff(6749,plain,
% 49.37/49.61 (~always5(s78)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6748, 6741])).
% 49.37/49.61 tff(6750,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s77, s78)) | (~always5(s77)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6751,plain,
% 49.37/49.61 (((~always5(s77)) | (~trans(s77, s78)) | always5(s78)) <=> ((~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6752,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s77, s78)) | (~always5(s77)) | always5(s78)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6751])).
% 49.37/49.61 tff(6753,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6752, 6750])).
% 49.37/49.61 tff(6754,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6755,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6754, 6753])).
% 49.37/49.61 tff(6756,plain,
% 49.37/49.61 ((~always5(s77)) | always5(s78)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6755, 6332, 2336])).
% 49.37/49.61 tff(6757,plain,
% 49.37/49.61 (~always5(s77)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6756, 6749])).
% 49.37/49.61 tff(6758,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s76, s77)) | (~always5(s76)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6759,plain,
% 49.37/49.61 (((~always5(s76)) | (~trans(s76, s77)) | always5(s77)) <=> ((~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6760,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s76, s77)) | (~always5(s76)) | always5(s77)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6759])).
% 49.37/49.61 tff(6761,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6760, 6758])).
% 49.37/49.61 tff(6762,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6763,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6762, 6761])).
% 49.37/49.61 tff(6764,plain,
% 49.37/49.61 ((~always5(s76)) | always5(s77)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6763, 6332, 2308])).
% 49.37/49.61 tff(6765,plain,
% 49.37/49.61 (~always5(s76)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6764, 6757])).
% 49.37/49.61 tff(6766,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s75, s76)) | (~always5(s75)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6767,plain,
% 49.37/49.61 (((~always5(s75)) | (~trans(s75, s76)) | always5(s76)) <=> ((~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6768,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s75, s76)) | (~always5(s75)) | always5(s76)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6767])).
% 49.37/49.61 tff(6769,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6768, 6766])).
% 49.37/49.61 tff(6770,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6771,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6770, 6769])).
% 49.37/49.61 tff(6772,plain,
% 49.37/49.61 ((~always5(s75)) | always5(s76)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6771, 6332, 2277])).
% 49.37/49.61 tff(6773,plain,
% 49.37/49.61 (~always5(s75)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6772, 6765])).
% 49.37/49.61 tff(6774,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s74, s75)) | (~always5(s74)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6775,plain,
% 49.37/49.61 (((~always5(s74)) | (~trans(s74, s75)) | always5(s75)) <=> ((~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6776,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s74, s75)) | (~always5(s74)) | always5(s75)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6775])).
% 49.37/49.61 tff(6777,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6776, 6774])).
% 49.37/49.61 tff(6778,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6779,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6778, 6777])).
% 49.37/49.61 tff(6780,plain,
% 49.37/49.61 ((~always5(s74)) | always5(s75)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6779, 6332, 2249])).
% 49.37/49.61 tff(6781,plain,
% 49.37/49.61 (~always5(s74)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6780, 6773])).
% 49.37/49.61 tff(6782,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s73, s74)) | (~always5(s73)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6783,plain,
% 49.37/49.61 (((~always5(s73)) | (~trans(s73, s74)) | always5(s74)) <=> ((~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6784,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s73, s74)) | (~always5(s73)) | always5(s74)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6783])).
% 49.37/49.61 tff(6785,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6784, 6782])).
% 49.37/49.61 tff(6786,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6787,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6786, 6785])).
% 49.37/49.61 tff(6788,plain,
% 49.37/49.61 ((~always5(s73)) | always5(s74)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6787, 6332, 2218])).
% 49.37/49.61 tff(6789,plain,
% 49.37/49.61 (~always5(s73)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6788, 6781])).
% 49.37/49.61 tff(6790,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s72, s73)) | (~always5(s72)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6791,plain,
% 49.37/49.61 (((~always5(s72)) | (~trans(s72, s73)) | always5(s73)) <=> ((~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6792,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s72, s73)) | (~always5(s72)) | always5(s73)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6791])).
% 49.37/49.61 tff(6793,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6792, 6790])).
% 49.37/49.61 tff(6794,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6795,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6794, 6793])).
% 49.37/49.61 tff(6796,plain,
% 49.37/49.61 ((~always5(s72)) | always5(s73)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6795, 6332, 2190])).
% 49.37/49.61 tff(6797,plain,
% 49.37/49.61 (~always5(s72)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6796, 6789])).
% 49.37/49.61 tff(6798,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s71, s72)) | (~always5(s71)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6799,plain,
% 49.37/49.61 (((~always5(s71)) | (~trans(s71, s72)) | always5(s72)) <=> ((~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6800,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s71, s72)) | (~always5(s71)) | always5(s72)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6799])).
% 49.37/49.61 tff(6801,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6800, 6798])).
% 49.37/49.61 tff(6802,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6803,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6802, 6801])).
% 49.37/49.61 tff(6804,plain,
% 49.37/49.61 ((~always5(s71)) | always5(s72)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6803, 6332, 2159])).
% 49.37/49.61 tff(6805,plain,
% 49.37/49.61 (~always5(s71)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6804, 6797])).
% 49.37/49.61 tff(6806,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s70, s71)) | (~always5(s70)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6807,plain,
% 49.37/49.61 (((~always5(s70)) | (~trans(s70, s71)) | always5(s71)) <=> ((~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6808,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s70, s71)) | (~always5(s70)) | always5(s71)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6807])).
% 49.37/49.61 tff(6809,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6808, 6806])).
% 49.37/49.61 tff(6810,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6811,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6810, 6809])).
% 49.37/49.61 tff(6812,plain,
% 49.37/49.61 ((~always5(s70)) | always5(s71)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6811, 6332, 2131])).
% 49.37/49.61 tff(6813,plain,
% 49.37/49.61 (~always5(s70)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6812, 6805])).
% 49.37/49.61 tff(6814,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s69, s70)) | (~always5(s69)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6815,plain,
% 49.37/49.61 (((~always5(s69)) | (~trans(s69, s70)) | always5(s70)) <=> ((~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6816,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s69, s70)) | (~always5(s69)) | always5(s70)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6815])).
% 49.37/49.61 tff(6817,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6816, 6814])).
% 49.37/49.61 tff(6818,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6819,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 49.37/49.61 tff(6820,plain,
% 49.37/49.61 ((~always5(s69)) | always5(s70)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6819, 6332, 2100])).
% 49.37/49.61 tff(6821,plain,
% 49.37/49.61 (~always5(s69)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6820, 6813])).
% 49.37/49.61 tff(6822,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s68, s69)) | (~always5(s68)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6823,plain,
% 49.37/49.61 (((~always5(s68)) | (~trans(s68, s69)) | always5(s69)) <=> ((~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6824,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s68, s69)) | (~always5(s68)) | always5(s69)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6823])).
% 49.37/49.61 tff(6825,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6824, 6822])).
% 49.37/49.61 tff(6826,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.61 tff(6827,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69)),
% 49.37/49.61 inference(modus_ponens,[status(thm)],[6826, 6825])).
% 49.37/49.61 tff(6828,plain,
% 49.37/49.61 ((~always5(s68)) | always5(s69)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6827, 6332, 2072])).
% 49.37/49.61 tff(6829,plain,
% 49.37/49.61 (~always5(s68)),
% 49.37/49.61 inference(unit_resolution,[status(thm)],[6828, 6821])).
% 49.37/49.61 tff(6830,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s67, s68)) | (~always5(s67)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6831,plain,
% 49.37/49.61 (((~always5(s67)) | (~trans(s67, s68)) | always5(s68)) <=> ((~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 49.37/49.61 inference(rewrite,[status(thm)],[])).
% 49.37/49.61 tff(6832,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s67, s68)) | (~always5(s67)) | always5(s68)))),
% 49.37/49.61 inference(monotonicity,[status(thm)],[6831])).
% 49.37/49.61 tff(6833,plain,
% 49.37/49.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 49.37/49.61 inference(transitivity,[status(thm)],[6832, 6830])).
% 49.37/49.61 tff(6834,plain,
% 49.37/49.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))),
% 49.37/49.61 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6835,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6834, 6833])).
% 49.37/49.62 tff(6836,plain,
% 49.37/49.62 ((~always5(s67)) | always5(s68)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6835, 6332, 2041])).
% 49.37/49.62 tff(6837,plain,
% 49.37/49.62 (~always5(s67)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6836, 6829])).
% 49.37/49.62 tff(6838,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s66, s67)) | (~always5(s66)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6839,plain,
% 49.37/49.62 (((~always5(s66)) | (~trans(s66, s67)) | always5(s67)) <=> ((~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6840,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s66, s67)) | (~always5(s66)) | always5(s67)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6839])).
% 49.37/49.62 tff(6841,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6840, 6838])).
% 49.37/49.62 tff(6842,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6843,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6842, 6841])).
% 49.37/49.62 tff(6844,plain,
% 49.37/49.62 ((~always5(s66)) | always5(s67)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6843, 6332, 2013])).
% 49.37/49.62 tff(6845,plain,
% 49.37/49.62 (~always5(s66)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6844, 6837])).
% 49.37/49.62 tff(6846,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s65, s66)) | (~always5(s65)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6847,plain,
% 49.37/49.62 (((~always5(s65)) | (~trans(s65, s66)) | always5(s66)) <=> ((~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6848,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s65, s66)) | (~always5(s65)) | always5(s66)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6847])).
% 49.37/49.62 tff(6849,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6848, 6846])).
% 49.37/49.62 tff(6850,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6851,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6850, 6849])).
% 49.37/49.62 tff(6852,plain,
% 49.37/49.62 ((~always5(s65)) | always5(s66)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6851, 6332, 1982])).
% 49.37/49.62 tff(6853,plain,
% 49.37/49.62 (~always5(s65)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6852, 6845])).
% 49.37/49.62 tff(6854,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s64, s65)) | (~always5(s64)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6855,plain,
% 49.37/49.62 (((~always5(s64)) | (~trans(s64, s65)) | always5(s65)) <=> ((~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6856,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s64, s65)) | (~always5(s64)) | always5(s65)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6855])).
% 49.37/49.62 tff(6857,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6856, 6854])).
% 49.37/49.62 tff(6858,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6859,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6858, 6857])).
% 49.37/49.62 tff(6860,plain,
% 49.37/49.62 ((~always5(s64)) | always5(s65)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6859, 6332, 1954])).
% 49.37/49.62 tff(6861,plain,
% 49.37/49.62 (~always5(s64)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6860, 6853])).
% 49.37/49.62 tff(6862,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s63, s64)) | (~always5(s63)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6863,plain,
% 49.37/49.62 (((~always5(s63)) | (~trans(s63, s64)) | always5(s64)) <=> ((~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6864,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s63, s64)) | (~always5(s63)) | always5(s64)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6863])).
% 49.37/49.62 tff(6865,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6864, 6862])).
% 49.37/49.62 tff(6866,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6867,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6866, 6865])).
% 49.37/49.62 tff(6868,plain,
% 49.37/49.62 ((~always5(s63)) | always5(s64)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6867, 6332, 1923])).
% 49.37/49.62 tff(6869,plain,
% 49.37/49.62 (~always5(s63)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6868, 6861])).
% 49.37/49.62 tff(6870,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s62, s63)) | (~always5(s62)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6871,plain,
% 49.37/49.62 (((~always5(s62)) | (~trans(s62, s63)) | always5(s63)) <=> ((~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6872,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s62, s63)) | (~always5(s62)) | always5(s63)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6871])).
% 49.37/49.62 tff(6873,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6872, 6870])).
% 49.37/49.62 tff(6874,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6875,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6874, 6873])).
% 49.37/49.62 tff(6876,plain,
% 49.37/49.62 ((~always5(s62)) | always5(s63)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6875, 6332, 1895])).
% 49.37/49.62 tff(6877,plain,
% 49.37/49.62 (~always5(s62)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6876, 6869])).
% 49.37/49.62 tff(6878,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s61, s62)) | (~always5(s61)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6879,plain,
% 49.37/49.62 (((~always5(s61)) | (~trans(s61, s62)) | always5(s62)) <=> ((~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6880,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s61, s62)) | (~always5(s61)) | always5(s62)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6879])).
% 49.37/49.62 tff(6881,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6880, 6878])).
% 49.37/49.62 tff(6882,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6883,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 49.37/49.62 tff(6884,plain,
% 49.37/49.62 ((~always5(s61)) | always5(s62)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6883, 6332, 1864])).
% 49.37/49.62 tff(6885,plain,
% 49.37/49.62 (~always5(s61)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6884, 6877])).
% 49.37/49.62 tff(6886,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s60, s61)) | (~always5(s60)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6887,plain,
% 49.37/49.62 (((~always5(s60)) | (~trans(s60, s61)) | always5(s61)) <=> ((~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6888,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s60, s61)) | (~always5(s60)) | always5(s61)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6887])).
% 49.37/49.62 tff(6889,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6888, 6886])).
% 49.37/49.62 tff(6890,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6891,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6890, 6889])).
% 49.37/49.62 tff(6892,plain,
% 49.37/49.62 ((~always5(s60)) | always5(s61)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6891, 6332, 1836])).
% 49.37/49.62 tff(6893,plain,
% 49.37/49.62 (~always5(s60)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6892, 6885])).
% 49.37/49.62 tff(6894,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s59, s60)) | (~always5(s59)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6895,plain,
% 49.37/49.62 (((~always5(s59)) | (~trans(s59, s60)) | always5(s60)) <=> ((~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6896,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s59, s60)) | (~always5(s59)) | always5(s60)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6895])).
% 49.37/49.62 tff(6897,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6896, 6894])).
% 49.37/49.62 tff(6898,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6899,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6898, 6897])).
% 49.37/49.62 tff(6900,plain,
% 49.37/49.62 ((~always5(s59)) | always5(s60)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6899, 6332, 1805])).
% 49.37/49.62 tff(6901,plain,
% 49.37/49.62 (~always5(s59)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6900, 6893])).
% 49.37/49.62 tff(6902,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s58, s59)) | (~always5(s58)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6903,plain,
% 49.37/49.62 (((~always5(s58)) | (~trans(s58, s59)) | always5(s59)) <=> ((~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6904,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s58, s59)) | (~always5(s58)) | always5(s59)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6903])).
% 49.37/49.62 tff(6905,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6904, 6902])).
% 49.37/49.62 tff(6906,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6907,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6906, 6905])).
% 49.37/49.62 tff(6908,plain,
% 49.37/49.62 ((~always5(s58)) | always5(s59)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6907, 6332, 1777])).
% 49.37/49.62 tff(6909,plain,
% 49.37/49.62 (~always5(s58)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6908, 6901])).
% 49.37/49.62 tff(6910,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6911,plain,
% 49.37/49.62 (((~always5(s57)) | (~trans(s57, s58)) | always5(s58)) <=> ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6912,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s57, s58)) | (~always5(s57)) | always5(s58)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6911])).
% 49.37/49.62 tff(6913,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6912, 6910])).
% 49.37/49.62 tff(6914,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6915,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6914, 6913])).
% 49.37/49.62 tff(6916,plain,
% 49.37/49.62 ((~always5(s57)) | always5(s58)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6915, 6332, 1746])).
% 49.37/49.62 tff(6917,plain,
% 49.37/49.62 (~always5(s57)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6916, 6909])).
% 49.37/49.62 tff(6918,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6919,plain,
% 49.37/49.62 (((~always5(s56)) | (~trans(s56, s57)) | always5(s57)) <=> ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6920,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s56, s57)) | (~always5(s56)) | always5(s57)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6919])).
% 49.37/49.62 tff(6921,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6920, 6918])).
% 49.37/49.62 tff(6922,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6923,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6922, 6921])).
% 49.37/49.62 tff(6924,plain,
% 49.37/49.62 ((~always5(s56)) | always5(s57)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6923, 6332, 1718])).
% 49.37/49.62 tff(6925,plain,
% 49.37/49.62 (~always5(s56)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6924, 6917])).
% 49.37/49.62 tff(6926,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6927,plain,
% 49.37/49.62 (((~always5(s55)) | (~trans(s55, s56)) | always5(s56)) <=> ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6928,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s55, s56)) | (~always5(s55)) | always5(s56)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6927])).
% 49.37/49.62 tff(6929,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6928, 6926])).
% 49.37/49.62 tff(6930,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6931,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6930, 6929])).
% 49.37/49.62 tff(6932,plain,
% 49.37/49.62 ((~always5(s55)) | always5(s56)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6931, 6332, 1687])).
% 49.37/49.62 tff(6933,plain,
% 49.37/49.62 (~always5(s55)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6932, 6925])).
% 49.37/49.62 tff(6934,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6935,plain,
% 49.37/49.62 (((~always5(s54)) | (~trans(s54, s55)) | always5(s55)) <=> ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6936,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s54, s55)) | (~always5(s54)) | always5(s55)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6935])).
% 49.37/49.62 tff(6937,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6936, 6934])).
% 49.37/49.62 tff(6938,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6939,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6938, 6937])).
% 49.37/49.62 tff(6940,plain,
% 49.37/49.62 ((~always5(s54)) | always5(s55)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6939, 6332, 1659])).
% 49.37/49.62 tff(6941,plain,
% 49.37/49.62 (~always5(s54)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6940, 6933])).
% 49.37/49.62 tff(6942,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6943,plain,
% 49.37/49.62 (((~always5(s53)) | (~trans(s53, s54)) | always5(s54)) <=> ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6944,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s53, s54)) | (~always5(s53)) | always5(s54)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6943])).
% 49.37/49.62 tff(6945,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6944, 6942])).
% 49.37/49.62 tff(6946,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6947,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6946, 6945])).
% 49.37/49.62 tff(6948,plain,
% 49.37/49.62 ((~always5(s53)) | always5(s54)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6947, 6332, 1628])).
% 49.37/49.62 tff(6949,plain,
% 49.37/49.62 (~always5(s53)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6948, 6941])).
% 49.37/49.62 tff(6950,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6951,plain,
% 49.37/49.62 (((~always5(s52)) | (~trans(s52, s53)) | always5(s53)) <=> ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6952,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s52, s53)) | (~always5(s52)) | always5(s53)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6951])).
% 49.37/49.62 tff(6953,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6952, 6950])).
% 49.37/49.62 tff(6954,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6955,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6954, 6953])).
% 49.37/49.62 tff(6956,plain,
% 49.37/49.62 ((~always5(s52)) | always5(s53)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6955, 6332, 1600])).
% 49.37/49.62 tff(6957,plain,
% 49.37/49.62 (~always5(s52)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6956, 6949])).
% 49.37/49.62 tff(6958,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6959,plain,
% 49.37/49.62 (((~always5(s51)) | (~trans(s51, s52)) | always5(s52)) <=> ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 49.37/49.62 inference(rewrite,[status(thm)],[])).
% 49.37/49.62 tff(6960,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s51, s52)) | (~always5(s51)) | always5(s52)))),
% 49.37/49.62 inference(monotonicity,[status(thm)],[6959])).
% 49.37/49.62 tff(6961,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 49.37/49.62 inference(transitivity,[status(thm)],[6960, 6958])).
% 49.37/49.62 tff(6962,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))),
% 49.37/49.62 inference(quant_inst,[status(thm)],[])).
% 49.37/49.62 tff(6963,plain,
% 49.37/49.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52)),
% 49.37/49.62 inference(modus_ponens,[status(thm)],[6962, 6961])).
% 49.37/49.62 tff(6964,plain,
% 49.37/49.62 ((~always5(s51)) | always5(s52)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6963, 6332, 1569])).
% 49.37/49.62 tff(6965,plain,
% 49.37/49.62 (~always5(s51)),
% 49.37/49.62 inference(unit_resolution,[status(thm)],[6964, 6957])).
% 49.37/49.62 tff(6966,plain,
% 49.37/49.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6967,plain,
% 49.37/49.63 (((~always5(s50)) | (~trans(s50, s51)) | always5(s51)) <=> ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6968,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s50, s51)) | (~always5(s50)) | always5(s51)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[6967])).
% 49.37/49.63 tff(6969,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 49.37/49.63 inference(transitivity,[status(thm)],[6968, 6966])).
% 49.37/49.63 tff(6970,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(6971,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[6970, 6969])).
% 49.37/49.63 tff(6972,plain,
% 49.37/49.63 ((~always5(s50)) | always5(s51)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6971, 6332, 1541])).
% 49.37/49.63 tff(6973,plain,
% 49.37/49.63 (~always5(s50)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6972, 6965])).
% 49.37/49.63 tff(6974,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6975,plain,
% 49.37/49.63 (((~always5(s49)) | (~trans(s49, s50)) | always5(s50)) <=> ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6976,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s49, s50)) | (~always5(s49)) | always5(s50)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[6975])).
% 49.37/49.63 tff(6977,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 49.37/49.63 inference(transitivity,[status(thm)],[6976, 6974])).
% 49.37/49.63 tff(6978,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(6979,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 49.37/49.63 tff(6980,plain,
% 49.37/49.63 ((~always5(s49)) | always5(s50)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6979, 6332, 1510])).
% 49.37/49.63 tff(6981,plain,
% 49.37/49.63 (~always5(s49)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6980, 6973])).
% 49.37/49.63 tff(6982,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6983,plain,
% 49.37/49.63 (((~always5(s48)) | (~trans(s48, s49)) | always5(s49)) <=> ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6984,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s48, s49)) | (~always5(s48)) | always5(s49)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[6983])).
% 49.37/49.63 tff(6985,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 49.37/49.63 inference(transitivity,[status(thm)],[6984, 6982])).
% 49.37/49.63 tff(6986,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(6987,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[6986, 6985])).
% 49.37/49.63 tff(6988,plain,
% 49.37/49.63 ((~always5(s48)) | always5(s49)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6987, 6332, 1482])).
% 49.37/49.63 tff(6989,plain,
% 49.37/49.63 (~always5(s48)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6988, 6981])).
% 49.37/49.63 tff(6990,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6991,plain,
% 49.37/49.63 (((~always5(s47)) | (~trans(s47, s48)) | always5(s48)) <=> ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6992,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s47, s48)) | (~always5(s47)) | always5(s48)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[6991])).
% 49.37/49.63 tff(6993,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 49.37/49.63 inference(transitivity,[status(thm)],[6992, 6990])).
% 49.37/49.63 tff(6994,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(6995,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[6994, 6993])).
% 49.37/49.63 tff(6996,plain,
% 49.37/49.63 ((~always5(s47)) | always5(s48)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6995, 6332, 1451])).
% 49.37/49.63 tff(6997,plain,
% 49.37/49.63 (~always5(s47)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[6996, 6989])).
% 49.37/49.63 tff(6998,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(6999,plain,
% 49.37/49.63 (((~always5(s46)) | (~trans(s46, s47)) | always5(s47)) <=> ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7000,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s46, s47)) | (~always5(s46)) | always5(s47)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[6999])).
% 49.37/49.63 tff(7001,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 49.37/49.63 inference(transitivity,[status(thm)],[7000, 6998])).
% 49.37/49.63 tff(7002,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(7003,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[7002, 7001])).
% 49.37/49.63 tff(7004,plain,
% 49.37/49.63 ((~always5(s46)) | always5(s47)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7003, 6332, 1423])).
% 49.37/49.63 tff(7005,plain,
% 49.37/49.63 (~always5(s46)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7004, 6997])).
% 49.37/49.63 tff(7006,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7007,plain,
% 49.37/49.63 (((~always5(s45)) | (~trans(s45, s46)) | always5(s46)) <=> ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7008,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s45, s46)) | (~always5(s45)) | always5(s46)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[7007])).
% 49.37/49.63 tff(7009,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 49.37/49.63 inference(transitivity,[status(thm)],[7008, 7006])).
% 49.37/49.63 tff(7010,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(7011,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[7010, 7009])).
% 49.37/49.63 tff(7012,plain,
% 49.37/49.63 ((~always5(s45)) | always5(s46)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7011, 6332, 1392])).
% 49.37/49.63 tff(7013,plain,
% 49.37/49.63 (~always5(s45)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7012, 7005])).
% 49.37/49.63 tff(7014,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7015,plain,
% 49.37/49.63 (((~always5(s44)) | (~trans(s44, s45)) | always5(s45)) <=> ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7016,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s44, s45)) | (~always5(s44)) | always5(s45)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[7015])).
% 49.37/49.63 tff(7017,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 49.37/49.63 inference(transitivity,[status(thm)],[7016, 7014])).
% 49.37/49.63 tff(7018,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))),
% 49.37/49.63 inference(quant_inst,[status(thm)],[])).
% 49.37/49.63 tff(7019,plain,
% 49.37/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45)),
% 49.37/49.63 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 49.37/49.63 tff(7020,plain,
% 49.37/49.63 ((~always5(s44)) | always5(s45)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7019, 6332, 1366])).
% 49.37/49.63 tff(7021,plain,
% 49.37/49.63 (~always5(s44)),
% 49.37/49.63 inference(unit_resolution,[status(thm)],[7020, 7013])).
% 49.37/49.63 tff(7022,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7023,plain,
% 49.37/49.63 (((~always5(s43)) | (~trans(s43, s44)) | always5(s44)) <=> ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 49.37/49.63 inference(rewrite,[status(thm)],[])).
% 49.37/49.63 tff(7024,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s43, s44)) | (~always5(s43)) | always5(s44)))),
% 49.37/49.63 inference(monotonicity,[status(thm)],[7023])).
% 49.37/49.63 tff(7025,plain,
% 49.37/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7024, 7022])).
% 49.47/49.63 tff(7026,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7027,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7026, 7025])).
% 49.47/49.63 tff(7028,plain,
% 49.47/49.63 ((~always5(s43)) | always5(s44)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7027, 6332, 1335])).
% 49.47/49.63 tff(7029,plain,
% 49.47/49.63 (~always5(s43)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7028, 7021])).
% 49.47/49.63 tff(7030,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7031,plain,
% 49.47/49.63 (((~always5(s42)) | (~trans(s42, s43)) | always5(s43)) <=> ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7032,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s42, s43)) | (~always5(s42)) | always5(s43)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7031])).
% 49.47/49.63 tff(7033,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7032, 7030])).
% 49.47/49.63 tff(7034,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7035,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7034, 7033])).
% 49.47/49.63 tff(7036,plain,
% 49.47/49.63 ((~always5(s42)) | always5(s43)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7035, 6332, 1307])).
% 49.47/49.63 tff(7037,plain,
% 49.47/49.63 (~always5(s42)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7036, 7029])).
% 49.47/49.63 tff(7038,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7039,plain,
% 49.47/49.63 (((~always5(s41)) | (~trans(s41, s42)) | always5(s42)) <=> ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7040,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s41, s42)) | (~always5(s41)) | always5(s42)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7039])).
% 49.47/49.63 tff(7041,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7040, 7038])).
% 49.47/49.63 tff(7042,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7043,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7042, 7041])).
% 49.47/49.63 tff(7044,plain,
% 49.47/49.63 ((~always5(s41)) | always5(s42)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7043, 6332, 1276])).
% 49.47/49.63 tff(7045,plain,
% 49.47/49.63 (~always5(s41)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7044, 7037])).
% 49.47/49.63 tff(7046,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7047,plain,
% 49.47/49.63 (((~always5(s40)) | (~trans(s40, s41)) | always5(s41)) <=> ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7048,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s40, s41)) | (~always5(s40)) | always5(s41)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7047])).
% 49.47/49.63 tff(7049,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7048, 7046])).
% 49.47/49.63 tff(7050,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7051,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7050, 7049])).
% 49.47/49.63 tff(7052,plain,
% 49.47/49.63 ((~always5(s40)) | always5(s41)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7051, 6332, 1248])).
% 49.47/49.63 tff(7053,plain,
% 49.47/49.63 (~always5(s40)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7052, 7045])).
% 49.47/49.63 tff(7054,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7055,plain,
% 49.47/49.63 (((~always5(s39)) | (~trans(s39, s40)) | always5(s40)) <=> ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7056,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s39, s40)) | (~always5(s39)) | always5(s40)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7055])).
% 49.47/49.63 tff(7057,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7056, 7054])).
% 49.47/49.63 tff(7058,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7059,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7058, 7057])).
% 49.47/49.63 tff(7060,plain,
% 49.47/49.63 ((~always5(s39)) | always5(s40)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7059, 6332, 1217])).
% 49.47/49.63 tff(7061,plain,
% 49.47/49.63 (~always5(s39)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7060, 7053])).
% 49.47/49.63 tff(7062,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7063,plain,
% 49.47/49.63 (((~always5(s38)) | (~trans(s38, s39)) | always5(s39)) <=> ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7064,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s38, s39)) | (~always5(s38)) | always5(s39)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7063])).
% 49.47/49.63 tff(7065,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7064, 7062])).
% 49.47/49.63 tff(7066,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7067,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7066, 7065])).
% 49.47/49.63 tff(7068,plain,
% 49.47/49.63 ((~always5(s38)) | always5(s39)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7067, 6332, 1189])).
% 49.47/49.63 tff(7069,plain,
% 49.47/49.63 (~always5(s38)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7068, 7061])).
% 49.47/49.63 tff(7070,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7071,plain,
% 49.47/49.63 (((~always5(s37)) | (~trans(s37, s38)) | always5(s38)) <=> ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7072,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s37, s38)) | (~always5(s37)) | always5(s38)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7071])).
% 49.47/49.63 tff(7073,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7072, 7070])).
% 49.47/49.63 tff(7074,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7075,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7074, 7073])).
% 49.47/49.63 tff(7076,plain,
% 49.47/49.63 ((~always5(s37)) | always5(s38)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7075, 6332, 1158])).
% 49.47/49.63 tff(7077,plain,
% 49.47/49.63 (~always5(s37)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7076, 7069])).
% 49.47/49.63 tff(7078,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7079,plain,
% 49.47/49.63 (((~always5(s36)) | (~trans(s36, s37)) | always5(s37)) <=> ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7080,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s36, s37)) | (~always5(s36)) | always5(s37)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7079])).
% 49.47/49.63 tff(7081,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7080, 7078])).
% 49.47/49.63 tff(7082,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7083,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7082, 7081])).
% 49.47/49.63 tff(7084,plain,
% 49.47/49.63 ((~always5(s36)) | always5(s37)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7083, 6332, 1130])).
% 49.47/49.63 tff(7085,plain,
% 49.47/49.63 (~always5(s36)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7084, 7077])).
% 49.47/49.63 tff(7086,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7087,plain,
% 49.47/49.63 (((~always5(s35)) | (~trans(s35, s36)) | always5(s36)) <=> ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7088,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s35, s36)) | (~always5(s35)) | always5(s36)))),
% 49.47/49.63 inference(monotonicity,[status(thm)],[7087])).
% 49.47/49.63 tff(7089,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 49.47/49.63 inference(transitivity,[status(thm)],[7088, 7086])).
% 49.47/49.63 tff(7090,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))),
% 49.47/49.63 inference(quant_inst,[status(thm)],[])).
% 49.47/49.63 tff(7091,plain,
% 49.47/49.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36)),
% 49.47/49.63 inference(modus_ponens,[status(thm)],[7090, 7089])).
% 49.47/49.63 tff(7092,plain,
% 49.47/49.63 ((~always5(s35)) | always5(s36)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7091, 6332, 1099])).
% 49.47/49.63 tff(7093,plain,
% 49.47/49.63 (~always5(s35)),
% 49.47/49.63 inference(unit_resolution,[status(thm)],[7092, 7085])).
% 49.47/49.63 tff(7094,plain,
% 49.47/49.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7095,plain,
% 49.47/49.63 (((~always5(s34)) | (~trans(s34, s35)) | always5(s35)) <=> ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 49.47/49.63 inference(rewrite,[status(thm)],[])).
% 49.47/49.63 tff(7096,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s34, s35)) | (~always5(s34)) | always5(s35)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7095])).
% 49.47/49.64 tff(7097,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7096, 7094])).
% 49.47/49.64 tff(7098,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7099,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7098, 7097])).
% 49.47/49.64 tff(7100,plain,
% 49.47/49.64 ((~always5(s34)) | always5(s35)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7099, 6332, 1071])).
% 49.47/49.64 tff(7101,plain,
% 49.47/49.64 (~always5(s34)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7100, 7093])).
% 49.47/49.64 tff(7102,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7103,plain,
% 49.47/49.64 (((~always5(s33)) | (~trans(s33, s34)) | always5(s34)) <=> ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7104,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s33, s34)) | (~always5(s33)) | always5(s34)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7103])).
% 49.47/49.64 tff(7105,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7104, 7102])).
% 49.47/49.64 tff(7106,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7107,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 49.47/49.64 tff(7108,plain,
% 49.47/49.64 ((~always5(s33)) | always5(s34)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7107, 6332, 1040])).
% 49.47/49.64 tff(7109,plain,
% 49.47/49.64 (~always5(s33)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7108, 7101])).
% 49.47/49.64 tff(7110,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7111,plain,
% 49.47/49.64 (((~always5(s32)) | (~trans(s32, s33)) | always5(s33)) <=> ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7112,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s32, s33)) | (~always5(s32)) | always5(s33)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7111])).
% 49.47/49.64 tff(7113,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7112, 7110])).
% 49.47/49.64 tff(7114,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7115,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7114, 7113])).
% 49.47/49.64 tff(7116,plain,
% 49.47/49.64 ((~always5(s32)) | always5(s33)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7115, 6332, 1012])).
% 49.47/49.64 tff(7117,plain,
% 49.47/49.64 (~always5(s32)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7116, 7109])).
% 49.47/49.64 tff(7118,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7119,plain,
% 49.47/49.64 (((~always5(s31)) | (~trans(s31, s32)) | always5(s32)) <=> ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7120,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s31, s32)) | (~always5(s31)) | always5(s32)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7119])).
% 49.47/49.64 tff(7121,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7120, 7118])).
% 49.47/49.64 tff(7122,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7123,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7122, 7121])).
% 49.47/49.64 tff(7124,plain,
% 49.47/49.64 ((~always5(s31)) | always5(s32)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7123, 6332, 981])).
% 49.47/49.64 tff(7125,plain,
% 49.47/49.64 (~always5(s31)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7124, 7117])).
% 49.47/49.64 tff(7126,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7127,plain,
% 49.47/49.64 (((~always5(s30)) | (~trans(s30, s31)) | always5(s31)) <=> ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7128,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s30, s31)) | (~always5(s30)) | always5(s31)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7127])).
% 49.47/49.64 tff(7129,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7128, 7126])).
% 49.47/49.64 tff(7130,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7131,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7130, 7129])).
% 49.47/49.64 tff(7132,plain,
% 49.47/49.64 ((~always5(s30)) | always5(s31)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7131, 6332, 953])).
% 49.47/49.64 tff(7133,plain,
% 49.47/49.64 (~always5(s30)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7132, 7125])).
% 49.47/49.64 tff(7134,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7135,plain,
% 49.47/49.64 (((~always5(s29)) | (~trans(s29, s30)) | always5(s30)) <=> ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7136,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s29, s30)) | (~always5(s29)) | always5(s30)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7135])).
% 49.47/49.64 tff(7137,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7136, 7134])).
% 49.47/49.64 tff(7138,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7139,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7138, 7137])).
% 49.47/49.64 tff(7140,plain,
% 49.47/49.64 ((~always5(s29)) | always5(s30)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7139, 6332, 922])).
% 49.47/49.64 tff(7141,plain,
% 49.47/49.64 (~always5(s29)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7140, 7133])).
% 49.47/49.64 tff(7142,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7143,plain,
% 49.47/49.64 (((~always5(s28)) | (~trans(s28, s29)) | always5(s29)) <=> ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7144,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s28, s29)) | (~always5(s28)) | always5(s29)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7143])).
% 49.47/49.64 tff(7145,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7144, 7142])).
% 49.47/49.64 tff(7146,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7147,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7146, 7145])).
% 49.47/49.64 tff(7148,plain,
% 49.47/49.64 ((~always5(s28)) | always5(s29)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7147, 6332, 894])).
% 49.47/49.64 tff(7149,plain,
% 49.47/49.64 (~always5(s28)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7148, 7141])).
% 49.47/49.64 tff(7150,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7151,plain,
% 49.47/49.64 (((~always5(s27)) | (~trans(s27, s28)) | always5(s28)) <=> ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7152,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s27, s28)) | (~always5(s27)) | always5(s28)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7151])).
% 49.47/49.64 tff(7153,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7152, 7150])).
% 49.47/49.64 tff(7154,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7155,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7154, 7153])).
% 49.47/49.64 tff(7156,plain,
% 49.47/49.64 ((~always5(s27)) | always5(s28)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7155, 6332, 865])).
% 49.47/49.64 tff(7157,plain,
% 49.47/49.64 (~always5(s27)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7156, 7149])).
% 49.47/49.64 tff(7158,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7159,plain,
% 49.47/49.64 (((~always5(s26)) | (~trans(s26, s27)) | always5(s27)) <=> ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7160,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s26, s27)) | (~always5(s26)) | always5(s27)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7159])).
% 49.47/49.64 tff(7161,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7160, 7158])).
% 49.47/49.64 tff(7162,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7163,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7162, 7161])).
% 49.47/49.64 tff(7164,plain,
% 49.47/49.64 ((~always5(s26)) | always5(s27)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7163, 6332, 837])).
% 49.47/49.64 tff(7165,plain,
% 49.47/49.64 (~always5(s26)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7164, 7157])).
% 49.47/49.64 tff(7166,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7167,plain,
% 49.47/49.64 (((~always5(s25)) | (~trans(s25, s26)) | always5(s26)) <=> ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7168,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s25, s26)) | (~always5(s25)) | always5(s26)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7167])).
% 49.47/49.64 tff(7169,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7168, 7166])).
% 49.47/49.64 tff(7170,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7171,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7170, 7169])).
% 49.47/49.64 tff(7172,plain,
% 49.47/49.64 ((~always5(s25)) | always5(s26)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7171, 6332, 806])).
% 49.47/49.64 tff(7173,plain,
% 49.47/49.64 (~always5(s25)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7172, 7165])).
% 49.47/49.64 tff(7174,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7175,plain,
% 49.47/49.64 (((~always5(s24)) | (~trans(s24, s25)) | always5(s25)) <=> ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7176,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s24, s25)) | (~always5(s24)) | always5(s25)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7175])).
% 49.47/49.64 tff(7177,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7176, 7174])).
% 49.47/49.64 tff(7178,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7179,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7178, 7177])).
% 49.47/49.64 tff(7180,plain,
% 49.47/49.64 ((~always5(s24)) | always5(s25)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7179, 6332, 780])).
% 49.47/49.64 tff(7181,plain,
% 49.47/49.64 (~always5(s24)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7180, 7173])).
% 49.47/49.64 tff(7182,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7183,plain,
% 49.47/49.64 (((~always5(s23)) | (~trans(s23, s24)) | always5(s24)) <=> ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7184,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s23, s24)) | (~always5(s23)) | always5(s24)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7183])).
% 49.47/49.64 tff(7185,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7184, 7182])).
% 49.47/49.64 tff(7186,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7187,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7186, 7185])).
% 49.47/49.64 tff(7188,plain,
% 49.47/49.64 ((~always5(s23)) | always5(s24)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7187, 6332, 749])).
% 49.47/49.64 tff(7189,plain,
% 49.47/49.64 (~always5(s23)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7188, 7181])).
% 49.47/49.64 tff(7190,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7191,plain,
% 49.47/49.64 (((~always5(s22)) | (~trans(s22, s23)) | always5(s23)) <=> ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7192,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s22, s23)) | (~always5(s22)) | always5(s23)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7191])).
% 49.47/49.64 tff(7193,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7192, 7190])).
% 49.47/49.64 tff(7194,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7195,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7194, 7193])).
% 49.47/49.64 tff(7196,plain,
% 49.47/49.64 ((~always5(s22)) | always5(s23)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7195, 6332, 721])).
% 49.47/49.64 tff(7197,plain,
% 49.47/49.64 (~always5(s22)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7196, 7189])).
% 49.47/49.64 tff(7198,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7199,plain,
% 49.47/49.64 (((~always5(s21)) | (~trans(s21, s22)) | always5(s22)) <=> ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7200,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s21, s22)) | (~always5(s21)) | always5(s22)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7199])).
% 49.47/49.64 tff(7201,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7200, 7198])).
% 49.47/49.64 tff(7202,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7203,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7202, 7201])).
% 49.47/49.64 tff(7204,plain,
% 49.47/49.64 ((~always5(s21)) | always5(s22)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7203, 6332, 690])).
% 49.47/49.64 tff(7205,plain,
% 49.47/49.64 (~always5(s21)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7204, 7197])).
% 49.47/49.64 tff(7206,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7207,plain,
% 49.47/49.64 (((~always5(s20)) | (~trans(s20, s21)) | always5(s21)) <=> ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7208,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s20, s21)) | (~always5(s20)) | always5(s21)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7207])).
% 49.47/49.64 tff(7209,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7208, 7206])).
% 49.47/49.64 tff(7210,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7211,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7210, 7209])).
% 49.47/49.64 tff(7212,plain,
% 49.47/49.64 ((~always5(s20)) | always5(s21)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7211, 6332, 662])).
% 49.47/49.64 tff(7213,plain,
% 49.47/49.64 (~always5(s20)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7212, 7205])).
% 49.47/49.64 tff(7214,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7215,plain,
% 49.47/49.64 (((~always5(s19)) | (~trans(s19, s20)) | always5(s20)) <=> ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7216,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s19, s20)) | (~always5(s19)) | always5(s20)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7215])).
% 49.47/49.64 tff(7217,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 49.47/49.64 inference(transitivity,[status(thm)],[7216, 7214])).
% 49.47/49.64 tff(7218,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))),
% 49.47/49.64 inference(quant_inst,[status(thm)],[])).
% 49.47/49.64 tff(7219,plain,
% 49.47/49.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20)),
% 49.47/49.64 inference(modus_ponens,[status(thm)],[7218, 7217])).
% 49.47/49.64 tff(7220,plain,
% 49.47/49.64 ((~always5(s19)) | always5(s20)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7219, 6332, 633])).
% 49.47/49.64 tff(7221,plain,
% 49.47/49.64 (~always5(s19)),
% 49.47/49.64 inference(unit_resolution,[status(thm)],[7220, 7213])).
% 49.47/49.64 tff(7222,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7223,plain,
% 49.47/49.64 (((~always5(s18)) | (~trans(s18, s19)) | always5(s19)) <=> ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 49.47/49.64 inference(rewrite,[status(thm)],[])).
% 49.47/49.64 tff(7224,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s18, s19)) | (~always5(s18)) | always5(s19)))),
% 49.47/49.64 inference(monotonicity,[status(thm)],[7223])).
% 49.47/49.64 tff(7225,plain,
% 49.47/49.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7224, 7222])).
% 49.47/49.65 tff(7226,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7227,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7226, 7225])).
% 49.47/49.65 tff(7228,plain,
% 49.47/49.65 ((~always5(s18)) | always5(s19)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7227, 6332, 605])).
% 49.47/49.65 tff(7229,plain,
% 49.47/49.65 (~always5(s18)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7228, 7221])).
% 49.47/49.65 tff(7230,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7231,plain,
% 49.47/49.65 (((~always5(s17)) | (~trans(s17, s18)) | always5(s18)) <=> ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7232,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s17, s18)) | (~always5(s17)) | always5(s18)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7231])).
% 49.47/49.65 tff(7233,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7232, 7230])).
% 49.47/49.65 tff(7234,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7235,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 49.47/49.65 tff(7236,plain,
% 49.47/49.65 ((~always5(s17)) | always5(s18)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7235, 6332, 574])).
% 49.47/49.65 tff(7237,plain,
% 49.47/49.65 (~always5(s17)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7236, 7229])).
% 49.47/49.65 tff(7238,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7239,plain,
% 49.47/49.65 (((~always5(s16)) | (~trans(s16, s17)) | always5(s17)) <=> ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7240,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s16, s17)) | (~always5(s16)) | always5(s17)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7239])).
% 49.47/49.65 tff(7241,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7240, 7238])).
% 49.47/49.65 tff(7242,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7243,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 49.47/49.65 tff(7244,plain,
% 49.47/49.65 ((~always5(s16)) | always5(s17)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7243, 6332, 546])).
% 49.47/49.65 tff(7245,plain,
% 49.47/49.65 (~always5(s16)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7244, 7237])).
% 49.47/49.65 tff(7246,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7247,plain,
% 49.47/49.65 (((~always5(s15)) | (~trans(s15, s16)) | always5(s16)) <=> ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7248,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s15, s16)) | (~always5(s15)) | always5(s16)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7247])).
% 49.47/49.65 tff(7249,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7248, 7246])).
% 49.47/49.65 tff(7250,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7251,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7250, 7249])).
% 49.47/49.65 tff(7252,plain,
% 49.47/49.65 ((~always5(s15)) | always5(s16)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7251, 6332, 517])).
% 49.47/49.65 tff(7253,plain,
% 49.47/49.65 (~always5(s15)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7252, 7245])).
% 49.47/49.65 tff(7254,assumption,(~always5(s15)), introduced(assumption)).
% 49.47/49.65 tff(7255,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7256,plain,
% 49.47/49.65 (((~always5(s14)) | (~trans(s14, s15)) | always5(s15)) <=> ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7257,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s14, s15)) | (~always5(s14)) | always5(s15)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7256])).
% 49.47/49.65 tff(7258,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7257, 7255])).
% 49.47/49.65 tff(7259,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7260,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7259, 7258])).
% 49.47/49.65 tff(7261,plain,
% 49.47/49.65 ((~always5(s14)) | always5(s15)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7260, 6332, 489])).
% 49.47/49.65 tff(7262,plain,
% 49.47/49.65 (~always5(s14)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7261, 7254])).
% 49.47/49.65 tff(7263,assumption,(~xuntil7(s15)), introduced(assumption)).
% 49.47/49.65 tff(7264,plain,
% 49.47/49.65 (^[X: $i] : refl((always5(X) | (~until6(X)) | xuntil7(X)) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 49.47/49.65 inference(bind,[status(th)],[])).
% 49.47/49.65 tff(7265,plain,
% 49.47/49.65 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(quant_intro,[status(thm)],[7264])).
% 49.47/49.65 tff(7266,plain,
% 49.47/49.65 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7267,plain,
% 49.47/49.65 (^[X: $i] : rewrite(((always5(X) | xuntil7(X)) | (~until6(X))) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 49.47/49.65 inference(bind,[status(th)],[])).
% 49.47/49.65 tff(7268,plain,
% 49.47/49.65 (![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X))) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(quant_intro,[status(thm)],[7267])).
% 49.47/49.65 tff(7269,axiom,(![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty4')).
% 49.47/49.65 tff(7270,plain,
% 49.47/49.65 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7269, 7268])).
% 49.47/49.65 tff(7271,plain,
% 49.47/49.65 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7270, 7266])).
% 49.47/49.65 tff(7272,plain,(
% 49.47/49.65 ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(skolemize,[status(sab)],[7271])).
% 49.47/49.65 tff(7273,plain,
% 49.47/49.65 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7272, 7265])).
% 49.47/49.65 tff(7274,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s15) | always5(s15) | (~until6(s15)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7275,plain,
% 49.47/49.65 ((always5(s15) | (~until6(s15)) | xuntil7(s15)) <=> (xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7276,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s15) | always5(s15) | (~until6(s15))))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7275])).
% 49.47/49.65 tff(7277,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7276, 7274])).
% 49.47/49.65 tff(7278,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7279,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7278, 7277])).
% 49.47/49.65 tff(7280,plain,
% 49.47/49.65 (always5(s15) | (~until6(s15))),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7279, 7273, 7263])).
% 49.47/49.65 tff(7281,plain,
% 49.47/49.65 (~until6(s15)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7280, 7254])).
% 49.47/49.65 tff(7282,plain,
% 49.47/49.65 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 49.47/49.65 inference(bind,[status(th)],[])).
% 49.47/49.65 tff(7283,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(quant_intro,[status(thm)],[7282])).
% 49.47/49.65 tff(7284,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7285,plain,
% 49.47/49.65 (^[Y: $i, X: $i] : rewrite(((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 49.47/49.65 inference(bind,[status(th)],[])).
% 49.47/49.65 tff(7286,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(quant_intro,[status(thm)],[7285])).
% 49.47/49.65 tff(7287,axiom,(![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty5')).
% 49.47/49.65 tff(7288,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7287, 7286])).
% 49.47/49.65 tff(7289,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7288, 7284])).
% 49.47/49.65 tff(7290,plain,(
% 49.47/49.65 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(skolemize,[status(sab)],[7289])).
% 49.47/49.65 tff(7291,plain,
% 49.47/49.65 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7290, 7283])).
% 49.47/49.65 tff(7292,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7293,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7294,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 49.47/49.65 tff(7295,plain,
% 49.47/49.65 ((~xuntil7(s14)) | until6(s15)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7294, 485, 7291])).
% 49.47/49.65 tff(7296,plain,
% 49.47/49.65 (~xuntil7(s14)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7295, 7281])).
% 49.47/49.65 tff(7297,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s14) | always5(s14) | (~until6(s14)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7298,plain,
% 49.47/49.65 ((always5(s14) | (~until6(s14)) | xuntil7(s14)) <=> (xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7299,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s14) | always5(s14) | (~until6(s14))))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7298])).
% 49.47/49.65 tff(7300,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7299, 7297])).
% 49.47/49.65 tff(7301,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7302,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7301, 7300])).
% 49.47/49.65 tff(7303,plain,
% 49.47/49.65 (~until6(s14)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7302, 7273, 7296, 7262])).
% 49.47/49.65 tff(7304,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7305,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7306,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7305, 7304])).
% 49.47/49.65 tff(7307,plain,
% 49.47/49.65 ((~xuntil7(s13)) | until6(s14)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7306, 454, 7291])).
% 49.47/49.65 tff(7308,plain,
% 49.47/49.65 (~xuntil7(s13)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7307, 7303])).
% 49.47/49.65 tff(7309,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7310,plain,
% 49.47/49.65 (((~always5(s13)) | (~trans(s13, s14)) | always5(s14)) <=> ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7311,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s13, s14)) | (~always5(s13)) | always5(s14)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7310])).
% 49.47/49.65 tff(7312,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7311, 7309])).
% 49.47/49.65 tff(7313,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7314,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7313, 7312])).
% 49.47/49.65 tff(7315,plain,
% 49.47/49.65 ((~always5(s13)) | always5(s14)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7314, 6332, 458])).
% 49.47/49.65 tff(7316,plain,
% 49.47/49.65 (~always5(s13)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7315, 7262])).
% 49.47/49.65 tff(7317,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s13) | always5(s13) | (~until6(s13)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7318,plain,
% 49.47/49.65 ((always5(s13) | (~until6(s13)) | xuntil7(s13)) <=> (xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7319,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s13) | always5(s13) | (~until6(s13))))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7318])).
% 49.47/49.65 tff(7320,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7319, 7317])).
% 49.47/49.65 tff(7321,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7322,plain,
% 49.47/49.65 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13))),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 49.47/49.65 tff(7323,plain,
% 49.47/49.65 (xuntil7(s13) | (~until6(s13))),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7322, 7273, 7316])).
% 49.47/49.65 tff(7324,plain,
% 49.47/49.65 (~until6(s13)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7323, 7308])).
% 49.47/49.65 tff(7325,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7326,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7327,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7326, 7325])).
% 49.47/49.65 tff(7328,plain,
% 49.47/49.65 ((~xuntil7(s12)) | until6(s13)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7327, 426, 7291])).
% 49.47/49.65 tff(7329,plain,
% 49.47/49.65 (~xuntil7(s12)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7328, 7324])).
% 49.47/49.65 tff(7330,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7331,plain,
% 49.47/49.65 (((~always5(s12)) | (~trans(s12, s13)) | always5(s13)) <=> ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7332,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s12, s13)) | (~always5(s12)) | always5(s13)))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7331])).
% 49.47/49.65 tff(7333,plain,
% 49.47/49.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7332, 7330])).
% 49.47/49.65 tff(7334,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))),
% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7335,plain,
% 49.47/49.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13)),
% 49.47/49.65 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 49.47/49.65 tff(7336,plain,
% 49.47/49.65 ((~always5(s12)) | always5(s13)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7335, 6332, 430])).
% 49.47/49.65 tff(7337,plain,
% 49.47/49.65 (~always5(s12)),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7336, 7316])).
% 49.47/49.65 tff(7338,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s12) | always5(s12) | (~until6(s12)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7339,plain,
% 49.47/49.65 ((always5(s12) | (~until6(s12)) | xuntil7(s12)) <=> (xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7340,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s12) | always5(s12) | (~until6(s12))))),
% 49.47/49.65 inference(monotonicity,[status(thm)],[7339])).
% 49.47/49.65 tff(7341,plain,
% 49.47/49.65 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 49.47/49.65 inference(transitivity,[status(thm)],[7340, 7338])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7343,plain,
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% 49.47/49.65 inference(modus_ponens,[status(thm)],[7342, 7341])).
% 49.47/49.65 tff(7344,plain,
% 49.47/49.65 (xuntil7(s12) | (~until6(s12))),
% 49.47/49.65 inference(unit_resolution,[status(thm)],[7343, 7273, 7337])).
% 49.47/49.65 tff(7345,plain,
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7344, 7329])).
% 49.47/49.65 tff(7346,plain,
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7347,plain,
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.65 inference(modus_ponens,[status(thm)],[7347, 7346])).
% 49.47/49.65 tff(7349,plain,
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7348, 395, 7291])).
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7349, 7345])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7352,plain,
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
% 49.47/49.65 tff(7353,plain,
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% 49.47/49.65 inference(monotonicity,[status(thm)],[7352])).
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% 49.47/49.65 inference(transitivity,[status(thm)],[7353, 7351])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
% 49.47/49.65 tff(7356,plain,
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% 49.47/49.65 inference(modus_ponens,[status(thm)],[7355, 7354])).
% 49.47/49.65 tff(7357,plain,
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7356, 6332, 399])).
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7357, 7337])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(monotonicity,[status(thm)],[7360])).
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% 49.47/49.65 inference(transitivity,[status(thm)],[7361, 7359])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.65 inference(modus_ponens,[status(thm)],[7363, 7362])).
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7364, 7273, 7358])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.65 inference(modus_ponens,[status(thm)],[7368, 7367])).
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% 49.47/49.65 inference(unit_resolution,[status(thm)],[7369, 367, 7291])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(monotonicity,[status(thm)],[7373])).
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% 49.47/49.65 inference(transitivity,[status(thm)],[7374, 7372])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.65 inference(rewrite,[status(thm)],[])).
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% 49.47/49.65 inference(monotonicity,[status(thm)],[7381])).
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% 49.47/49.65 inference(transitivity,[status(thm)],[7382, 7380])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.65 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.66 inference(modus_ponens,[status(thm)],[7389, 7388])).
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% 49.47/49.66 inference(rewrite,[status(thm)],[])).
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% 49.47/49.66 inference(monotonicity,[status(thm)],[7394])).
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% 49.47/49.66 inference(transitivity,[status(thm)],[7395, 7393])).
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% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.66 inference(rewrite,[status(thm)],[])).
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% 49.47/49.66 inference(monotonicity,[status(thm)],[7402])).
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% 49.47/49.66 inference(transitivity,[status(thm)],[7403, 7401])).
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% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.66 tff(7408,plain,
% 49.47/49.66 (~until6(s9)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7407, 7392])).
% 49.47/49.66 tff(7409,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7410,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7411,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7410, 7409])).
% 49.47/49.66 tff(7412,plain,
% 49.47/49.66 ((~xuntil7(s8)) | until6(s9)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7411, 310, 7291])).
% 49.47/49.66 tff(7413,plain,
% 49.47/49.66 (~xuntil7(s8)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7412, 7408])).
% 49.47/49.66 tff(7414,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7415,plain,
% 49.47/49.66 (((~always5(s8)) | (~trans(s8, s9)) | always5(s9)) <=> ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7416,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s8, s9)) | (~always5(s8)) | always5(s9)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7415])).
% 49.47/49.66 tff(7417,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7416, 7414])).
% 49.47/49.66 tff(7418,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7419,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 49.47/49.66 tff(7420,plain,
% 49.47/49.66 ((~always5(s8)) | always5(s9)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7419, 6332, 314])).
% 49.47/49.66 tff(7421,plain,
% 49.47/49.66 (~always5(s8)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7420, 7400])).
% 49.47/49.66 tff(7422,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s8) | always5(s8) | (~until6(s8)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7423,plain,
% 49.47/49.66 ((always5(s8) | (~until6(s8)) | xuntil7(s8)) <=> (xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7424,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s8) | always5(s8) | (~until6(s8))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7423])).
% 49.47/49.66 tff(7425,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7424, 7422])).
% 49.47/49.66 tff(7426,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7427,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8))),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 49.47/49.66 tff(7428,plain,
% 49.47/49.66 (xuntil7(s8) | (~until6(s8))),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7427, 7273, 7421])).
% 49.47/49.66 tff(7429,plain,
% 49.47/49.66 (~until6(s8)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7428, 7413])).
% 49.47/49.66 tff(7430,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7431,plain,
% 49.47/49.66 (((~always5(s7)) | (~trans(s7, s8)) | always5(s8)) <=> ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7432,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s7, s8)) | (~always5(s7)) | always5(s8)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7431])).
% 49.47/49.66 tff(7433,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7432, 7430])).
% 49.47/49.66 tff(7434,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7435,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7434, 7433])).
% 49.47/49.66 tff(7436,plain,
% 49.47/49.66 ((~always5(s7)) | always5(s8)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7435, 6332, 285])).
% 49.47/49.66 tff(7437,plain,
% 49.47/49.66 (~always5(s7)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7436, 7421])).
% 49.47/49.66 tff(7438,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7439,plain,
% 49.47/49.66 (((~always5(s6)) | (~trans(s6, s7)) | always5(s7)) <=> ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7440,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s6, s7)) | (~always5(s6)) | always5(s7)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7439])).
% 49.47/49.66 tff(7441,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7440, 7438])).
% 49.47/49.66 tff(7442,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7443,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 49.47/49.66 tff(7444,plain,
% 49.47/49.66 ((~always5(s6)) | always5(s7)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7443, 6332, 14])).
% 49.47/49.66 tff(7445,plain,
% 49.47/49.66 (~always5(s6)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7444, 7437])).
% 49.47/49.66 tff(7446,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7447,plain,
% 49.47/49.66 (((~always5(s5)) | (~trans(s5, s6)) | always5(s6)) <=> ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7448,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s5, s6)) | (~always5(s5)) | always5(s6)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7447])).
% 49.47/49.66 tff(7449,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7448, 7446])).
% 49.47/49.66 tff(7450,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7451,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7450, 7449])).
% 49.47/49.66 tff(7452,plain,
% 49.47/49.66 ((~always5(s5)) | always5(s6)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7451, 6332, 238])).
% 49.47/49.66 tff(7453,plain,
% 49.47/49.66 (~always5(s5)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7452, 7445])).
% 49.47/49.66 tff(7454,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7455,plain,
% 49.47/49.66 (((~always5(s4)) | (~trans(s4, s5)) | always5(s5)) <=> ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7456,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s4, s5)) | (~always5(s4)) | always5(s5)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7455])).
% 49.47/49.66 tff(7457,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7456, 7454])).
% 49.47/49.66 tff(7458,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7459,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7458, 7457])).
% 49.47/49.66 tff(7460,plain,
% 49.47/49.66 ((~always5(s4)) | always5(s5)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7459, 6332, 210])).
% 49.47/49.66 tff(7461,plain,
% 49.47/49.66 (~always5(s4)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7460, 7453])).
% 49.47/49.66 tff(7462,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7463,plain,
% 49.47/49.66 (((~always5(s3)) | (~trans(s3, s4)) | always5(s4)) <=> ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7464,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s3, s4)) | (~always5(s3)) | always5(s4)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7463])).
% 49.47/49.66 tff(7465,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7464, 7462])).
% 49.47/49.66 tff(7466,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7467,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 49.47/49.66 tff(7468,plain,
% 49.47/49.66 ((~always5(s3)) | always5(s4)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7467, 6332, 181])).
% 49.47/49.66 tff(7469,plain,
% 49.47/49.66 (~always5(s3)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7468, 7461])).
% 49.47/49.66 tff(7470,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7471,plain,
% 49.47/49.66 (((~always5(s2)) | (~trans(s2, s3)) | always5(s3)) <=> ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7472,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s2, s3)) | (~always5(s2)) | always5(s3)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7471])).
% 49.47/49.66 tff(7473,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7472, 7470])).
% 49.47/49.66 tff(7474,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7475,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7474, 7473])).
% 49.47/49.66 tff(7476,plain,
% 49.47/49.66 ((~always5(s2)) | always5(s3)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7475, 6332, 155])).
% 49.47/49.66 tff(7477,plain,
% 49.47/49.66 (~always5(s2)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7476, 7469])).
% 49.47/49.66 tff(7478,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7479,plain,
% 49.47/49.66 (((~always5(s1)) | (~trans(s1, s2)) | always5(s2)) <=> ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7480,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s1, s2)) | (~always5(s1)) | always5(s2)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7479])).
% 49.47/49.66 tff(7481,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7480, 7478])).
% 49.47/49.66 tff(7482,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7483,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7482, 7481])).
% 49.47/49.66 tff(7484,plain,
% 49.47/49.66 ((~always5(s1)) | always5(s2)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7483, 6332, 116])).
% 49.47/49.66 tff(7485,plain,
% 49.47/49.66 (~always5(s1)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7484, 7477])).
% 49.47/49.66 tff(7486,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7487,plain,
% 49.47/49.66 (((~always5(s0)) | (~trans(s0, s1)) | always5(s1)) <=> ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7488,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s0, s1)) | (~always5(s0)) | always5(s1)))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7487])).
% 49.47/49.66 tff(7489,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7488, 7486])).
% 49.47/49.66 tff(7490,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7491,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7490, 7489])).
% 49.47/49.66 tff(7492,plain,
% 49.47/49.66 ((~always5(s0)) | always5(s1)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7491, 6332, 70])).
% 49.47/49.66 tff(7493,plain,
% 49.47/49.66 (~always5(s0)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7492, 7485])).
% 49.47/49.66 tff(7494,plain,
% 49.47/49.66 (until6(s0) <=> until6(s0)),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7495,axiom,(until6(s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty11')).
% 49.47/49.66 tff(7496,plain,
% 49.47/49.66 (until6(s0)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7495, 7494])).
% 49.47/49.66 tff(7497,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s0) | always5(s0) | (~until6(s0)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7498,plain,
% 49.47/49.66 ((always5(s0) | (~until6(s0)) | xuntil7(s0)) <=> (xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7499,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s0) | always5(s0) | (~until6(s0))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7498])).
% 49.47/49.66 tff(7500,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7499, 7497])).
% 49.47/49.66 tff(7501,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7502,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0))),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7501, 7500])).
% 49.47/49.66 tff(7503,plain,
% 49.47/49.66 (xuntil7(s0) | always5(s0)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7502, 7273, 7496])).
% 49.47/49.66 tff(7504,plain,
% 49.47/49.66 (xuntil7(s0)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7503, 7493])).
% 49.47/49.66 tff(7505,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7506,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7507,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7506, 7505])).
% 49.47/49.66 tff(7508,plain,
% 49.47/49.66 ((~xuntil7(s0)) | until6(s1)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7507, 66, 7291])).
% 49.47/49.66 tff(7509,plain,
% 49.47/49.66 (until6(s1)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7508, 7504])).
% 49.47/49.66 tff(7510,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s1) | always5(s1) | (~until6(s1)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7511,plain,
% 49.47/49.66 ((always5(s1) | (~until6(s1)) | xuntil7(s1)) <=> (xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7512,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s1) | always5(s1) | (~until6(s1))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7511])).
% 49.47/49.66 tff(7513,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7512, 7510])).
% 49.47/49.66 tff(7514,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7515,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1))),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7514, 7513])).
% 49.47/49.66 tff(7516,plain,
% 49.47/49.66 (xuntil7(s1)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7515, 7273, 7509, 7485])).
% 49.47/49.66 tff(7517,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7518,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7519,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7518, 7517])).
% 49.47/49.66 tff(7520,plain,
% 49.47/49.66 ((~xuntil7(s1)) | until6(s2)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7519, 112, 7291])).
% 49.47/49.66 tff(7521,plain,
% 49.47/49.66 (until6(s2)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7520, 7516])).
% 49.47/49.66 tff(7522,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s2) | always5(s2) | (~until6(s2)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7523,plain,
% 49.47/49.66 ((always5(s2) | (~until6(s2)) | xuntil7(s2)) <=> (xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7524,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s2) | always5(s2) | (~until6(s2))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7523])).
% 49.47/49.66 tff(7525,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7524, 7522])).
% 49.47/49.66 tff(7526,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7527,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2))),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7526, 7525])).
% 49.47/49.66 tff(7528,plain,
% 49.47/49.66 (xuntil7(s2) | (~until6(s2))),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7527, 7273, 7477])).
% 49.47/49.66 tff(7529,plain,
% 49.47/49.66 (xuntil7(s2)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7528, 7521])).
% 49.47/49.66 tff(7530,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7531,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7532,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7531, 7530])).
% 49.47/49.66 tff(7533,plain,
% 49.47/49.66 ((~xuntil7(s2)) | until6(s3)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7532, 151, 7291])).
% 49.47/49.66 tff(7534,plain,
% 49.47/49.66 (until6(s3)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7533, 7529])).
% 49.47/49.66 tff(7535,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s3) | always5(s3) | (~until6(s3)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7536,plain,
% 49.47/49.66 ((always5(s3) | (~until6(s3)) | xuntil7(s3)) <=> (xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7537,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s3) | always5(s3) | (~until6(s3))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7536])).
% 49.47/49.66 tff(7538,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7537, 7535])).
% 49.47/49.66 tff(7539,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7540,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3))),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7539, 7538])).
% 49.47/49.66 tff(7541,plain,
% 49.47/49.66 (xuntil7(s3) | (~until6(s3))),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7540, 7273, 7469])).
% 49.47/49.66 tff(7542,plain,
% 49.47/49.66 (xuntil7(s3)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7541, 7534])).
% 49.47/49.66 tff(7543,plain,
% 49.47/49.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7544,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7545,plain,
% 49.47/49.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4)),
% 49.47/49.66 inference(modus_ponens,[status(thm)],[7544, 7543])).
% 49.47/49.66 tff(7546,plain,
% 49.47/49.66 ((~xuntil7(s3)) | until6(s4)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7545, 177, 7291])).
% 49.47/49.66 tff(7547,plain,
% 49.47/49.66 (until6(s4)),
% 49.47/49.66 inference(unit_resolution,[status(thm)],[7546, 7542])).
% 49.47/49.66 tff(7548,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s4) | always5(s4) | (~until6(s4)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7549,plain,
% 49.47/49.66 ((always5(s4) | (~until6(s4)) | xuntil7(s4)) <=> (xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 49.47/49.66 inference(rewrite,[status(thm)],[])).
% 49.47/49.66 tff(7550,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s4) | always5(s4) | (~until6(s4))))),
% 49.47/49.66 inference(monotonicity,[status(thm)],[7549])).
% 49.47/49.66 tff(7551,plain,
% 49.47/49.66 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 49.47/49.66 inference(transitivity,[status(thm)],[7550, 7548])).
% 49.47/49.66 tff(7552,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))),
% 49.47/49.66 inference(quant_inst,[status(thm)],[])).
% 49.47/49.66 tff(7553,plain,
% 49.47/49.66 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7552, 7551])).
% 49.47/49.67 tff(7554,plain,
% 49.47/49.67 (xuntil7(s4) | (~until6(s4))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7553, 7273, 7461])).
% 49.47/49.67 tff(7555,plain,
% 49.47/49.67 (xuntil7(s4)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7554, 7547])).
% 49.47/49.67 tff(7556,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7557,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7558,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7557, 7556])).
% 49.47/49.67 tff(7559,plain,
% 49.47/49.67 ((~xuntil7(s4)) | until6(s5)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7558, 206, 7291])).
% 49.47/49.67 tff(7560,plain,
% 49.47/49.67 (until6(s5)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7559, 7555])).
% 49.47/49.67 tff(7561,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s5) | always5(s5) | (~until6(s5)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7562,plain,
% 49.47/49.67 ((always5(s5) | (~until6(s5)) | xuntil7(s5)) <=> (xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7563,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s5) | always5(s5) | (~until6(s5))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7562])).
% 49.47/49.67 tff(7564,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7563, 7561])).
% 49.47/49.67 tff(7565,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7566,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7565, 7564])).
% 49.47/49.67 tff(7567,plain,
% 49.47/49.67 (xuntil7(s5) | (~until6(s5))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7566, 7273, 7453])).
% 49.47/49.67 tff(7568,plain,
% 49.47/49.67 (xuntil7(s5)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7567, 7560])).
% 49.47/49.67 tff(7569,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7570,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7571,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7570, 7569])).
% 49.47/49.67 tff(7572,plain,
% 49.47/49.67 ((~xuntil7(s5)) | until6(s6)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7571, 234, 7291])).
% 49.47/49.67 tff(7573,plain,
% 49.47/49.67 (until6(s6)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7572, 7568])).
% 49.47/49.67 tff(7574,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s6) | always5(s6) | (~until6(s6)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7575,plain,
% 49.47/49.67 ((always5(s6) | (~until6(s6)) | xuntil7(s6)) <=> (xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7576,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s6) | always5(s6) | (~until6(s6))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7575])).
% 49.47/49.67 tff(7577,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7576, 7574])).
% 49.47/49.67 tff(7578,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7579,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7578, 7577])).
% 49.47/49.67 tff(7580,plain,
% 49.47/49.67 (xuntil7(s6) | (~until6(s6))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7579, 7273, 7445])).
% 49.47/49.67 tff(7581,plain,
% 49.47/49.67 (xuntil7(s6)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7580, 7573])).
% 49.47/49.67 tff(7582,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7583,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7584,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7583, 7582])).
% 49.47/49.67 tff(7585,plain,
% 49.47/49.67 ((~xuntil7(s6)) | until6(s7)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7584, 10, 7291])).
% 49.47/49.67 tff(7586,plain,
% 49.47/49.67 (until6(s7)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7585, 7581])).
% 49.47/49.67 tff(7587,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s7) | always5(s7) | (~until6(s7)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7588,plain,
% 49.47/49.67 ((always5(s7) | (~until6(s7)) | xuntil7(s7)) <=> (xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7589,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s7) | always5(s7) | (~until6(s7))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7588])).
% 49.47/49.67 tff(7590,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7589, 7587])).
% 49.47/49.67 tff(7591,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7592,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7591, 7590])).
% 49.47/49.67 tff(7593,plain,
% 49.47/49.67 (xuntil7(s7) | (~until6(s7))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7592, 7273, 7437])).
% 49.47/49.67 tff(7594,plain,
% 49.47/49.67 (xuntil7(s7)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7593, 7586])).
% 49.47/49.67 tff(7595,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7596,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7597,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7596, 7595])).
% 49.47/49.67 tff(7598,plain,
% 49.47/49.67 ((~xuntil7(s7)) | until6(s8)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7597, 281, 7291])).
% 49.47/49.67 tff(7599,plain,
% 49.47/49.67 ($false),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7598, 7594, 7429])).
% 49.47/49.67 tff(7600,plain,(always5(s15) | xuntil7(s15)), inference(lemma,lemma(discharge,[]))).
% 49.47/49.67 tff(7601,plain,
% 49.47/49.67 (xuntil7(s15)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7600, 7253])).
% 49.47/49.67 tff(7602,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7603,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7604,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7603, 7602])).
% 49.47/49.67 tff(7605,plain,
% 49.47/49.67 ((~xuntil7(s15)) | until6(s16)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7604, 513, 7291])).
% 49.47/49.67 tff(7606,plain,
% 49.47/49.67 (until6(s16)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7605, 7601])).
% 49.47/49.67 tff(7607,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s16) | always5(s16) | (~until6(s16)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7608,plain,
% 49.47/49.67 ((always5(s16) | (~until6(s16)) | xuntil7(s16)) <=> (xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7609,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s16) | always5(s16) | (~until6(s16))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7608])).
% 49.47/49.67 tff(7610,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7609, 7607])).
% 49.47/49.67 tff(7611,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7612,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7611, 7610])).
% 49.47/49.67 tff(7613,plain,
% 49.47/49.67 (xuntil7(s16)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7612, 7273, 7606, 7245])).
% 49.47/49.67 tff(7614,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7615,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7616,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 49.47/49.67 tff(7617,plain,
% 49.47/49.67 ((~xuntil7(s16)) | until6(s17)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7616, 542, 7291])).
% 49.47/49.67 tff(7618,plain,
% 49.47/49.67 (until6(s17)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7617, 7613])).
% 49.47/49.67 tff(7619,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s17) | always5(s17) | (~until6(s17)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7620,plain,
% 49.47/49.67 ((always5(s17) | (~until6(s17)) | xuntil7(s17)) <=> (xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7621,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s17) | always5(s17) | (~until6(s17))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7620])).
% 49.47/49.67 tff(7622,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7621, 7619])).
% 49.47/49.67 tff(7623,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7624,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7623, 7622])).
% 49.47/49.67 tff(7625,plain,
% 49.47/49.67 (xuntil7(s17) | (~until6(s17))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7624, 7273, 7237])).
% 49.47/49.67 tff(7626,plain,
% 49.47/49.67 (xuntil7(s17)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7625, 7618])).
% 49.47/49.67 tff(7627,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7628,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7629,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7628, 7627])).
% 49.47/49.67 tff(7630,plain,
% 49.47/49.67 ((~xuntil7(s17)) | until6(s18)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7629, 570, 7291])).
% 49.47/49.67 tff(7631,plain,
% 49.47/49.67 (until6(s18)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7630, 7626])).
% 49.47/49.67 tff(7632,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s18) | always5(s18) | (~until6(s18)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7633,plain,
% 49.47/49.67 ((always5(s18) | (~until6(s18)) | xuntil7(s18)) <=> (xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7634,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s18) | always5(s18) | (~until6(s18))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7633])).
% 49.47/49.67 tff(7635,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7634, 7632])).
% 49.47/49.67 tff(7636,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7637,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 49.47/49.67 tff(7638,plain,
% 49.47/49.67 (xuntil7(s18) | (~until6(s18))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7637, 7273, 7229])).
% 49.47/49.67 tff(7639,plain,
% 49.47/49.67 (xuntil7(s18)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7638, 7631])).
% 49.47/49.67 tff(7640,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7641,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7642,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7641, 7640])).
% 49.47/49.67 tff(7643,plain,
% 49.47/49.67 ((~xuntil7(s18)) | until6(s19)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7642, 601, 7291])).
% 49.47/49.67 tff(7644,plain,
% 49.47/49.67 (until6(s19)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7643, 7639])).
% 49.47/49.67 tff(7645,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s19) | always5(s19) | (~until6(s19)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7646,plain,
% 49.47/49.67 ((always5(s19) | (~until6(s19)) | xuntil7(s19)) <=> (xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7647,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s19) | always5(s19) | (~until6(s19))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7646])).
% 49.47/49.67 tff(7648,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7647, 7645])).
% 49.47/49.67 tff(7649,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7650,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7649, 7648])).
% 49.47/49.67 tff(7651,plain,
% 49.47/49.67 (xuntil7(s19) | (~until6(s19))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7650, 7273, 7221])).
% 49.47/49.67 tff(7652,plain,
% 49.47/49.67 (xuntil7(s19)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7651, 7644])).
% 49.47/49.67 tff(7653,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7654,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7655,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7654, 7653])).
% 49.47/49.67 tff(7656,plain,
% 49.47/49.67 ((~xuntil7(s19)) | until6(s20)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7655, 629, 7291])).
% 49.47/49.67 tff(7657,plain,
% 49.47/49.67 (until6(s20)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7656, 7652])).
% 49.47/49.67 tff(7658,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s20) | always5(s20) | (~until6(s20)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7659,plain,
% 49.47/49.67 ((always5(s20) | (~until6(s20)) | xuntil7(s20)) <=> (xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7660,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s20) | always5(s20) | (~until6(s20))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7659])).
% 49.47/49.67 tff(7661,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7660, 7658])).
% 49.47/49.67 tff(7662,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7663,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7662, 7661])).
% 49.47/49.67 tff(7664,plain,
% 49.47/49.67 (xuntil7(s20) | (~until6(s20))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7663, 7273, 7213])).
% 49.47/49.67 tff(7665,plain,
% 49.47/49.67 (xuntil7(s20)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7664, 7657])).
% 49.47/49.67 tff(7666,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7667,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7668,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7667, 7666])).
% 49.47/49.67 tff(7669,plain,
% 49.47/49.67 ((~xuntil7(s20)) | until6(s21)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7668, 658, 7291])).
% 49.47/49.67 tff(7670,plain,
% 49.47/49.67 (until6(s21)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7669, 7665])).
% 49.47/49.67 tff(7671,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s21) | always5(s21) | (~until6(s21)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7672,plain,
% 49.47/49.67 ((always5(s21) | (~until6(s21)) | xuntil7(s21)) <=> (xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7673,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s21) | always5(s21) | (~until6(s21))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7672])).
% 49.47/49.67 tff(7674,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7673, 7671])).
% 49.47/49.67 tff(7675,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7676,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7675, 7674])).
% 49.47/49.67 tff(7677,plain,
% 49.47/49.67 (xuntil7(s21) | (~until6(s21))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7676, 7273, 7205])).
% 49.47/49.67 tff(7678,plain,
% 49.47/49.67 (xuntil7(s21)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7677, 7670])).
% 49.47/49.67 tff(7679,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7680,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7681,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7680, 7679])).
% 49.47/49.67 tff(7682,plain,
% 49.47/49.67 ((~xuntil7(s21)) | until6(s22)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7681, 686, 7291])).
% 49.47/49.67 tff(7683,plain,
% 49.47/49.67 (until6(s22)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7682, 7678])).
% 49.47/49.67 tff(7684,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s22) | always5(s22) | (~until6(s22)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7685,plain,
% 49.47/49.67 ((always5(s22) | (~until6(s22)) | xuntil7(s22)) <=> (xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7686,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s22) | always5(s22) | (~until6(s22))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7685])).
% 49.47/49.67 tff(7687,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7686, 7684])).
% 49.47/49.67 tff(7688,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7689,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7688, 7687])).
% 49.47/49.67 tff(7690,plain,
% 49.47/49.67 (xuntil7(s22) | (~until6(s22))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7689, 7273, 7197])).
% 49.47/49.67 tff(7691,plain,
% 49.47/49.67 (xuntil7(s22)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7690, 7683])).
% 49.47/49.67 tff(7692,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7693,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7694,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7693, 7692])).
% 49.47/49.67 tff(7695,plain,
% 49.47/49.67 ((~xuntil7(s22)) | until6(s23)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7694, 717, 7291])).
% 49.47/49.67 tff(7696,plain,
% 49.47/49.67 (until6(s23)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7695, 7691])).
% 49.47/49.67 tff(7697,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s23) | always5(s23) | (~until6(s23)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7698,plain,
% 49.47/49.67 ((always5(s23) | (~until6(s23)) | xuntil7(s23)) <=> (xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7699,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s23) | always5(s23) | (~until6(s23))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7698])).
% 49.47/49.67 tff(7700,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7699, 7697])).
% 49.47/49.67 tff(7701,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7702,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7701, 7700])).
% 49.47/49.67 tff(7703,plain,
% 49.47/49.67 (xuntil7(s23) | (~until6(s23))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7702, 7273, 7189])).
% 49.47/49.67 tff(7704,plain,
% 49.47/49.67 (xuntil7(s23)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7703, 7696])).
% 49.47/49.67 tff(7705,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7706,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7707,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7706, 7705])).
% 49.47/49.67 tff(7708,plain,
% 49.47/49.67 ((~xuntil7(s23)) | until6(s24)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7707, 745, 7291])).
% 49.47/49.67 tff(7709,plain,
% 49.47/49.67 (until6(s24)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7708, 7704])).
% 49.47/49.67 tff(7710,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s24) | always5(s24) | (~until6(s24)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7711,plain,
% 49.47/49.67 ((always5(s24) | (~until6(s24)) | xuntil7(s24)) <=> (xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7712,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s24) | always5(s24) | (~until6(s24))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7711])).
% 49.47/49.67 tff(7713,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 49.47/49.67 inference(transitivity,[status(thm)],[7712, 7710])).
% 49.47/49.67 tff(7714,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7715,plain,
% 49.47/49.67 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24))),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7714, 7713])).
% 49.47/49.67 tff(7716,plain,
% 49.47/49.67 (xuntil7(s24) | (~until6(s24))),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7715, 7273, 7181])).
% 49.47/49.67 tff(7717,plain,
% 49.47/49.67 (xuntil7(s24)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7716, 7709])).
% 49.47/49.67 tff(7718,plain,
% 49.47/49.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7719,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 49.47/49.67 inference(quant_inst,[status(thm)],[])).
% 49.47/49.67 tff(7720,plain,
% 49.47/49.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25)),
% 49.47/49.67 inference(modus_ponens,[status(thm)],[7719, 7718])).
% 49.47/49.67 tff(7721,plain,
% 49.47/49.67 ((~xuntil7(s24)) | until6(s25)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7720, 776, 7291])).
% 49.47/49.67 tff(7722,plain,
% 49.47/49.67 (until6(s25)),
% 49.47/49.67 inference(unit_resolution,[status(thm)],[7721, 7717])).
% 49.47/49.67 tff(7723,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s25) | always5(s25) | (~until6(s25)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7724,plain,
% 49.47/49.67 ((always5(s25) | (~until6(s25)) | xuntil7(s25)) <=> (xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 49.47/49.67 inference(rewrite,[status(thm)],[])).
% 49.47/49.67 tff(7725,plain,
% 49.47/49.67 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s25) | always5(s25) | (~until6(s25))))),
% 49.47/49.67 inference(monotonicity,[status(thm)],[7724])).
% 49.47/49.68 tff(7726,plain,
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% 49.47/49.68 inference(transitivity,[status(thm)],[7725, 7723])).
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7728,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7727, 7726])).
% 49.47/49.68 tff(7729,plain,
% 49.47/49.68 (xuntil7(s25) | (~until6(s25))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7728, 7273, 7173])).
% 49.47/49.68 tff(7730,plain,
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7729, 7722])).
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7732,plain,
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7733,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7732, 7731])).
% 49.47/49.68 tff(7734,plain,
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7733, 802, 7291])).
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7734, 7730])).
% 49.47/49.68 tff(7736,plain,
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7737,plain,
% 49.47/49.68 ((always5(s26) | (~until6(s26)) | xuntil7(s26)) <=> (xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7738,plain,
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% 49.47/49.68 inference(monotonicity,[status(thm)],[7737])).
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% 49.47/49.68 inference(transitivity,[status(thm)],[7738, 7736])).
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7740, 7739])).
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7741, 7273, 7165])).
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7745,plain,
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7746,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7745, 7744])).
% 49.47/49.68 tff(7747,plain,
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7746, 833, 7291])).
% 49.47/49.68 tff(7748,plain,
% 49.47/49.68 (until6(s27)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7747, 7743])).
% 49.47/49.68 tff(7749,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s27) | always5(s27) | (~until6(s27)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7750,plain,
% 49.47/49.68 ((always5(s27) | (~until6(s27)) | xuntil7(s27)) <=> (xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7751,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s27) | always5(s27) | (~until6(s27))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7750])).
% 49.47/49.68 tff(7752,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7751, 7749])).
% 49.47/49.68 tff(7753,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7754,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7753, 7752])).
% 49.47/49.68 tff(7755,plain,
% 49.47/49.68 (xuntil7(s27) | (~until6(s27))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7754, 7273, 7157])).
% 49.47/49.68 tff(7756,plain,
% 49.47/49.68 (xuntil7(s27)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7755, 7748])).
% 49.47/49.68 tff(7757,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7758,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7759,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7758, 7757])).
% 49.47/49.68 tff(7760,plain,
% 49.47/49.68 ((~xuntil7(s27)) | until6(s28)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7759, 861, 7291])).
% 49.47/49.68 tff(7761,plain,
% 49.47/49.68 (until6(s28)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7760, 7756])).
% 49.47/49.68 tff(7762,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s28) | always5(s28) | (~until6(s28)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7763,plain,
% 49.47/49.68 ((always5(s28) | (~until6(s28)) | xuntil7(s28)) <=> (xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7764,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s28) | always5(s28) | (~until6(s28))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7763])).
% 49.47/49.68 tff(7765,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7764, 7762])).
% 49.47/49.68 tff(7766,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7767,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 49.47/49.68 tff(7768,plain,
% 49.47/49.68 (xuntil7(s28) | (~until6(s28))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7767, 7273, 7149])).
% 49.47/49.68 tff(7769,plain,
% 49.47/49.68 (xuntil7(s28)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7768, 7761])).
% 49.47/49.68 tff(7770,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7771,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7772,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7771, 7770])).
% 49.47/49.68 tff(7773,plain,
% 49.47/49.68 ((~xuntil7(s28)) | until6(s29)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7772, 890, 7291])).
% 49.47/49.68 tff(7774,plain,
% 49.47/49.68 (until6(s29)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7773, 7769])).
% 49.47/49.68 tff(7775,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s29) | always5(s29) | (~until6(s29)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7776,plain,
% 49.47/49.68 ((always5(s29) | (~until6(s29)) | xuntil7(s29)) <=> (xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7777,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s29) | always5(s29) | (~until6(s29))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7776])).
% 49.47/49.68 tff(7778,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7777, 7775])).
% 49.47/49.68 tff(7779,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7780,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7779, 7778])).
% 49.47/49.68 tff(7781,plain,
% 49.47/49.68 (xuntil7(s29) | (~until6(s29))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7780, 7273, 7141])).
% 49.47/49.68 tff(7782,plain,
% 49.47/49.68 (xuntil7(s29)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7781, 7774])).
% 49.47/49.68 tff(7783,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7784,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7785,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7784, 7783])).
% 49.47/49.68 tff(7786,plain,
% 49.47/49.68 ((~xuntil7(s29)) | until6(s30)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7785, 918, 7291])).
% 49.47/49.68 tff(7787,plain,
% 49.47/49.68 (until6(s30)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7786, 7782])).
% 49.47/49.68 tff(7788,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s30) | always5(s30) | (~until6(s30)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7789,plain,
% 49.47/49.68 ((always5(s30) | (~until6(s30)) | xuntil7(s30)) <=> (xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7790,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s30) | always5(s30) | (~until6(s30))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7789])).
% 49.47/49.68 tff(7791,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7790, 7788])).
% 49.47/49.68 tff(7792,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7793,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7792, 7791])).
% 49.47/49.68 tff(7794,plain,
% 49.47/49.68 (xuntil7(s30) | (~until6(s30))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7793, 7273, 7133])).
% 49.47/49.68 tff(7795,plain,
% 49.47/49.68 (xuntil7(s30)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7794, 7787])).
% 49.47/49.68 tff(7796,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7797,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7798,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7797, 7796])).
% 49.47/49.68 tff(7799,plain,
% 49.47/49.68 ((~xuntil7(s30)) | until6(s31)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7798, 949, 7291])).
% 49.47/49.68 tff(7800,plain,
% 49.47/49.68 (until6(s31)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7799, 7795])).
% 49.47/49.68 tff(7801,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s31) | always5(s31) | (~until6(s31)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7802,plain,
% 49.47/49.68 ((always5(s31) | (~until6(s31)) | xuntil7(s31)) <=> (xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7803,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s31) | always5(s31) | (~until6(s31))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7802])).
% 49.47/49.68 tff(7804,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7803, 7801])).
% 49.47/49.68 tff(7805,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7806,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7805, 7804])).
% 49.47/49.68 tff(7807,plain,
% 49.47/49.68 (xuntil7(s31) | (~until6(s31))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7806, 7273, 7125])).
% 49.47/49.68 tff(7808,plain,
% 49.47/49.68 (xuntil7(s31)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7807, 7800])).
% 49.47/49.68 tff(7809,plain,
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7810,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7811,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7810, 7809])).
% 49.47/49.68 tff(7812,plain,
% 49.47/49.68 ((~xuntil7(s31)) | until6(s32)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7811, 977, 7291])).
% 49.47/49.68 tff(7813,plain,
% 49.47/49.68 (until6(s32)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7812, 7808])).
% 49.47/49.68 tff(7814,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s32) | always5(s32) | (~until6(s32)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7815,plain,
% 49.47/49.68 ((always5(s32) | (~until6(s32)) | xuntil7(s32)) <=> (xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7816,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s32) | always5(s32) | (~until6(s32))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7815])).
% 49.47/49.68 tff(7817,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7816, 7814])).
% 49.47/49.68 tff(7818,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7819,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7818, 7817])).
% 49.47/49.68 tff(7820,plain,
% 49.47/49.68 (xuntil7(s32) | (~until6(s32))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7819, 7273, 7117])).
% 49.47/49.68 tff(7821,plain,
% 49.47/49.68 (xuntil7(s32)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7820, 7813])).
% 49.47/49.68 tff(7822,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7823,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7824,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7823, 7822])).
% 49.47/49.68 tff(7825,plain,
% 49.47/49.68 ((~xuntil7(s32)) | until6(s33)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7824, 1008, 7291])).
% 49.47/49.68 tff(7826,plain,
% 49.47/49.68 (until6(s33)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7825, 7821])).
% 49.47/49.68 tff(7827,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s33) | always5(s33) | (~until6(s33)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7828,plain,
% 49.47/49.68 ((always5(s33) | (~until6(s33)) | xuntil7(s33)) <=> (xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7829,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s33) | always5(s33) | (~until6(s33))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7828])).
% 49.47/49.68 tff(7830,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7829, 7827])).
% 49.47/49.68 tff(7831,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7832,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7831, 7830])).
% 49.47/49.68 tff(7833,plain,
% 49.47/49.68 (xuntil7(s33) | (~until6(s33))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7832, 7273, 7109])).
% 49.47/49.68 tff(7834,plain,
% 49.47/49.68 (xuntil7(s33)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7833, 7826])).
% 49.47/49.68 tff(7835,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7836,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7837,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7836, 7835])).
% 49.47/49.68 tff(7838,plain,
% 49.47/49.68 ((~xuntil7(s33)) | until6(s34)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7837, 1036, 7291])).
% 49.47/49.68 tff(7839,plain,
% 49.47/49.68 (until6(s34)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7838, 7834])).
% 49.47/49.68 tff(7840,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s34) | always5(s34) | (~until6(s34)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7841,plain,
% 49.47/49.68 ((always5(s34) | (~until6(s34)) | xuntil7(s34)) <=> (xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7842,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s34) | always5(s34) | (~until6(s34))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7841])).
% 49.47/49.68 tff(7843,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7842, 7840])).
% 49.47/49.68 tff(7844,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7845,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7844, 7843])).
% 49.47/49.68 tff(7846,plain,
% 49.47/49.68 (xuntil7(s34) | (~until6(s34))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7845, 7273, 7101])).
% 49.47/49.68 tff(7847,plain,
% 49.47/49.68 (xuntil7(s34)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7846, 7839])).
% 49.47/49.68 tff(7848,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7849,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7850,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7849, 7848])).
% 49.47/49.68 tff(7851,plain,
% 49.47/49.68 ((~xuntil7(s34)) | until6(s35)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7850, 1067, 7291])).
% 49.47/49.68 tff(7852,plain,
% 49.47/49.68 (until6(s35)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7851, 7847])).
% 49.47/49.68 tff(7853,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s35) | always5(s35) | (~until6(s35)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7854,plain,
% 49.47/49.68 ((always5(s35) | (~until6(s35)) | xuntil7(s35)) <=> (xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7855,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s35) | always5(s35) | (~until6(s35))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7854])).
% 49.47/49.68 tff(7856,plain,
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% 49.47/49.68 inference(transitivity,[status(thm)],[7855, 7853])).
% 49.47/49.68 tff(7857,plain,
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7858,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7857, 7856])).
% 49.47/49.68 tff(7859,plain,
% 49.47/49.68 (xuntil7(s35) | (~until6(s35))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7858, 7273, 7093])).
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7859, 7852])).
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7862,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7863,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7862, 7861])).
% 49.47/49.68 tff(7864,plain,
% 49.47/49.68 ((~xuntil7(s35)) | until6(s36)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7863, 1095, 7291])).
% 49.47/49.68 tff(7865,plain,
% 49.47/49.68 (until6(s36)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7864, 7860])).
% 49.47/49.68 tff(7866,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s36) | always5(s36) | (~until6(s36)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7867,plain,
% 49.47/49.68 ((always5(s36) | (~until6(s36)) | xuntil7(s36)) <=> (xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7868,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s36) | always5(s36) | (~until6(s36))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7867])).
% 49.47/49.68 tff(7869,plain,
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% 49.47/49.68 inference(transitivity,[status(thm)],[7868, 7866])).
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7871,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7870, 7869])).
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% 49.47/49.68 (xuntil7(s36) | (~until6(s36))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7871, 7273, 7085])).
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7872, 7865])).
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7875,plain,
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7876,plain,
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7875, 7874])).
% 49.47/49.68 tff(7877,plain,
% 49.47/49.68 ((~xuntil7(s36)) | until6(s37)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7876, 1126, 7291])).
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% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7880,plain,
% 49.47/49.68 ((always5(s37) | (~until6(s37)) | xuntil7(s37)) <=> (xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7881,plain,
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% 49.47/49.68 inference(monotonicity,[status(thm)],[7880])).
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% 49.47/49.68 inference(transitivity,[status(thm)],[7881, 7879])).
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% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.68 inference(modus_ponens,[status(thm)],[7883, 7882])).
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% 49.47/49.68 inference(unit_resolution,[status(thm)],[7885, 7878])).
% 49.47/49.68 tff(7887,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7888,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7889,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7888, 7887])).
% 49.47/49.68 tff(7890,plain,
% 49.47/49.68 ((~xuntil7(s37)) | until6(s38)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7889, 1154, 7291])).
% 49.47/49.68 tff(7891,plain,
% 49.47/49.68 (until6(s38)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7890, 7886])).
% 49.47/49.68 tff(7892,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s38) | always5(s38) | (~until6(s38)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7893,plain,
% 49.47/49.68 ((always5(s38) | (~until6(s38)) | xuntil7(s38)) <=> (xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7894,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s38) | always5(s38) | (~until6(s38))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7893])).
% 49.47/49.68 tff(7895,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7894, 7892])).
% 49.47/49.68 tff(7896,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7897,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7896, 7895])).
% 49.47/49.68 tff(7898,plain,
% 49.47/49.68 (xuntil7(s38) | (~until6(s38))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7897, 7273, 7069])).
% 49.47/49.68 tff(7899,plain,
% 49.47/49.68 (xuntil7(s38)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7898, 7891])).
% 49.47/49.68 tff(7900,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7901,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7902,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 49.47/49.68 tff(7903,plain,
% 49.47/49.68 ((~xuntil7(s38)) | until6(s39)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7902, 1185, 7291])).
% 49.47/49.68 tff(7904,plain,
% 49.47/49.68 (until6(s39)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7903, 7899])).
% 49.47/49.68 tff(7905,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s39) | always5(s39) | (~until6(s39)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7906,plain,
% 49.47/49.68 ((always5(s39) | (~until6(s39)) | xuntil7(s39)) <=> (xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7907,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s39) | always5(s39) | (~until6(s39))))),
% 49.47/49.68 inference(monotonicity,[status(thm)],[7906])).
% 49.47/49.68 tff(7908,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 49.47/49.68 inference(transitivity,[status(thm)],[7907, 7905])).
% 49.47/49.68 tff(7909,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7910,plain,
% 49.47/49.68 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39))),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7909, 7908])).
% 49.47/49.68 tff(7911,plain,
% 49.47/49.68 (xuntil7(s39) | (~until6(s39))),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7910, 7273, 7061])).
% 49.47/49.68 tff(7912,plain,
% 49.47/49.68 (xuntil7(s39)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7911, 7904])).
% 49.47/49.68 tff(7913,plain,
% 49.47/49.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 49.47/49.68 inference(rewrite,[status(thm)],[])).
% 49.47/49.68 tff(7914,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 49.47/49.68 inference(quant_inst,[status(thm)],[])).
% 49.47/49.68 tff(7915,plain,
% 49.47/49.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40)),
% 49.47/49.68 inference(modus_ponens,[status(thm)],[7914, 7913])).
% 49.47/49.68 tff(7916,plain,
% 49.47/49.68 ((~xuntil7(s39)) | until6(s40)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7915, 1213, 7291])).
% 49.47/49.68 tff(7917,plain,
% 49.47/49.68 (until6(s40)),
% 49.47/49.68 inference(unit_resolution,[status(thm)],[7916, 7912])).
% 49.47/49.68 tff(7918,plain,
% 49.47/49.68 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s40) | always5(s40) | (~until6(s40)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7919,plain,
% 49.47/49.69 ((always5(s40) | (~until6(s40)) | xuntil7(s40)) <=> (xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7920,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s40) | always5(s40) | (~until6(s40))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7919])).
% 49.47/49.69 tff(7921,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[7920, 7918])).
% 49.47/49.69 tff(7922,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7923,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7922, 7921])).
% 49.47/49.69 tff(7924,plain,
% 49.47/49.69 (xuntil7(s40) | (~until6(s40))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7923, 7273, 7053])).
% 49.47/49.69 tff(7925,plain,
% 49.47/49.69 (xuntil7(s40)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7924, 7917])).
% 49.47/49.69 tff(7926,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7927,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7928,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7927, 7926])).
% 49.47/49.69 tff(7929,plain,
% 49.47/49.69 ((~xuntil7(s40)) | until6(s41)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7928, 1244, 7291])).
% 49.47/49.69 tff(7930,plain,
% 49.47/49.69 (until6(s41)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7929, 7925])).
% 49.47/49.69 tff(7931,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s41) | always5(s41) | (~until6(s41)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7932,plain,
% 49.47/49.69 ((always5(s41) | (~until6(s41)) | xuntil7(s41)) <=> (xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7933,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s41) | always5(s41) | (~until6(s41))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7932])).
% 49.47/49.69 tff(7934,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[7933, 7931])).
% 49.47/49.69 tff(7935,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7936,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7935, 7934])).
% 49.47/49.69 tff(7937,plain,
% 49.47/49.69 (xuntil7(s41) | (~until6(s41))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7936, 7273, 7045])).
% 49.47/49.69 tff(7938,plain,
% 49.47/49.69 (xuntil7(s41)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7937, 7930])).
% 49.47/49.69 tff(7939,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7940,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7941,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7940, 7939])).
% 49.47/49.69 tff(7942,plain,
% 49.47/49.69 ((~xuntil7(s41)) | until6(s42)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7941, 1272, 7291])).
% 49.47/49.69 tff(7943,plain,
% 49.47/49.69 (until6(s42)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7942, 7938])).
% 49.47/49.69 tff(7944,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s42) | always5(s42) | (~until6(s42)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7945,plain,
% 49.47/49.69 ((always5(s42) | (~until6(s42)) | xuntil7(s42)) <=> (xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7946,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s42) | always5(s42) | (~until6(s42))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7945])).
% 49.47/49.69 tff(7947,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[7946, 7944])).
% 49.47/49.69 tff(7948,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7949,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7948, 7947])).
% 49.47/49.69 tff(7950,plain,
% 49.47/49.69 (xuntil7(s42) | (~until6(s42))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7949, 7273, 7037])).
% 49.47/49.69 tff(7951,plain,
% 49.47/49.69 (xuntil7(s42)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7950, 7943])).
% 49.47/49.69 tff(7952,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7953,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7954,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7953, 7952])).
% 49.47/49.69 tff(7955,plain,
% 49.47/49.69 ((~xuntil7(s42)) | until6(s43)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7954, 1303, 7291])).
% 49.47/49.69 tff(7956,plain,
% 49.47/49.69 (until6(s43)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7955, 7951])).
% 49.47/49.69 tff(7957,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s43) | always5(s43) | (~until6(s43)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7958,plain,
% 49.47/49.69 ((always5(s43) | (~until6(s43)) | xuntil7(s43)) <=> (xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7959,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s43) | always5(s43) | (~until6(s43))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7958])).
% 49.47/49.69 tff(7960,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[7959, 7957])).
% 49.47/49.69 tff(7961,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7962,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 49.47/49.69 tff(7963,plain,
% 49.47/49.69 (xuntil7(s43) | (~until6(s43))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7962, 7273, 7029])).
% 49.47/49.69 tff(7964,plain,
% 49.47/49.69 (xuntil7(s43)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7963, 7956])).
% 49.47/49.69 tff(7965,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7966,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7967,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7966, 7965])).
% 49.47/49.69 tff(7968,plain,
% 49.47/49.69 ((~xuntil7(s43)) | until6(s44)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7967, 1331, 7291])).
% 49.47/49.69 tff(7969,plain,
% 49.47/49.69 (until6(s44)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7968, 7964])).
% 49.47/49.69 tff(7970,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s44) | always5(s44) | (~until6(s44)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7971,plain,
% 49.47/49.69 ((always5(s44) | (~until6(s44)) | xuntil7(s44)) <=> (xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7972,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s44) | always5(s44) | (~until6(s44))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7971])).
% 49.47/49.69 tff(7973,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[7972, 7970])).
% 49.47/49.69 tff(7974,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7975,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7974, 7973])).
% 49.47/49.69 tff(7976,plain,
% 49.47/49.69 (xuntil7(s44) | (~until6(s44))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7975, 7273, 7021])).
% 49.47/49.69 tff(7977,plain,
% 49.47/49.69 (xuntil7(s44)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7976, 7969])).
% 49.47/49.69 tff(7978,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7979,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7980,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7979, 7978])).
% 49.47/49.69 tff(7981,plain,
% 49.47/49.69 ((~xuntil7(s44)) | until6(s45)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7980, 1362, 7291])).
% 49.47/49.69 tff(7982,plain,
% 49.47/49.69 (until6(s45)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7981, 7977])).
% 49.47/49.69 tff(7983,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s45) | always5(s45) | (~until6(s45)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7984,plain,
% 49.47/49.69 ((always5(s45) | (~until6(s45)) | xuntil7(s45)) <=> (xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7985,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s45) | always5(s45) | (~until6(s45))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7984])).
% 49.47/49.69 tff(7986,plain,
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% 49.47/49.69 inference(transitivity,[status(thm)],[7985, 7983])).
% 49.47/49.69 tff(7987,plain,
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% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7988,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7987, 7986])).
% 49.47/49.69 tff(7989,plain,
% 49.47/49.69 (xuntil7(s45) | (~until6(s45))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7988, 7273, 7013])).
% 49.47/49.69 tff(7990,plain,
% 49.47/49.69 (xuntil7(s45)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7989, 7982])).
% 49.47/49.69 tff(7991,plain,
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% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7992,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(7993,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[7992, 7991])).
% 49.47/49.69 tff(7994,plain,
% 49.47/49.69 ((~xuntil7(s45)) | until6(s46)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7993, 1388, 7291])).
% 49.47/49.69 tff(7995,plain,
% 49.47/49.69 (until6(s46)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[7994, 7990])).
% 49.47/49.69 tff(7996,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s46) | always5(s46) | (~until6(s46)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7997,plain,
% 49.47/49.69 ((always5(s46) | (~until6(s46)) | xuntil7(s46)) <=> (xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(7998,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s46) | always5(s46) | (~until6(s46))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[7997])).
% 49.47/49.69 tff(7999,plain,
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% 49.47/49.69 inference(transitivity,[status(thm)],[7998, 7996])).
% 49.47/49.69 tff(8000,plain,
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% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8001,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8000, 7999])).
% 49.47/49.69 tff(8002,plain,
% 49.47/49.69 (xuntil7(s46) | (~until6(s46))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8001, 7273, 7005])).
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% 49.47/49.69 (xuntil7(s46)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8002, 7995])).
% 49.47/49.69 tff(8004,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8005,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8006,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8005, 8004])).
% 49.47/49.69 tff(8007,plain,
% 49.47/49.69 ((~xuntil7(s46)) | until6(s47)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8006, 1419, 7291])).
% 49.47/49.69 tff(8008,plain,
% 49.47/49.69 (until6(s47)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8007, 8003])).
% 49.47/49.69 tff(8009,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s47) | always5(s47) | (~until6(s47)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8010,plain,
% 49.47/49.69 ((always5(s47) | (~until6(s47)) | xuntil7(s47)) <=> (xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8011,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s47) | always5(s47) | (~until6(s47))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[8010])).
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% 49.47/49.69 inference(transitivity,[status(thm)],[8011, 8009])).
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% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.69 inference(modus_ponens,[status(thm)],[8013, 8012])).
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% 49.47/49.69 inference(unit_resolution,[status(thm)],[8015, 8008])).
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% 49.47/49.69 inference(rewrite,[status(thm)],[])).
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% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
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% 49.47/49.69 inference(modus_ponens,[status(thm)],[8018, 8017])).
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% 49.47/49.69 inference(unit_resolution,[status(thm)],[8019, 1447, 7291])).
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% 49.47/49.69 inference(unit_resolution,[status(thm)],[8020, 8016])).
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% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8023,plain,
% 49.47/49.69 ((always5(s48) | (~until6(s48)) | xuntil7(s48)) <=> (xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8024,plain,
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% 49.47/49.69 inference(monotonicity,[status(thm)],[8023])).
% 49.47/49.69 tff(8025,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[8024, 8022])).
% 49.47/49.69 tff(8026,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8027,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8026, 8025])).
% 49.47/49.69 tff(8028,plain,
% 49.47/49.69 (xuntil7(s48) | (~until6(s48))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8027, 7273, 6989])).
% 49.47/49.69 tff(8029,plain,
% 49.47/49.69 (xuntil7(s48)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8028, 8021])).
% 49.47/49.69 tff(8030,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8031,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8032,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 49.47/49.69 tff(8033,plain,
% 49.47/49.69 ((~xuntil7(s48)) | until6(s49)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8032, 1478, 7291])).
% 49.47/49.69 tff(8034,plain,
% 49.47/49.69 (until6(s49)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8033, 8029])).
% 49.47/49.69 tff(8035,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s49) | always5(s49) | (~until6(s49)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8036,plain,
% 49.47/49.69 ((always5(s49) | (~until6(s49)) | xuntil7(s49)) <=> (xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8037,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s49) | always5(s49) | (~until6(s49))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[8036])).
% 49.47/49.69 tff(8038,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[8037, 8035])).
% 49.47/49.69 tff(8039,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8040,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8039, 8038])).
% 49.47/49.69 tff(8041,plain,
% 49.47/49.69 (xuntil7(s49) | (~until6(s49))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8040, 7273, 6981])).
% 49.47/49.69 tff(8042,plain,
% 49.47/49.69 (xuntil7(s49)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8041, 8034])).
% 49.47/49.69 tff(8043,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8044,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8045,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8044, 8043])).
% 49.47/49.69 tff(8046,plain,
% 49.47/49.69 ((~xuntil7(s49)) | until6(s50)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8045, 1506, 7291])).
% 49.47/49.69 tff(8047,plain,
% 49.47/49.69 (until6(s50)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8046, 8042])).
% 49.47/49.69 tff(8048,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s50) | always5(s50) | (~until6(s50)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8049,plain,
% 49.47/49.69 ((always5(s50) | (~until6(s50)) | xuntil7(s50)) <=> (xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8050,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s50) | always5(s50) | (~until6(s50))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[8049])).
% 49.47/49.69 tff(8051,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[8050, 8048])).
% 49.47/49.69 tff(8052,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8053,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50))),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 49.47/49.69 tff(8054,plain,
% 49.47/49.69 (xuntil7(s50) | (~until6(s50))),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8053, 7273, 6973])).
% 49.47/49.69 tff(8055,plain,
% 49.47/49.69 (xuntil7(s50)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8054, 8047])).
% 49.47/49.69 tff(8056,plain,
% 49.47/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8057,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8058,plain,
% 49.47/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51)),
% 49.47/49.69 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 49.47/49.69 tff(8059,plain,
% 49.47/49.69 ((~xuntil7(s50)) | until6(s51)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8058, 1537, 7291])).
% 49.47/49.69 tff(8060,plain,
% 49.47/49.69 (until6(s51)),
% 49.47/49.69 inference(unit_resolution,[status(thm)],[8059, 8055])).
% 49.47/49.69 tff(8061,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s51) | always5(s51) | (~until6(s51)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8062,plain,
% 49.47/49.69 ((always5(s51) | (~until6(s51)) | xuntil7(s51)) <=> (xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 49.47/49.69 inference(rewrite,[status(thm)],[])).
% 49.47/49.69 tff(8063,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s51) | always5(s51) | (~until6(s51))))),
% 49.47/49.69 inference(monotonicity,[status(thm)],[8062])).
% 49.47/49.69 tff(8064,plain,
% 49.47/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 49.47/49.69 inference(transitivity,[status(thm)],[8063, 8061])).
% 49.47/49.69 tff(8065,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))),
% 49.47/49.69 inference(quant_inst,[status(thm)],[])).
% 49.47/49.69 tff(8066,plain,
% 49.47/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51))),
% 49.53/49.69 inference(modus_ponens,[status(thm)],[8065, 8064])).
% 49.53/49.69 tff(8067,plain,
% 49.53/49.69 (xuntil7(s51) | (~until6(s51))),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8066, 7273, 6965])).
% 49.53/49.69 tff(8068,plain,
% 49.53/49.69 (xuntil7(s51)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8067, 8060])).
% 49.53/49.69 tff(8069,plain,
% 49.53/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 49.53/49.69 inference(rewrite,[status(thm)],[])).
% 49.53/49.69 tff(8070,plain,
% 49.53/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 49.53/49.69 inference(quant_inst,[status(thm)],[])).
% 49.53/49.69 tff(8071,plain,
% 49.53/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52)),
% 49.53/49.69 inference(modus_ponens,[status(thm)],[8070, 8069])).
% 49.53/49.69 tff(8072,plain,
% 49.53/49.69 ((~xuntil7(s51)) | until6(s52)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8071, 1565, 7291])).
% 49.53/49.69 tff(8073,plain,
% 49.53/49.69 (until6(s52)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8072, 8068])).
% 49.53/49.69 tff(8074,plain,
% 49.53/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s52) | always5(s52) | (~until6(s52)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 49.53/49.69 inference(rewrite,[status(thm)],[])).
% 49.53/49.69 tff(8075,plain,
% 49.53/49.69 ((always5(s52) | (~until6(s52)) | xuntil7(s52)) <=> (xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 49.53/49.69 inference(rewrite,[status(thm)],[])).
% 49.53/49.69 tff(8076,plain,
% 49.53/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s52) | always5(s52) | (~until6(s52))))),
% 49.53/49.69 inference(monotonicity,[status(thm)],[8075])).
% 49.53/49.69 tff(8077,plain,
% 49.53/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 49.53/49.69 inference(transitivity,[status(thm)],[8076, 8074])).
% 49.53/49.69 tff(8078,plain,
% 49.53/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))),
% 49.53/49.69 inference(quant_inst,[status(thm)],[])).
% 49.53/49.69 tff(8079,plain,
% 49.53/49.69 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52))),
% 49.53/49.69 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 49.53/49.69 tff(8080,plain,
% 49.53/49.69 (xuntil7(s52) | (~until6(s52))),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8079, 7273, 6957])).
% 49.53/49.69 tff(8081,plain,
% 49.53/49.69 (xuntil7(s52)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8080, 8073])).
% 49.53/49.69 tff(8082,plain,
% 49.53/49.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 49.53/49.69 inference(rewrite,[status(thm)],[])).
% 49.53/49.69 tff(8083,plain,
% 49.53/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 49.53/49.69 inference(quant_inst,[status(thm)],[])).
% 49.53/49.69 tff(8084,plain,
% 49.53/49.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53)),
% 49.53/49.69 inference(modus_ponens,[status(thm)],[8083, 8082])).
% 49.53/49.69 tff(8085,plain,
% 49.53/49.69 ((~xuntil7(s52)) | until6(s53)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8084, 1596, 7291])).
% 49.53/49.69 tff(8086,plain,
% 49.53/49.69 (until6(s53)),
% 49.53/49.69 inference(unit_resolution,[status(thm)],[8085, 8081])).
% 49.53/49.69 tff(8087,plain,
% 49.53/49.69 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s53) | always5(s53) | (~until6(s53)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 49.53/49.69 inference(rewrite,[status(thm)],[])).
% 49.53/49.69 tff(8088,plain,
% 49.53/49.69 ((always5(s53) | (~until6(s53)) | xuntil7(s53)) <=> (xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8089,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s53) | always5(s53) | (~until6(s53))))),
% 49.53/49.70 inference(monotonicity,[status(thm)],[8088])).
% 49.53/49.70 tff(8090,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 49.53/49.70 inference(transitivity,[status(thm)],[8089, 8087])).
% 49.53/49.70 tff(8091,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))),
% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8092,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53))),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8091, 8090])).
% 49.53/49.70 tff(8093,plain,
% 49.53/49.70 (xuntil7(s53) | (~until6(s53))),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8092, 7273, 6949])).
% 49.53/49.70 tff(8094,plain,
% 49.53/49.70 (xuntil7(s53)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8093, 8086])).
% 49.53/49.70 tff(8095,plain,
% 49.53/49.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8096,plain,
% 49.53/49.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8097,plain,
% 49.53/49.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54)),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8096, 8095])).
% 49.53/49.70 tff(8098,plain,
% 49.53/49.70 ((~xuntil7(s53)) | until6(s54)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8097, 1624, 7291])).
% 49.53/49.70 tff(8099,plain,
% 49.53/49.70 (until6(s54)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8098, 8094])).
% 49.53/49.70 tff(8100,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s54) | always5(s54) | (~until6(s54)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8101,plain,
% 49.53/49.70 ((always5(s54) | (~until6(s54)) | xuntil7(s54)) <=> (xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8102,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s54) | always5(s54) | (~until6(s54))))),
% 49.53/49.70 inference(monotonicity,[status(thm)],[8101])).
% 49.53/49.70 tff(8103,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 49.53/49.70 inference(transitivity,[status(thm)],[8102, 8100])).
% 49.53/49.70 tff(8104,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))),
% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8105,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54))),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8104, 8103])).
% 49.53/49.70 tff(8106,plain,
% 49.53/49.70 (xuntil7(s54) | (~until6(s54))),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8105, 7273, 6941])).
% 49.53/49.70 tff(8107,plain,
% 49.53/49.70 (xuntil7(s54)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8106, 8099])).
% 49.53/49.70 tff(8108,plain,
% 49.53/49.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8109,plain,
% 49.53/49.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8110,plain,
% 49.53/49.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55)),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8109, 8108])).
% 49.53/49.70 tff(8111,plain,
% 49.53/49.70 ((~xuntil7(s54)) | until6(s55)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8110, 1655, 7291])).
% 49.53/49.70 tff(8112,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8111, 8107])).
% 49.53/49.70 tff(8113,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s55) | always5(s55) | (~until6(s55)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8114,plain,
% 49.53/49.70 ((always5(s55) | (~until6(s55)) | xuntil7(s55)) <=> (xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8115,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s55) | always5(s55) | (~until6(s55))))),
% 49.53/49.70 inference(monotonicity,[status(thm)],[8114])).
% 49.53/49.70 tff(8116,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 49.53/49.70 inference(transitivity,[status(thm)],[8115, 8113])).
% 49.53/49.70 tff(8117,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8118,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55))),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8117, 8116])).
% 49.53/49.70 tff(8119,plain,
% 49.53/49.70 (xuntil7(s55) | (~until6(s55))),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8118, 7273, 6933])).
% 49.53/49.70 tff(8120,plain,
% 49.53/49.70 (xuntil7(s55)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8119, 8112])).
% 49.53/49.70 tff(8121,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8122,plain,
% 49.53/49.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))),
% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8123,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 49.53/49.70 tff(8124,plain,
% 49.53/49.70 ((~xuntil7(s55)) | until6(s56)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8123, 1683, 7291])).
% 49.53/49.70 tff(8125,plain,
% 49.53/49.70 (until6(s56)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8124, 8120])).
% 49.53/49.70 tff(8126,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s56) | always5(s56) | (~until6(s56)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8127,plain,
% 49.53/49.70 ((always5(s56) | (~until6(s56)) | xuntil7(s56)) <=> (xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8128,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s56) | always5(s56) | (~until6(s56))))),
% 49.53/49.70 inference(monotonicity,[status(thm)],[8127])).
% 49.53/49.70 tff(8129,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 49.53/49.70 inference(transitivity,[status(thm)],[8128, 8126])).
% 49.53/49.70 tff(8130,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8131,plain,
% 49.53/49.70 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56))),
% 49.53/49.70 inference(modus_ponens,[status(thm)],[8130, 8129])).
% 49.53/49.70 tff(8132,plain,
% 49.53/49.70 (xuntil7(s56) | (~until6(s56))),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8131, 7273, 6925])).
% 49.53/49.70 tff(8133,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8132, 8125])).
% 49.53/49.70 tff(8134,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8135,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8136,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8135, 8134])).
% 49.53/49.70 tff(8137,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8136, 1714, 7291])).
% 49.53/49.70 tff(8138,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8137, 8133])).
% 49.53/49.70 tff(8139,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8140,plain,
% 49.53/49.70 ((always5(s57) | (~until6(s57)) | xuntil7(s57)) <=> (xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8141,plain,
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8140])).
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% 49.53/49.70 inference(transitivity,[status(thm)],[8141, 8139])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8143, 8142])).
% 49.53/49.70 tff(8145,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8144, 7273, 6917])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8145, 8138])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8148,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8149,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8148, 8147])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8149, 1742, 7291])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8153])).
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% 49.53/49.70 inference(transitivity,[status(thm)],[8154, 8152])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8161, 8160])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8163, 8159])).
% 49.53/49.70 tff(8165,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s59) | always5(s59) | (~until6(s59)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s59) | always5(s59) | (~until6(s59)))),
% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8166,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8167,plain,
% 49.53/49.70 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s59) | always5(s59) | (~until6(s59))))),
% 49.53/49.70 inference(monotonicity,[status(thm)],[8166])).
% 49.53/49.70 tff(8168,plain,
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% 49.53/49.70 inference(transitivity,[status(thm)],[8167, 8165])).
% 49.53/49.70 tff(8169,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8170,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 49.53/49.70 tff(8171,plain,
% 49.53/49.70 (xuntil7(s59) | (~until6(s59))),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8170, 7273, 6901])).
% 49.53/49.70 tff(8172,plain,
% 49.53/49.70 (xuntil7(s59)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8171, 8164])).
% 49.53/49.70 tff(8173,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8174,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8175,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 49.53/49.70 tff(8176,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8175, 1801, 7291])).
% 49.53/49.70 tff(8177,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8176, 8172])).
% 49.53/49.70 tff(8178,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8179,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8180,plain,
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8179])).
% 49.53/49.70 tff(8181,plain,
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% 49.53/49.70 inference(transitivity,[status(thm)],[8180, 8178])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8183,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 49.53/49.70 tff(8184,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8183, 7273, 6893])).
% 49.53/49.70 tff(8185,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8184, 8177])).
% 49.53/49.70 tff(8186,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8187,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8188,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8187, 8186])).
% 49.53/49.70 tff(8189,plain,
% 49.53/49.70 ((~xuntil7(s60)) | until6(s61)),
% 49.53/49.70 inference(unit_resolution,[status(thm)],[8188, 1832, 7291])).
% 49.53/49.70 tff(8190,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8189, 8185])).
% 49.53/49.70 tff(8191,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8193,plain,
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8192])).
% 49.53/49.70 tff(8194,plain,
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% 49.53/49.70 inference(transitivity,[status(thm)],[8193, 8191])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8196,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8195, 8194])).
% 49.53/49.70 tff(8197,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8196, 7273, 6885])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8197, 8190])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8200,plain,
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
% 49.53/49.70 tff(8201,plain,
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 49.53/49.70 tff(8202,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8201, 1860, 7291])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8202, 8198])).
% 49.53/49.70 tff(8204,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8206,plain,
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8205])).
% 49.53/49.70 tff(8207,plain,
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% 49.53/49.70 inference(transitivity,[status(thm)],[8206, 8204])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8208, 8207])).
% 49.53/49.70 tff(8210,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8209, 7273, 6877])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8210, 8203])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8213, 8212])).
% 49.53/49.70 tff(8215,plain,
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8214, 1891, 7291])).
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% 49.53/49.70 inference(unit_resolution,[status(thm)],[8215, 8211])).
% 49.53/49.70 tff(8217,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8218])).
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% 49.53/49.70 inference(transitivity,[status(thm)],[8219, 8217])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
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% 49.53/49.70 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8231,plain,
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% 49.53/49.70 inference(rewrite,[status(thm)],[])).
% 49.53/49.70 tff(8232,plain,
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% 49.53/49.70 inference(monotonicity,[status(thm)],[8231])).
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% 49.53/49.70 inference(transitivity,[status(thm)],[8232, 8230])).
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% 49.53/49.70 inference(modus_ponens,[status(thm)],[8239, 8238])).
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% 49.53/49.71 inference(unit_resolution,[status(thm)],[8301, 8294])).
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% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8304,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8305,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8304, 8303])).
% 49.53/49.71 tff(8306,plain,
% 49.53/49.71 ((~xuntil7(s69)) | until6(s70)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8305, 2096, 7291])).
% 49.53/49.71 tff(8307,plain,
% 49.53/49.71 (until6(s70)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8306, 8302])).
% 49.53/49.71 tff(8308,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s70) | always5(s70) | (~until6(s70)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8309,plain,
% 49.53/49.71 ((always5(s70) | (~until6(s70)) | xuntil7(s70)) <=> (xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8310,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s70) | always5(s70) | (~until6(s70))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8309])).
% 49.53/49.71 tff(8311,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8310, 8308])).
% 49.53/49.71 tff(8312,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8313,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8312, 8311])).
% 49.53/49.71 tff(8314,plain,
% 49.53/49.71 (xuntil7(s70) | (~until6(s70))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8313, 7273, 6813])).
% 49.53/49.71 tff(8315,plain,
% 49.53/49.71 (xuntil7(s70)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8314, 8307])).
% 49.53/49.71 tff(8316,plain,
% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8317,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8318,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8317, 8316])).
% 49.53/49.71 tff(8319,plain,
% 49.53/49.71 ((~xuntil7(s70)) | until6(s71)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8318, 2127, 7291])).
% 49.53/49.71 tff(8320,plain,
% 49.53/49.71 (until6(s71)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8319, 8315])).
% 49.53/49.71 tff(8321,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s71) | always5(s71) | (~until6(s71)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8322,plain,
% 49.53/49.71 ((always5(s71) | (~until6(s71)) | xuntil7(s71)) <=> (xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8323,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s71) | (~until6(s71)) | xuntil7(s71))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s71) | always5(s71) | (~until6(s71))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8322])).
% 49.53/49.71 tff(8324,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s71) | (~until6(s71)) | xuntil7(s71))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8323, 8321])).
% 49.53/49.71 tff(8325,plain,
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8326,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8325, 8324])).
% 49.53/49.71 tff(8327,plain,
% 49.53/49.71 (xuntil7(s71) | (~until6(s71))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8326, 7273, 6805])).
% 49.53/49.71 tff(8328,plain,
% 49.53/49.71 (xuntil7(s71)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8327, 8320])).
% 49.53/49.71 tff(8329,plain,
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8330,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s71, s72)) | (~xuntil7(s71)) | until6(s72))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8331,plain,
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% 49.53/49.71 inference(modus_ponens,[status(thm)],[8330, 8329])).
% 49.53/49.71 tff(8332,plain,
% 49.53/49.71 ((~xuntil7(s71)) | until6(s72)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8331, 2155, 7291])).
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% 49.53/49.71 (until6(s72)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8332, 8328])).
% 49.53/49.71 tff(8334,plain,
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 ((always5(s72) | (~until6(s72)) | xuntil7(s72)) <=> (xuntil7(s72) | always5(s72) | (~until6(s72)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8336,plain,
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% 49.53/49.71 inference(monotonicity,[status(thm)],[8335])).
% 49.53/49.71 tff(8337,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s72) | (~until6(s72)) | xuntil7(s72))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s72) | always5(s72) | (~until6(s72)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8336, 8334])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8339,plain,
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% 49.53/49.71 inference(modus_ponens,[status(thm)],[8338, 8337])).
% 49.53/49.71 tff(8340,plain,
% 49.53/49.71 (xuntil7(s72) | (~until6(s72))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8339, 7273, 6797])).
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% 49.53/49.71 inference(unit_resolution,[status(thm)],[8340, 8333])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8344,plain,
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% 49.53/49.71 inference(modus_ponens,[status(thm)],[8343, 8342])).
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% 49.53/49.71 inference(unit_resolution,[status(thm)],[8344, 2186, 7291])).
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% 49.53/49.71 tff(8347,plain,
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8349,plain,
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% 49.53/49.71 inference(monotonicity,[status(thm)],[8348])).
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% 49.53/49.71 inference(transitivity,[status(thm)],[8349, 8347])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.71 inference(modus_ponens,[status(thm)],[8351, 8350])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.71 inference(modus_ponens,[status(thm)],[8356, 8355])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(monotonicity,[status(thm)],[8361])).
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% 49.53/49.71 inference(transitivity,[status(thm)],[8362, 8360])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
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% 49.53/49.71 inference(unit_resolution,[status(thm)],[8371, 8367])).
% 49.53/49.71 tff(8373,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s75) | always5(s75) | (~until6(s75)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8374,plain,
% 49.53/49.71 ((always5(s75) | (~until6(s75)) | xuntil7(s75)) <=> (xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8375,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s75) | always5(s75) | (~until6(s75))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8374])).
% 49.53/49.71 tff(8376,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8375, 8373])).
% 49.53/49.71 tff(8377,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8378,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8377, 8376])).
% 49.53/49.71 tff(8379,plain,
% 49.53/49.71 (xuntil7(s75) | (~until6(s75))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8378, 7273, 6773])).
% 49.53/49.71 tff(8380,plain,
% 49.53/49.71 (xuntil7(s75)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8379, 8372])).
% 49.53/49.71 tff(8381,plain,
% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8382,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8383,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8382, 8381])).
% 49.53/49.71 tff(8384,plain,
% 49.53/49.71 ((~xuntil7(s75)) | until6(s76)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8383, 2273, 7291])).
% 49.53/49.71 tff(8385,plain,
% 49.53/49.71 (until6(s76)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8384, 8380])).
% 49.53/49.71 tff(8386,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s76) | always5(s76) | (~until6(s76)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8387,plain,
% 49.53/49.71 ((always5(s76) | (~until6(s76)) | xuntil7(s76)) <=> (xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8388,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s76) | always5(s76) | (~until6(s76))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8387])).
% 49.53/49.71 tff(8389,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8388, 8386])).
% 49.53/49.71 tff(8390,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8391,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 49.53/49.71 tff(8392,plain,
% 49.53/49.71 (xuntil7(s76) | (~until6(s76))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8391, 7273, 6765])).
% 49.53/49.71 tff(8393,plain,
% 49.53/49.71 (xuntil7(s76)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8392, 8385])).
% 49.53/49.71 tff(8394,plain,
% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8395,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8396,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8395, 8394])).
% 49.53/49.71 tff(8397,plain,
% 49.53/49.71 ((~xuntil7(s76)) | until6(s77)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8396, 2304, 7291])).
% 49.53/49.71 tff(8398,plain,
% 49.53/49.71 (until6(s77)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8397, 8393])).
% 49.53/49.71 tff(8399,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s77) | always5(s77) | (~until6(s77)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8400,plain,
% 49.53/49.71 ((always5(s77) | (~until6(s77)) | xuntil7(s77)) <=> (xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8401,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s77) | always5(s77) | (~until6(s77))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8400])).
% 49.53/49.71 tff(8402,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8401, 8399])).
% 49.53/49.71 tff(8403,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8404,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 49.53/49.71 tff(8405,plain,
% 49.53/49.71 (xuntil7(s77) | (~until6(s77))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8404, 7273, 6757])).
% 49.53/49.71 tff(8406,plain,
% 49.53/49.71 (xuntil7(s77)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8405, 8398])).
% 49.53/49.71 tff(8407,plain,
% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8408,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8409,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8408, 8407])).
% 49.53/49.71 tff(8410,plain,
% 49.53/49.71 ((~xuntil7(s77)) | until6(s78)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8409, 2332, 7291])).
% 49.53/49.71 tff(8411,plain,
% 49.53/49.71 (until6(s78)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8410, 8406])).
% 49.53/49.71 tff(8412,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s78) | always5(s78) | (~until6(s78)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8413,plain,
% 49.53/49.71 ((always5(s78) | (~until6(s78)) | xuntil7(s78)) <=> (xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8414,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s78) | always5(s78) | (~until6(s78))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8413])).
% 49.53/49.71 tff(8415,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8414, 8412])).
% 49.53/49.71 tff(8416,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8417,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8416, 8415])).
% 49.53/49.71 tff(8418,plain,
% 49.53/49.71 (xuntil7(s78) | (~until6(s78))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8417, 7273, 6749])).
% 49.53/49.71 tff(8419,plain,
% 49.53/49.71 (xuntil7(s78)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8418, 8411])).
% 49.53/49.71 tff(8420,plain,
% 49.53/49.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8421,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8422,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8421, 8420])).
% 49.53/49.71 tff(8423,plain,
% 49.53/49.71 ((~xuntil7(s78)) | until6(s79)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8422, 2363, 7291])).
% 49.53/49.71 tff(8424,plain,
% 49.53/49.71 (until6(s79)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8423, 8419])).
% 49.53/49.71 tff(8425,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s79) | always5(s79) | (~until6(s79)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8426,plain,
% 49.53/49.71 ((always5(s79) | (~until6(s79)) | xuntil7(s79)) <=> (xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8427,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s79) | (~until6(s79)) | xuntil7(s79))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s79) | always5(s79) | (~until6(s79))))),
% 49.53/49.71 inference(monotonicity,[status(thm)],[8426])).
% 49.53/49.71 tff(8428,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s79) | (~until6(s79)) | xuntil7(s79))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 49.53/49.71 inference(transitivity,[status(thm)],[8427, 8425])).
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% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8430,plain,
% 49.53/49.71 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79))),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8429, 8428])).
% 49.53/49.71 tff(8431,plain,
% 49.53/49.71 (xuntil7(s79) | (~until6(s79))),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8430, 7273, 6741])).
% 49.53/49.71 tff(8432,plain,
% 49.53/49.71 (xuntil7(s79)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8431, 8424])).
% 49.53/49.71 tff(8433,plain,
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% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8434,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80))),
% 49.53/49.71 inference(quant_inst,[status(thm)],[])).
% 49.53/49.71 tff(8435,plain,
% 49.53/49.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80)),
% 49.53/49.71 inference(modus_ponens,[status(thm)],[8434, 8433])).
% 49.53/49.71 tff(8436,plain,
% 49.53/49.71 ((~xuntil7(s79)) | until6(s80)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8435, 2391, 7291])).
% 49.53/49.71 tff(8437,plain,
% 49.53/49.71 (until6(s80)),
% 49.53/49.71 inference(unit_resolution,[status(thm)],[8436, 8432])).
% 49.53/49.71 tff(8438,plain,
% 49.53/49.71 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s80) | always5(s80) | (~until6(s80)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 49.53/49.71 inference(rewrite,[status(thm)],[])).
% 49.53/49.71 tff(8439,plain,
% 49.53/49.71 ((always5(s80) | (~until6(s80)) | xuntil7(s80)) <=> (xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8440,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s80) | always5(s80) | (~until6(s80))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8439])).
% 49.53/49.72 tff(8441,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8440, 8438])).
% 49.53/49.72 tff(8442,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8443,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8442, 8441])).
% 49.53/49.72 tff(8444,plain,
% 49.53/49.72 (xuntil7(s80) | (~until6(s80))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8443, 7273, 6733])).
% 49.53/49.72 tff(8445,plain,
% 49.53/49.72 (xuntil7(s80)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8444, 8437])).
% 49.53/49.72 tff(8446,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8447,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8448,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 49.53/49.72 tff(8449,plain,
% 49.53/49.72 ((~xuntil7(s80)) | until6(s81)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8448, 2422, 7291])).
% 49.53/49.72 tff(8450,plain,
% 49.53/49.72 (until6(s81)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8449, 8445])).
% 49.53/49.72 tff(8451,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s81) | always5(s81) | (~until6(s81)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8452,plain,
% 49.53/49.72 ((always5(s81) | (~until6(s81)) | xuntil7(s81)) <=> (xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8453,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s81) | always5(s81) | (~until6(s81))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8452])).
% 49.53/49.72 tff(8454,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8453, 8451])).
% 49.53/49.72 tff(8455,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8456,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8455, 8454])).
% 49.53/49.72 tff(8457,plain,
% 49.53/49.72 (xuntil7(s81) | (~until6(s81))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8456, 7273, 6725])).
% 49.53/49.72 tff(8458,plain,
% 49.53/49.72 (xuntil7(s81)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8457, 8450])).
% 49.53/49.72 tff(8459,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8460,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8461,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8460, 8459])).
% 49.53/49.72 tff(8462,plain,
% 49.53/49.72 ((~xuntil7(s81)) | until6(s82)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8461, 2450, 7291])).
% 49.53/49.72 tff(8463,plain,
% 49.53/49.72 (until6(s82)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8462, 8458])).
% 49.53/49.72 tff(8464,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s82) | always5(s82) | (~until6(s82)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8465,plain,
% 49.53/49.72 ((always5(s82) | (~until6(s82)) | xuntil7(s82)) <=> (xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8466,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s82) | always5(s82) | (~until6(s82))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8465])).
% 49.53/49.72 tff(8467,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8466, 8464])).
% 49.53/49.72 tff(8468,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8469,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8468, 8467])).
% 49.53/49.72 tff(8470,plain,
% 49.53/49.72 (xuntil7(s82) | (~until6(s82))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8469, 7273, 6717])).
% 49.53/49.72 tff(8471,plain,
% 49.53/49.72 (xuntil7(s82)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8470, 8463])).
% 49.53/49.72 tff(8472,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8473,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8474,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8473, 8472])).
% 49.53/49.72 tff(8475,plain,
% 49.53/49.72 ((~xuntil7(s82)) | until6(s83)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8474, 2481, 7291])).
% 49.53/49.72 tff(8476,plain,
% 49.53/49.72 (until6(s83)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8475, 8471])).
% 49.53/49.72 tff(8477,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s83) | always5(s83) | (~until6(s83)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8478,plain,
% 49.53/49.72 ((always5(s83) | (~until6(s83)) | xuntil7(s83)) <=> (xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8479,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s83) | always5(s83) | (~until6(s83))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8478])).
% 49.53/49.72 tff(8480,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8479, 8477])).
% 49.53/49.72 tff(8481,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8482,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8481, 8480])).
% 49.53/49.72 tff(8483,plain,
% 49.53/49.72 (xuntil7(s83) | (~until6(s83))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8482, 7273, 6709])).
% 49.53/49.72 tff(8484,plain,
% 49.53/49.72 (xuntil7(s83)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8483, 8476])).
% 49.53/49.72 tff(8485,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8486,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8487,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8486, 8485])).
% 49.53/49.72 tff(8488,plain,
% 49.53/49.72 ((~xuntil7(s83)) | until6(s84)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8487, 2509, 7291])).
% 49.53/49.72 tff(8489,plain,
% 49.53/49.72 (until6(s84)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8488, 8484])).
% 49.53/49.72 tff(8490,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s84) | always5(s84) | (~until6(s84)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8491,plain,
% 49.53/49.72 ((always5(s84) | (~until6(s84)) | xuntil7(s84)) <=> (xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8492,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s84) | always5(s84) | (~until6(s84))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8491])).
% 49.53/49.72 tff(8493,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8492, 8490])).
% 49.53/49.72 tff(8494,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8495,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8494, 8493])).
% 49.53/49.72 tff(8496,plain,
% 49.53/49.72 (xuntil7(s84) | (~until6(s84))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8495, 7273, 6701])).
% 49.53/49.72 tff(8497,plain,
% 49.53/49.72 (xuntil7(s84)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8496, 8489])).
% 49.53/49.72 tff(8498,plain,
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% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8499,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8500,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8499, 8498])).
% 49.53/49.72 tff(8501,plain,
% 49.53/49.72 ((~xuntil7(s84)) | until6(s85)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8500, 2540, 7291])).
% 49.53/49.72 tff(8502,plain,
% 49.53/49.72 (until6(s85)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8501, 8497])).
% 49.53/49.72 tff(8503,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s85) | always5(s85) | (~until6(s85)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8504,plain,
% 49.53/49.72 ((always5(s85) | (~until6(s85)) | xuntil7(s85)) <=> (xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8505,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s85) | (~until6(s85)) | xuntil7(s85))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s85) | always5(s85) | (~until6(s85))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8504])).
% 49.53/49.72 tff(8506,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s85) | (~until6(s85)) | xuntil7(s85))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8505, 8503])).
% 49.53/49.72 tff(8507,plain,
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% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8508,plain,
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% 49.53/49.72 inference(modus_ponens,[status(thm)],[8507, 8506])).
% 49.53/49.72 tff(8509,plain,
% 49.53/49.72 (xuntil7(s85) | (~until6(s85))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8508, 7273, 6693])).
% 49.53/49.72 tff(8510,plain,
% 49.53/49.72 (xuntil7(s85)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8509, 8502])).
% 49.53/49.72 tff(8511,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8512,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8513,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8512, 8511])).
% 49.53/49.72 tff(8514,plain,
% 49.53/49.72 ((~xuntil7(s85)) | until6(s86)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8513, 2568, 7291])).
% 49.53/49.72 tff(8515,plain,
% 49.53/49.72 (until6(s86)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8514, 8510])).
% 49.53/49.72 tff(8516,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s86) | always5(s86) | (~until6(s86)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8517,plain,
% 49.53/49.72 ((always5(s86) | (~until6(s86)) | xuntil7(s86)) <=> (xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8518,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s86) | always5(s86) | (~until6(s86))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8517])).
% 49.53/49.72 tff(8519,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8518, 8516])).
% 49.53/49.72 tff(8520,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8521,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8520, 8519])).
% 49.53/49.72 tff(8522,plain,
% 49.53/49.72 (xuntil7(s86) | (~until6(s86))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8521, 7273, 6685])).
% 49.53/49.72 tff(8523,plain,
% 49.53/49.72 (xuntil7(s86)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8522, 8515])).
% 49.53/49.72 tff(8524,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8525,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8526,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8525, 8524])).
% 49.53/49.72 tff(8527,plain,
% 49.53/49.72 ((~xuntil7(s86)) | until6(s87)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8526, 2599, 7291])).
% 49.53/49.72 tff(8528,plain,
% 49.53/49.72 (until6(s87)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8527, 8523])).
% 49.53/49.72 tff(8529,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s87) | always5(s87) | (~until6(s87)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8530,plain,
% 49.53/49.72 ((always5(s87) | (~until6(s87)) | xuntil7(s87)) <=> (xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8531,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s87) | always5(s87) | (~until6(s87))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8530])).
% 49.53/49.72 tff(8532,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8531, 8529])).
% 49.53/49.72 tff(8533,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8534,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8533, 8532])).
% 49.53/49.72 tff(8535,plain,
% 49.53/49.72 (xuntil7(s87) | (~until6(s87))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8534, 7273, 6677])).
% 49.53/49.72 tff(8536,plain,
% 49.53/49.72 (xuntil7(s87)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8535, 8528])).
% 49.53/49.72 tff(8537,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8538,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8539,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8538, 8537])).
% 49.53/49.72 tff(8540,plain,
% 49.53/49.72 ((~xuntil7(s87)) | until6(s88)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8539, 2627, 7291])).
% 49.53/49.72 tff(8541,plain,
% 49.53/49.72 (until6(s88)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8540, 8536])).
% 49.53/49.72 tff(8542,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s88) | always5(s88) | (~until6(s88)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8543,plain,
% 49.53/49.72 ((always5(s88) | (~until6(s88)) | xuntil7(s88)) <=> (xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8544,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s88) | always5(s88) | (~until6(s88))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8543])).
% 49.53/49.72 tff(8545,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8544, 8542])).
% 49.53/49.72 tff(8546,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8547,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8546, 8545])).
% 49.53/49.72 tff(8548,plain,
% 49.53/49.72 (xuntil7(s88) | (~until6(s88))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8547, 7273, 6669])).
% 49.53/49.72 tff(8549,plain,
% 49.53/49.72 (xuntil7(s88)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8548, 8541])).
% 49.53/49.72 tff(8550,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8551,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8552,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8551, 8550])).
% 49.53/49.72 tff(8553,plain,
% 49.53/49.72 ((~xuntil7(s88)) | until6(s89)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8552, 2658, 7291])).
% 49.53/49.72 tff(8554,plain,
% 49.53/49.72 (until6(s89)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8553, 8549])).
% 49.53/49.72 tff(8555,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s89) | always5(s89) | (~until6(s89)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8556,plain,
% 49.53/49.72 ((always5(s89) | (~until6(s89)) | xuntil7(s89)) <=> (xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8557,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s89) | always5(s89) | (~until6(s89))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8556])).
% 49.53/49.72 tff(8558,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8557, 8555])).
% 49.53/49.72 tff(8559,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8560,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8559, 8558])).
% 49.53/49.72 tff(8561,plain,
% 49.53/49.72 (xuntil7(s89) | (~until6(s89))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8560, 7273, 6661])).
% 49.53/49.72 tff(8562,plain,
% 49.53/49.72 (xuntil7(s89)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8561, 8554])).
% 49.53/49.72 tff(8563,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8564,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8565,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8564, 8563])).
% 49.53/49.72 tff(8566,plain,
% 49.53/49.72 ((~xuntil7(s89)) | until6(s90)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8565, 2686, 7291])).
% 49.53/49.72 tff(8567,plain,
% 49.53/49.72 (until6(s90)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8566, 8562])).
% 49.53/49.72 tff(8568,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s90) | always5(s90) | (~until6(s90)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8569,plain,
% 49.53/49.72 ((always5(s90) | (~until6(s90)) | xuntil7(s90)) <=> (xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8570,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s90) | always5(s90) | (~until6(s90))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8569])).
% 49.53/49.72 tff(8571,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8570, 8568])).
% 49.53/49.72 tff(8572,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8573,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8572, 8571])).
% 49.53/49.72 tff(8574,plain,
% 49.53/49.72 (xuntil7(s90) | (~until6(s90))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8573, 7273, 6653])).
% 49.53/49.72 tff(8575,plain,
% 49.53/49.72 (xuntil7(s90)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8574, 8567])).
% 49.53/49.72 tff(8576,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8577,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8578,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8577, 8576])).
% 49.53/49.72 tff(8579,plain,
% 49.53/49.72 ((~xuntil7(s90)) | until6(s91)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8578, 2715, 7291])).
% 49.53/49.72 tff(8580,plain,
% 49.53/49.72 (until6(s91)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8579, 8575])).
% 49.53/49.72 tff(8581,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s91) | always5(s91) | (~until6(s91)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8582,plain,
% 49.53/49.72 ((always5(s91) | (~until6(s91)) | xuntil7(s91)) <=> (xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8583,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s91) | always5(s91) | (~until6(s91))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8582])).
% 49.53/49.72 tff(8584,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8583, 8581])).
% 49.53/49.72 tff(8585,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8586,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 49.53/49.72 tff(8587,plain,
% 49.53/49.72 (xuntil7(s91) | (~until6(s91))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8586, 7273, 6645])).
% 49.53/49.72 tff(8588,plain,
% 49.53/49.72 (xuntil7(s91)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8587, 8580])).
% 49.53/49.72 tff(8589,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8590,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8591,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8590, 8589])).
% 49.53/49.72 tff(8592,plain,
% 49.53/49.72 ((~xuntil7(s91)) | until6(s92)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8591, 2741, 7291])).
% 49.53/49.72 tff(8593,plain,
% 49.53/49.72 (until6(s92)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8592, 8588])).
% 49.53/49.72 tff(8594,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s92) | always5(s92) | (~until6(s92)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8595,plain,
% 49.53/49.72 ((always5(s92) | (~until6(s92)) | xuntil7(s92)) <=> (xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8596,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s92) | always5(s92) | (~until6(s92))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8595])).
% 49.53/49.72 tff(8597,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8596, 8594])).
% 49.53/49.72 tff(8598,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8599,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8598, 8597])).
% 49.53/49.72 tff(8600,plain,
% 49.53/49.72 (xuntil7(s92) | (~until6(s92))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8599, 7273, 6637])).
% 49.53/49.72 tff(8601,plain,
% 49.53/49.72 (xuntil7(s92)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8600, 8593])).
% 49.53/49.72 tff(8602,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8603,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8604,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8603, 8602])).
% 49.53/49.72 tff(8605,plain,
% 49.53/49.72 ((~xuntil7(s92)) | until6(s93)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8604, 2772, 7291])).
% 49.53/49.72 tff(8606,plain,
% 49.53/49.72 (until6(s93)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8605, 8601])).
% 49.53/49.72 tff(8607,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s93) | always5(s93) | (~until6(s93)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8608,plain,
% 49.53/49.72 ((always5(s93) | (~until6(s93)) | xuntil7(s93)) <=> (xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8609,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s93) | always5(s93) | (~until6(s93))))),
% 49.53/49.72 inference(monotonicity,[status(thm)],[8608])).
% 49.53/49.72 tff(8610,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 49.53/49.72 inference(transitivity,[status(thm)],[8609, 8607])).
% 49.53/49.72 tff(8611,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8612,plain,
% 49.53/49.72 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93))),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8611, 8610])).
% 49.53/49.72 tff(8613,plain,
% 49.53/49.72 (xuntil7(s93) | (~until6(s93))),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8612, 7273, 6629])).
% 49.53/49.72 tff(8614,plain,
% 49.53/49.72 (xuntil7(s93)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8613, 8606])).
% 49.53/49.72 tff(8615,plain,
% 49.53/49.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))),
% 49.53/49.72 inference(rewrite,[status(thm)],[])).
% 49.53/49.72 tff(8616,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))),
% 49.53/49.72 inference(quant_inst,[status(thm)],[])).
% 49.53/49.72 tff(8617,plain,
% 49.53/49.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94)),
% 49.53/49.72 inference(modus_ponens,[status(thm)],[8616, 8615])).
% 49.53/49.72 tff(8618,plain,
% 49.53/49.72 ((~xuntil7(s93)) | until6(s94)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8617, 2800, 7291])).
% 49.53/49.72 tff(8619,plain,
% 49.53/49.72 (until6(s94)),
% 49.53/49.72 inference(unit_resolution,[status(thm)],[8618, 8614])).
% 49.53/49.72 tff(8620,plain,
% 49.53/49.72 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s94) | always5(s94) | (~until6(s94)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8621,plain,
% 49.53/49.73 ((always5(s94) | (~until6(s94)) | xuntil7(s94)) <=> (xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8622,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s94) | always5(s94) | (~until6(s94))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8621])).
% 49.53/49.73 tff(8623,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8622, 8620])).
% 49.53/49.73 tff(8624,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8625,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8624, 8623])).
% 49.53/49.73 tff(8626,plain,
% 49.53/49.73 (xuntil7(s94) | (~until6(s94))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8625, 7273, 6621])).
% 49.53/49.73 tff(8627,plain,
% 49.53/49.73 (xuntil7(s94)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8626, 8619])).
% 49.53/49.73 tff(8628,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8629,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8630,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8629, 8628])).
% 49.53/49.73 tff(8631,plain,
% 49.53/49.73 ((~xuntil7(s94)) | until6(s95)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8630, 6110, 7291])).
% 49.53/49.73 tff(8632,plain,
% 49.53/49.73 (until6(s95)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8631, 8627])).
% 49.53/49.73 tff(8633,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s95) | always5(s95) | (~until6(s95)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8634,plain,
% 49.53/49.73 ((always5(s95) | (~until6(s95)) | xuntil7(s95)) <=> (xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8635,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s95) | always5(s95) | (~until6(s95))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8634])).
% 49.53/49.73 tff(8636,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8635, 8633])).
% 49.53/49.73 tff(8637,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8638,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8637, 8636])).
% 49.53/49.73 tff(8639,plain,
% 49.53/49.73 (xuntil7(s95) | (~until6(s95))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8638, 7273, 6613])).
% 49.53/49.73 tff(8640,plain,
% 49.53/49.73 (xuntil7(s95)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8639, 8632])).
% 49.53/49.73 tff(8641,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8642,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8643,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8642, 8641])).
% 49.53/49.73 tff(8644,plain,
% 49.53/49.73 ((~xuntil7(s95)) | until6(s96)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8643, 6218, 7291])).
% 49.53/49.73 tff(8645,plain,
% 49.53/49.73 (until6(s96)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8644, 8640])).
% 49.53/49.73 tff(8646,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s96) | always5(s96) | (~until6(s96)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8647,plain,
% 49.53/49.73 ((always5(s96) | (~until6(s96)) | xuntil7(s96)) <=> (xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8648,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s96) | always5(s96) | (~until6(s96))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8647])).
% 49.53/49.73 tff(8649,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8648, 8646])).
% 49.53/49.73 tff(8650,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8651,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8650, 8649])).
% 49.53/49.73 tff(8652,plain,
% 49.53/49.73 (xuntil7(s96) | (~until6(s96))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8651, 7273, 6612])).
% 49.53/49.73 tff(8653,plain,
% 49.53/49.73 (xuntil7(s96)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8652, 8645])).
% 49.53/49.73 tff(8654,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8655,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8656,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8655, 8654])).
% 49.53/49.73 tff(8657,plain,
% 49.53/49.73 ((~xuntil7(s96)) | until6(s97)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8656, 6306, 7291])).
% 49.53/49.73 tff(8658,plain,
% 49.53/49.73 (until6(s97)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8657, 8653])).
% 49.53/49.73 tff(8659,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s97) | always5(s97) | (~until6(s97)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8660,plain,
% 49.53/49.73 ((always5(s97) | (~until6(s97)) | xuntil7(s97)) <=> (xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8661,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s97) | always5(s97) | (~until6(s97))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8660])).
% 49.53/49.73 tff(8662,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8661, 8659])).
% 49.53/49.73 tff(8663,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8664,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8663, 8662])).
% 49.53/49.73 tff(8665,plain,
% 49.53/49.73 (xuntil7(s97) | (~until6(s97))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8664, 7273, 6611])).
% 49.53/49.73 tff(8666,plain,
% 49.53/49.73 (xuntil7(s97)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8665, 8658])).
% 49.53/49.73 tff(8667,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8668,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8669,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8668, 8667])).
% 49.53/49.73 tff(8670,plain,
% 49.53/49.73 ((~xuntil7(s97)) | until6(s98)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8669, 6367, 7291])).
% 49.53/49.73 tff(8671,plain,
% 49.53/49.73 (until6(s98)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8670, 8666])).
% 49.53/49.73 tff(8672,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s98) | always5(s98) | (~until6(s98)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8673,plain,
% 49.53/49.73 ((always5(s98) | (~until6(s98)) | xuntil7(s98)) <=> (xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8674,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s98) | always5(s98) | (~until6(s98))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8673])).
% 49.53/49.73 tff(8675,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8674, 8672])).
% 49.53/49.73 tff(8676,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8677,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8676, 8675])).
% 49.53/49.73 tff(8678,plain,
% 49.53/49.73 (xuntil7(s98) | (~until6(s98))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8677, 7273, 6603])).
% 49.53/49.73 tff(8679,plain,
% 49.53/49.73 (xuntil7(s98)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8678, 8671])).
% 49.53/49.73 tff(8680,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8681,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8682,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8681, 8680])).
% 49.53/49.73 tff(8683,plain,
% 49.53/49.73 ((~xuntil7(s98)) | until6(s99)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8682, 6386, 7291])).
% 49.53/49.73 tff(8684,plain,
% 49.53/49.73 (until6(s99)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8683, 8679])).
% 49.53/49.73 tff(8685,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | xuntil7(s99) | (~until6(s99)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8686,plain,
% 49.53/49.73 ((always5(s99) | (~until6(s99)) | xuntil7(s99)) <=> (always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8687,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | xuntil7(s99) | (~until6(s99))))),
% 49.53/49.73 inference(monotonicity,[status(thm)],[8686])).
% 49.53/49.73 tff(8688,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 49.53/49.73 inference(transitivity,[status(thm)],[8687, 8685])).
% 49.53/49.73 tff(8689,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8690,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8689, 8688])).
% 49.53/49.73 tff(8691,plain,
% 49.53/49.73 (xuntil7(s99)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8690, 7273, 8684, 6595])).
% 49.53/49.73 tff(8692,plain,
% 49.53/49.73 (^[X: $i] : refl(((~last(X)) | (~xuntil2p9(X))) <=> ((~last(X)) | (~xuntil2p9(X))))),
% 49.53/49.73 inference(bind,[status(th)],[])).
% 49.53/49.73 tff(8693,plain,
% 49.53/49.73 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(quant_intro,[status(thm)],[8692])).
% 49.53/49.73 tff(8694,plain,
% 49.53/49.73 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8695,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p9(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty10')).
% 49.53/49.73 tff(8696,plain,
% 49.53/49.73 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8695, 8694])).
% 49.53/49.73 tff(8697,plain,(
% 49.53/49.73 ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(skolemize,[status(sab)],[8696])).
% 49.53/49.73 tff(8698,plain,
% 49.53/49.73 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8697, 8693])).
% 49.53/49.73 tff(8699,plain,
% 49.53/49.73 (last(s99) <=> last(s99)),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8700,axiom,(last(s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound100')).
% 49.53/49.73 tff(8701,plain,
% 49.53/49.73 (last(s99)),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8700, 8699])).
% 49.53/49.73 tff(8702,plain,
% 49.53/49.73 (((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s99)) | (~xuntil2p9(s99)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s99)) | (~xuntil2p9(s99)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8703,plain,
% 49.53/49.73 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s99)) | (~xuntil2p9(s99)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8704,plain,
% 49.53/49.73 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s99)) | (~xuntil2p9(s99))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8703, 8702])).
% 49.53/49.73 tff(8705,plain,
% 49.53/49.73 (~xuntil2p9(s99)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8704, 8701, 8698])).
% 49.53/49.73 tff(8706,plain,
% 49.53/49.73 (^[X: $i] : refl((always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 49.53/49.73 inference(bind,[status(th)],[])).
% 49.53/49.73 tff(8707,plain,
% 49.53/49.73 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(quant_intro,[status(thm)],[8706])).
% 49.53/49.73 tff(8708,plain,
% 49.53/49.73 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8709,plain,
% 49.53/49.73 (^[X: $i] : rewrite(((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 49.53/49.73 inference(bind,[status(th)],[])).
% 49.53/49.73 tff(8710,plain,
% 49.53/49.73 (![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(quant_intro,[status(thm)],[8709])).
% 49.53/49.73 tff(8711,axiom,(![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty8')).
% 49.53/49.73 tff(8712,plain,
% 49.53/49.73 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8711, 8710])).
% 49.53/49.73 tff(8713,plain,
% 49.53/49.73 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8712, 8708])).
% 49.53/49.73 tff(8714,plain,(
% 49.53/49.73 ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(skolemize,[status(sab)],[8713])).
% 49.53/49.73 tff(8715,plain,
% 49.53/49.73 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8714, 8707])).
% 49.53/49.73 tff(8716,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8717,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8718,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s99) | xuntil2p9(s99) | (~until2p8(s99))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8717, 8716])).
% 49.53/49.73 tff(8719,plain,
% 49.53/49.73 (always5(s99) | (~until2p8(s99))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8718, 8715, 8705])).
% 49.53/49.73 tff(8720,plain,
% 49.53/49.73 (~until2p8(s99)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8719, 6595])).
% 49.53/49.73 tff(8721,plain,
% 49.53/49.73 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 49.53/49.73 inference(bind,[status(th)],[])).
% 49.53/49.73 tff(8722,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(quant_intro,[status(thm)],[8721])).
% 49.53/49.73 tff(8723,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8724,plain,
% 49.53/49.73 (^[Y: $i, X: $i] : rewrite(((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 49.53/49.73 inference(bind,[status(th)],[])).
% 49.53/49.73 tff(8725,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(quant_intro,[status(thm)],[8724])).
% 49.53/49.73 tff(8726,axiom,(![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty9')).
% 49.53/49.73 tff(8727,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8726, 8725])).
% 49.53/49.73 tff(8728,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8727, 8723])).
% 49.53/49.73 tff(8729,plain,(
% 49.53/49.73 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(skolemize,[status(sab)],[8728])).
% 49.53/49.73 tff(8730,plain,
% 49.53/49.73 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8729, 8722])).
% 49.53/49.73 tff(8731,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8732,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8733,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8732, 8731])).
% 49.53/49.73 tff(8734,plain,
% 49.53/49.73 (until2p8(s99) | (~xuntil2p9(s98))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8733, 6386, 8730])).
% 49.53/49.73 tff(8735,plain,
% 49.53/49.73 (~xuntil2p9(s98)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8734, 8720])).
% 49.53/49.73 tff(8736,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8737,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8738,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s98) | xuntil2p9(s98) | (~until2p8(s98))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 49.53/49.73 tff(8739,plain,
% 49.53/49.73 (~until2p8(s98)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8738, 8715, 8735, 6603])).
% 49.53/49.73 tff(8740,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8741,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8742,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8741, 8740])).
% 49.53/49.73 tff(8743,plain,
% 49.53/49.73 (until2p8(s98) | (~xuntil2p9(s97))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8742, 6367, 8730])).
% 49.53/49.73 tff(8744,plain,
% 49.53/49.73 (~xuntil2p9(s97)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8743, 8739])).
% 49.53/49.73 tff(8745,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8746,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8747,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s97) | xuntil2p9(s97) | (~until2p8(s97))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8746, 8745])).
% 49.53/49.73 tff(8748,plain,
% 49.53/49.73 (xuntil2p9(s97) | (~until2p8(s97))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8747, 8715, 6611])).
% 49.53/49.73 tff(8749,plain,
% 49.53/49.73 (~until2p8(s97)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8748, 8744])).
% 49.53/49.73 tff(8750,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8751,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8752,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8751, 8750])).
% 49.53/49.73 tff(8753,plain,
% 49.53/49.73 (until2p8(s97) | (~xuntil2p9(s96))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8752, 6306, 8730])).
% 49.53/49.73 tff(8754,plain,
% 49.53/49.73 (~xuntil2p9(s96)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8753, 8749])).
% 49.53/49.73 tff(8755,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8756,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8757,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s96) | xuntil2p9(s96) | (~until2p8(s96))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8756, 8755])).
% 49.53/49.73 tff(8758,plain,
% 49.53/49.73 (xuntil2p9(s96) | (~until2p8(s96))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8757, 8715, 6612])).
% 49.53/49.73 tff(8759,plain,
% 49.53/49.73 (~until2p8(s96)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8758, 8754])).
% 49.53/49.73 tff(8760,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8761,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8762,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8761, 8760])).
% 49.53/49.73 tff(8763,plain,
% 49.53/49.73 (until2p8(s96) | (~xuntil2p9(s95))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8762, 6218, 8730])).
% 49.53/49.73 tff(8764,plain,
% 49.53/49.73 (~xuntil2p9(s95)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8763, 8759])).
% 49.53/49.73 tff(8765,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8766,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8767,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s95) | xuntil2p9(s95) | (~until2p8(s95))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8766, 8765])).
% 49.53/49.73 tff(8768,plain,
% 49.53/49.73 (xuntil2p9(s95) | (~until2p8(s95))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8767, 8715, 6613])).
% 49.53/49.73 tff(8769,plain,
% 49.53/49.73 (~until2p8(s95)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8768, 8764])).
% 49.53/49.73 tff(8770,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8771,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8772,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8771, 8770])).
% 49.53/49.73 tff(8773,plain,
% 49.53/49.73 (until2p8(s95) | (~xuntil2p9(s94))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8772, 6110, 8730])).
% 49.53/49.73 tff(8774,plain,
% 49.53/49.73 (~xuntil2p9(s94)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8773, 8769])).
% 49.53/49.73 tff(8775,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8776,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8777,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s94) | xuntil2p9(s94) | (~until2p8(s94))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8776, 8775])).
% 49.53/49.73 tff(8778,plain,
% 49.53/49.73 (xuntil2p9(s94) | (~until2p8(s94))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8777, 8715, 6621])).
% 49.53/49.73 tff(8779,plain,
% 49.53/49.73 (~until2p8(s94)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8778, 8774])).
% 49.53/49.73 tff(8780,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8781,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8782,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8781, 8780])).
% 49.53/49.73 tff(8783,plain,
% 49.53/49.73 (until2p8(s94) | (~xuntil2p9(s93))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8782, 2800, 8730])).
% 49.53/49.73 tff(8784,plain,
% 49.53/49.73 (~xuntil2p9(s93)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8783, 8779])).
% 49.53/49.73 tff(8785,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8786,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8787,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s93) | xuntil2p9(s93) | (~until2p8(s93))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8786, 8785])).
% 49.53/49.73 tff(8788,plain,
% 49.53/49.73 (xuntil2p9(s93) | (~until2p8(s93))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8787, 8715, 6629])).
% 49.53/49.73 tff(8789,plain,
% 49.53/49.73 (~until2p8(s93)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8788, 8784])).
% 49.53/49.73 tff(8790,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8791,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8792,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8791, 8790])).
% 49.53/49.73 tff(8793,plain,
% 49.53/49.73 (until2p8(s93) | (~xuntil2p9(s92))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8792, 2772, 8730])).
% 49.53/49.73 tff(8794,plain,
% 49.53/49.73 (~xuntil2p9(s92)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8793, 8789])).
% 49.53/49.73 tff(8795,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8796,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8797,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s92) | xuntil2p9(s92) | (~until2p8(s92))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 49.53/49.73 tff(8798,plain,
% 49.53/49.73 (xuntil2p9(s92) | (~until2p8(s92))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8797, 8715, 6637])).
% 49.53/49.73 tff(8799,plain,
% 49.53/49.73 (~until2p8(s92)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8798, 8794])).
% 49.53/49.73 tff(8800,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8801,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8802,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8801, 8800])).
% 49.53/49.73 tff(8803,plain,
% 49.53/49.73 (until2p8(s92) | (~xuntil2p9(s91))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8802, 2741, 8730])).
% 49.53/49.73 tff(8804,plain,
% 49.53/49.73 (~xuntil2p9(s91)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8803, 8799])).
% 49.53/49.73 tff(8805,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8806,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8807,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s91) | xuntil2p9(s91) | (~until2p8(s91))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8806, 8805])).
% 49.53/49.73 tff(8808,plain,
% 49.53/49.73 (xuntil2p9(s91) | (~until2p8(s91))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8807, 8715, 6645])).
% 49.53/49.73 tff(8809,plain,
% 49.53/49.73 (~until2p8(s91)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8808, 8804])).
% 49.53/49.73 tff(8810,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8811,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8812,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8811, 8810])).
% 49.53/49.73 tff(8813,plain,
% 49.53/49.73 (until2p8(s91) | (~xuntil2p9(s90))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8812, 2715, 8730])).
% 49.53/49.73 tff(8814,plain,
% 49.53/49.73 (~xuntil2p9(s90)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8813, 8809])).
% 49.53/49.73 tff(8815,plain,
% 49.53/49.73 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8816,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8817,plain,
% 49.53/49.73 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s90) | xuntil2p9(s90) | (~until2p8(s90))),
% 49.53/49.73 inference(modus_ponens,[status(thm)],[8816, 8815])).
% 49.53/49.73 tff(8818,plain,
% 49.53/49.73 (xuntil2p9(s90) | (~until2p8(s90))),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8817, 8715, 6653])).
% 49.53/49.73 tff(8819,plain,
% 49.53/49.73 (~until2p8(s90)),
% 49.53/49.73 inference(unit_resolution,[status(thm)],[8818, 8814])).
% 49.53/49.73 tff(8820,plain,
% 49.53/49.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))),
% 49.53/49.73 inference(rewrite,[status(thm)],[])).
% 49.53/49.73 tff(8821,plain,
% 49.53/49.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))),
% 49.53/49.73 inference(quant_inst,[status(thm)],[])).
% 49.53/49.73 tff(8822,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8821, 8820])).
% 49.53/49.74 tff(8823,plain,
% 49.53/49.74 (until2p8(s90) | (~xuntil2p9(s89))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8822, 2686, 8730])).
% 49.53/49.74 tff(8824,plain,
% 49.53/49.74 (~xuntil2p9(s89)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8823, 8819])).
% 49.53/49.74 tff(8825,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8826,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8827,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s89) | xuntil2p9(s89) | (~until2p8(s89))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8826, 8825])).
% 49.53/49.74 tff(8828,plain,
% 49.53/49.74 (xuntil2p9(s89) | (~until2p8(s89))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8827, 8715, 6661])).
% 49.53/49.74 tff(8829,plain,
% 49.53/49.74 (~until2p8(s89)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8828, 8824])).
% 49.53/49.74 tff(8830,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8831,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8832,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8831, 8830])).
% 49.53/49.74 tff(8833,plain,
% 49.53/49.74 (until2p8(s89) | (~xuntil2p9(s88))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8832, 2658, 8730])).
% 49.53/49.74 tff(8834,plain,
% 49.53/49.74 (~xuntil2p9(s88)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8833, 8829])).
% 49.53/49.74 tff(8835,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8836,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8837,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s88) | xuntil2p9(s88) | (~until2p8(s88))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8836, 8835])).
% 49.53/49.74 tff(8838,plain,
% 49.53/49.74 (xuntil2p9(s88) | (~until2p8(s88))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8837, 8715, 6669])).
% 49.53/49.74 tff(8839,plain,
% 49.53/49.74 (~until2p8(s88)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8838, 8834])).
% 49.53/49.74 tff(8840,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8841,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8842,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8841, 8840])).
% 49.53/49.74 tff(8843,plain,
% 49.53/49.74 (until2p8(s88) | (~xuntil2p9(s87))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8842, 2627, 8730])).
% 49.53/49.74 tff(8844,plain,
% 49.53/49.74 (~xuntil2p9(s87)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8843, 8839])).
% 49.53/49.74 tff(8845,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8846,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8847,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s87) | xuntil2p9(s87) | (~until2p8(s87))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8846, 8845])).
% 49.53/49.74 tff(8848,plain,
% 49.53/49.74 (xuntil2p9(s87) | (~until2p8(s87))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8847, 8715, 6677])).
% 49.53/49.74 tff(8849,plain,
% 49.53/49.74 (~until2p8(s87)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8848, 8844])).
% 49.53/49.74 tff(8850,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8851,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8852,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8851, 8850])).
% 49.53/49.74 tff(8853,plain,
% 49.53/49.74 (until2p8(s87) | (~xuntil2p9(s86))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8852, 2599, 8730])).
% 49.53/49.74 tff(8854,plain,
% 49.53/49.74 (~xuntil2p9(s86)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8853, 8849])).
% 49.53/49.74 tff(8855,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8856,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8857,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s86) | xuntil2p9(s86) | (~until2p8(s86))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8856, 8855])).
% 49.53/49.74 tff(8858,plain,
% 49.53/49.74 (xuntil2p9(s86) | (~until2p8(s86))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8857, 8715, 6685])).
% 49.53/49.74 tff(8859,plain,
% 49.53/49.74 (~until2p8(s86)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8858, 8854])).
% 49.53/49.74 tff(8860,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8861,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8862,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8861, 8860])).
% 49.53/49.74 tff(8863,plain,
% 49.53/49.74 (until2p8(s86) | (~xuntil2p9(s85))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8862, 2568, 8730])).
% 49.53/49.74 tff(8864,plain,
% 49.53/49.74 (~xuntil2p9(s85)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8863, 8859])).
% 49.53/49.74 tff(8865,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8866,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8867,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s85) | xuntil2p9(s85) | (~until2p8(s85))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8866, 8865])).
% 49.53/49.74 tff(8868,plain,
% 49.53/49.74 (xuntil2p9(s85) | (~until2p8(s85))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8867, 8715, 6693])).
% 49.53/49.74 tff(8869,plain,
% 49.53/49.74 (~until2p8(s85)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8868, 8864])).
% 49.53/49.74 tff(8870,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8871,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8872,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8871, 8870])).
% 49.53/49.74 tff(8873,plain,
% 49.53/49.74 (until2p8(s85) | (~xuntil2p9(s84))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8872, 2540, 8730])).
% 49.53/49.74 tff(8874,plain,
% 49.53/49.74 (~xuntil2p9(s84)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8873, 8869])).
% 49.53/49.74 tff(8875,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8876,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8877,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s84) | xuntil2p9(s84) | (~until2p8(s84))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8876, 8875])).
% 49.53/49.74 tff(8878,plain,
% 49.53/49.74 (xuntil2p9(s84) | (~until2p8(s84))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8877, 8715, 6701])).
% 49.53/49.74 tff(8879,plain,
% 49.53/49.74 (~until2p8(s84)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8878, 8874])).
% 49.53/49.74 tff(8880,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8881,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8882,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8881, 8880])).
% 49.53/49.74 tff(8883,plain,
% 49.53/49.74 (until2p8(s84) | (~xuntil2p9(s83))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8882, 2509, 8730])).
% 49.53/49.74 tff(8884,plain,
% 49.53/49.74 (~xuntil2p9(s83)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8883, 8879])).
% 49.53/49.74 tff(8885,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8886,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8887,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s83) | xuntil2p9(s83) | (~until2p8(s83))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8886, 8885])).
% 49.53/49.74 tff(8888,plain,
% 49.53/49.74 (xuntil2p9(s83) | (~until2p8(s83))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8887, 8715, 6709])).
% 49.53/49.74 tff(8889,plain,
% 49.53/49.74 (~until2p8(s83)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8888, 8884])).
% 49.53/49.74 tff(8890,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8891,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8892,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8891, 8890])).
% 49.53/49.74 tff(8893,plain,
% 49.53/49.74 (until2p8(s83) | (~xuntil2p9(s82))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8892, 2481, 8730])).
% 49.53/49.74 tff(8894,plain,
% 49.53/49.74 (~xuntil2p9(s82)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8893, 8889])).
% 49.53/49.74 tff(8895,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8896,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8897,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s82) | xuntil2p9(s82) | (~until2p8(s82))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8896, 8895])).
% 49.53/49.74 tff(8898,plain,
% 49.53/49.74 (xuntil2p9(s82) | (~until2p8(s82))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8897, 8715, 6717])).
% 49.53/49.74 tff(8899,plain,
% 49.53/49.74 (~until2p8(s82)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8898, 8894])).
% 49.53/49.74 tff(8900,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8901,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8902,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8901, 8900])).
% 49.53/49.74 tff(8903,plain,
% 49.53/49.74 (until2p8(s82) | (~xuntil2p9(s81))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8902, 2450, 8730])).
% 49.53/49.74 tff(8904,plain,
% 49.53/49.74 (~xuntil2p9(s81)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8903, 8899])).
% 49.53/49.74 tff(8905,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8906,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8907,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s81) | xuntil2p9(s81) | (~until2p8(s81))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8906, 8905])).
% 49.53/49.74 tff(8908,plain,
% 49.53/49.74 (xuntil2p9(s81) | (~until2p8(s81))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8907, 8715, 6725])).
% 49.53/49.74 tff(8909,plain,
% 49.53/49.74 (~until2p8(s81)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8908, 8904])).
% 49.53/49.74 tff(8910,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8911,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8912,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8911, 8910])).
% 49.53/49.74 tff(8913,plain,
% 49.53/49.74 (until2p8(s81) | (~xuntil2p9(s80))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8912, 2422, 8730])).
% 49.53/49.74 tff(8914,plain,
% 49.53/49.74 (~xuntil2p9(s80)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8913, 8909])).
% 49.53/49.74 tff(8915,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8916,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8917,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s80) | xuntil2p9(s80) | (~until2p8(s80))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8916, 8915])).
% 49.53/49.74 tff(8918,plain,
% 49.53/49.74 (xuntil2p9(s80) | (~until2p8(s80))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8917, 8715, 6733])).
% 49.53/49.74 tff(8919,plain,
% 49.53/49.74 (~until2p8(s80)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8918, 8914])).
% 49.53/49.74 tff(8920,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8921,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8922,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8921, 8920])).
% 49.53/49.74 tff(8923,plain,
% 49.53/49.74 (until2p8(s80) | (~xuntil2p9(s79))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8922, 2391, 8730])).
% 49.53/49.74 tff(8924,plain,
% 49.53/49.74 (~xuntil2p9(s79)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8923, 8919])).
% 49.53/49.74 tff(8925,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8926,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8927,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s79) | xuntil2p9(s79) | (~until2p8(s79))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8926, 8925])).
% 49.53/49.74 tff(8928,plain,
% 49.53/49.74 (xuntil2p9(s79) | (~until2p8(s79))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8927, 8715, 6741])).
% 49.53/49.74 tff(8929,plain,
% 49.53/49.74 (~until2p8(s79)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8928, 8924])).
% 49.53/49.74 tff(8930,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8931,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8932,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8931, 8930])).
% 49.53/49.74 tff(8933,plain,
% 49.53/49.74 (until2p8(s79) | (~xuntil2p9(s78))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8932, 2363, 8730])).
% 49.53/49.74 tff(8934,plain,
% 49.53/49.74 (~xuntil2p9(s78)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8933, 8929])).
% 49.53/49.74 tff(8935,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8936,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8937,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s78) | xuntil2p9(s78) | (~until2p8(s78))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 49.53/49.74 tff(8938,plain,
% 49.53/49.74 (xuntil2p9(s78) | (~until2p8(s78))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8937, 8715, 6749])).
% 49.53/49.74 tff(8939,plain,
% 49.53/49.74 (~until2p8(s78)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8938, 8934])).
% 49.53/49.74 tff(8940,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8941,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8942,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8941, 8940])).
% 49.53/49.74 tff(8943,plain,
% 49.53/49.74 (until2p8(s78) | (~xuntil2p9(s77))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8942, 2332, 8730])).
% 49.53/49.74 tff(8944,plain,
% 49.53/49.74 (~xuntil2p9(s77)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8943, 8939])).
% 49.53/49.74 tff(8945,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8946,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8947,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s77) | xuntil2p9(s77) | (~until2p8(s77))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8946, 8945])).
% 49.53/49.74 tff(8948,plain,
% 49.53/49.74 (xuntil2p9(s77) | (~until2p8(s77))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8947, 8715, 6757])).
% 49.53/49.74 tff(8949,plain,
% 49.53/49.74 (~until2p8(s77)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8948, 8944])).
% 49.53/49.74 tff(8950,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8951,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8952,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8951, 8950])).
% 49.53/49.74 tff(8953,plain,
% 49.53/49.74 (until2p8(s77) | (~xuntil2p9(s76))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8952, 2304, 8730])).
% 49.53/49.74 tff(8954,plain,
% 49.53/49.74 (~xuntil2p9(s76)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8953, 8949])).
% 49.53/49.74 tff(8955,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8956,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8957,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s76) | xuntil2p9(s76) | (~until2p8(s76))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8956, 8955])).
% 49.53/49.74 tff(8958,plain,
% 49.53/49.74 (xuntil2p9(s76) | (~until2p8(s76))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8957, 8715, 6765])).
% 49.53/49.74 tff(8959,plain,
% 49.53/49.74 (~until2p8(s76)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8958, 8954])).
% 49.53/49.74 tff(8960,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8961,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8962,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8961, 8960])).
% 49.53/49.74 tff(8963,plain,
% 49.53/49.74 (until2p8(s76) | (~xuntil2p9(s75))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8962, 2273, 8730])).
% 49.53/49.74 tff(8964,plain,
% 49.53/49.74 (~xuntil2p9(s75)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8963, 8959])).
% 49.53/49.74 tff(8965,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8966,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8967,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s75) | xuntil2p9(s75) | (~until2p8(s75))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8966, 8965])).
% 49.53/49.74 tff(8968,plain,
% 49.53/49.74 (xuntil2p9(s75) | (~until2p8(s75))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8967, 8715, 6773])).
% 49.53/49.74 tff(8969,plain,
% 49.53/49.74 (~until2p8(s75)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8968, 8964])).
% 49.53/49.74 tff(8970,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8971,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8972,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8971, 8970])).
% 49.53/49.74 tff(8973,plain,
% 49.53/49.74 (until2p8(s75) | (~xuntil2p9(s74))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8972, 2245, 8730])).
% 49.53/49.74 tff(8974,plain,
% 49.53/49.74 (~xuntil2p9(s74)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8973, 8969])).
% 49.53/49.74 tff(8975,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8976,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8977,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s74) | xuntil2p9(s74) | (~until2p8(s74))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8976, 8975])).
% 49.53/49.74 tff(8978,plain,
% 49.53/49.74 (xuntil2p9(s74) | (~until2p8(s74))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8977, 8715, 6781])).
% 49.53/49.74 tff(8979,plain,
% 49.53/49.74 (~until2p8(s74)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8978, 8974])).
% 49.53/49.74 tff(8980,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8981,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8982,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8981, 8980])).
% 49.53/49.74 tff(8983,plain,
% 49.53/49.74 (until2p8(s74) | (~xuntil2p9(s73))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8982, 2214, 8730])).
% 49.53/49.74 tff(8984,plain,
% 49.53/49.74 (~xuntil2p9(s73)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8983, 8979])).
% 49.53/49.74 tff(8985,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8986,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8987,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s73) | xuntil2p9(s73) | (~until2p8(s73))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8986, 8985])).
% 49.53/49.74 tff(8988,plain,
% 49.53/49.74 (xuntil2p9(s73) | (~until2p8(s73))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8987, 8715, 6789])).
% 49.53/49.74 tff(8989,plain,
% 49.53/49.74 (~until2p8(s73)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8988, 8984])).
% 49.53/49.74 tff(8990,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8991,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8992,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8991, 8990])).
% 49.53/49.74 tff(8993,plain,
% 49.53/49.74 (until2p8(s73) | (~xuntil2p9(s72))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8992, 2186, 8730])).
% 49.53/49.74 tff(8994,plain,
% 49.53/49.74 (~xuntil2p9(s72)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8993, 8989])).
% 49.53/49.74 tff(8995,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(8996,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(8997,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s72) | xuntil2p9(s72) | (~until2p8(s72))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[8996, 8995])).
% 49.53/49.74 tff(8998,plain,
% 49.53/49.74 (xuntil2p9(s72) | (~until2p8(s72))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8997, 8715, 6797])).
% 49.53/49.74 tff(8999,plain,
% 49.53/49.74 (~until2p8(s72)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[8998, 8994])).
% 49.53/49.74 tff(9000,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(9001,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(9002,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[9001, 9000])).
% 49.53/49.74 tff(9003,plain,
% 49.53/49.74 (until2p8(s72) | (~xuntil2p9(s71))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9002, 2155, 8730])).
% 49.53/49.74 tff(9004,plain,
% 49.53/49.74 (~xuntil2p9(s71)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9003, 8999])).
% 49.53/49.74 tff(9005,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(9006,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(9007,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s71) | xuntil2p9(s71) | (~until2p8(s71))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[9006, 9005])).
% 49.53/49.74 tff(9008,plain,
% 49.53/49.74 (xuntil2p9(s71) | (~until2p8(s71))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9007, 8715, 6805])).
% 49.53/49.74 tff(9009,plain,
% 49.53/49.74 (~until2p8(s71)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9008, 9004])).
% 49.53/49.74 tff(9010,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(9011,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(9012,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[9011, 9010])).
% 49.53/49.74 tff(9013,plain,
% 49.53/49.74 (until2p8(s71) | (~xuntil2p9(s70))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9012, 2127, 8730])).
% 49.53/49.74 tff(9014,plain,
% 49.53/49.74 (~xuntil2p9(s70)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9013, 9009])).
% 49.53/49.74 tff(9015,plain,
% 49.53/49.74 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(9016,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(9017,plain,
% 49.53/49.74 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s70) | xuntil2p9(s70) | (~until2p8(s70))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[9016, 9015])).
% 49.53/49.74 tff(9018,plain,
% 49.53/49.74 (xuntil2p9(s70) | (~until2p8(s70))),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9017, 8715, 6813])).
% 49.53/49.74 tff(9019,plain,
% 49.53/49.74 (~until2p8(s70)),
% 49.53/49.74 inference(unit_resolution,[status(thm)],[9018, 9014])).
% 49.53/49.74 tff(9020,plain,
% 49.53/49.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))),
% 49.53/49.74 inference(rewrite,[status(thm)],[])).
% 49.53/49.74 tff(9021,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))),
% 49.53/49.74 inference(quant_inst,[status(thm)],[])).
% 49.53/49.74 tff(9022,plain,
% 49.53/49.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69))),
% 49.53/49.74 inference(modus_ponens,[status(thm)],[9021, 9020])).
% 49.53/49.74 tff(9023,plain,
% 49.53/49.75 (until2p8(s70) | (~xuntil2p9(s69))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9022, 2096, 8730])).
% 49.53/49.75 tff(9024,plain,
% 49.53/49.75 (~xuntil2p9(s69)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9023, 9019])).
% 49.53/49.75 tff(9025,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9026,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9027,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s69) | xuntil2p9(s69) | (~until2p8(s69))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9026, 9025])).
% 49.53/49.75 tff(9028,plain,
% 49.53/49.75 (xuntil2p9(s69) | (~until2p8(s69))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9027, 8715, 6821])).
% 49.53/49.75 tff(9029,plain,
% 49.53/49.75 (~until2p8(s69)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9028, 9024])).
% 49.53/49.75 tff(9030,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9031,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9032,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9031, 9030])).
% 49.53/49.75 tff(9033,plain,
% 49.53/49.75 (until2p8(s69) | (~xuntil2p9(s68))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9032, 2068, 8730])).
% 49.53/49.75 tff(9034,plain,
% 49.53/49.75 (~xuntil2p9(s68)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9033, 9029])).
% 49.53/49.75 tff(9035,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9036,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9037,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s68) | xuntil2p9(s68) | (~until2p8(s68))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9036, 9035])).
% 49.53/49.75 tff(9038,plain,
% 49.53/49.75 (xuntil2p9(s68) | (~until2p8(s68))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9037, 8715, 6829])).
% 49.53/49.75 tff(9039,plain,
% 49.53/49.75 (~until2p8(s68)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9038, 9034])).
% 49.53/49.75 tff(9040,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9041,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9042,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9041, 9040])).
% 49.53/49.75 tff(9043,plain,
% 49.53/49.75 (until2p8(s68) | (~xuntil2p9(s67))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9042, 2037, 8730])).
% 49.53/49.75 tff(9044,plain,
% 49.53/49.75 (~xuntil2p9(s67)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9043, 9039])).
% 49.53/49.75 tff(9045,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9046,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9047,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s67) | xuntil2p9(s67) | (~until2p8(s67))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9046, 9045])).
% 49.53/49.75 tff(9048,plain,
% 49.53/49.75 (xuntil2p9(s67) | (~until2p8(s67))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9047, 8715, 6837])).
% 49.53/49.75 tff(9049,plain,
% 49.53/49.75 (~until2p8(s67)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9048, 9044])).
% 49.53/49.75 tff(9050,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9051,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9052,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9051, 9050])).
% 49.53/49.75 tff(9053,plain,
% 49.53/49.75 (until2p8(s67) | (~xuntil2p9(s66))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9052, 2009, 8730])).
% 49.53/49.75 tff(9054,plain,
% 49.53/49.75 (~xuntil2p9(s66)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9053, 9049])).
% 49.53/49.75 tff(9055,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9056,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9057,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s66) | xuntil2p9(s66) | (~until2p8(s66))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9056, 9055])).
% 49.53/49.75 tff(9058,plain,
% 49.53/49.75 (xuntil2p9(s66) | (~until2p8(s66))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9057, 8715, 6845])).
% 49.53/49.75 tff(9059,plain,
% 49.53/49.75 (~until2p8(s66)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9058, 9054])).
% 49.53/49.75 tff(9060,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9061,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9062,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9061, 9060])).
% 49.53/49.75 tff(9063,plain,
% 49.53/49.75 (until2p8(s66) | (~xuntil2p9(s65))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9062, 1978, 8730])).
% 49.53/49.75 tff(9064,plain,
% 49.53/49.75 (~xuntil2p9(s65)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9063, 9059])).
% 49.53/49.75 tff(9065,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9066,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9067,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s65) | xuntil2p9(s65) | (~until2p8(s65))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9066, 9065])).
% 49.53/49.75 tff(9068,plain,
% 49.53/49.75 (xuntil2p9(s65) | (~until2p8(s65))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9067, 8715, 6853])).
% 49.53/49.75 tff(9069,plain,
% 49.53/49.75 (~until2p8(s65)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9068, 9064])).
% 49.53/49.75 tff(9070,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9071,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9072,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 49.53/49.75 tff(9073,plain,
% 49.53/49.75 (until2p8(s65) | (~xuntil2p9(s64))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9072, 1950, 8730])).
% 49.53/49.75 tff(9074,plain,
% 49.53/49.75 (~xuntil2p9(s64)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9073, 9069])).
% 49.53/49.75 tff(9075,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9076,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9077,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s64) | xuntil2p9(s64) | (~until2p8(s64))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 49.53/49.75 tff(9078,plain,
% 49.53/49.75 (xuntil2p9(s64) | (~until2p8(s64))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9077, 8715, 6861])).
% 49.53/49.75 tff(9079,plain,
% 49.53/49.75 (~until2p8(s64)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9078, 9074])).
% 49.53/49.75 tff(9080,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9081,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9082,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9081, 9080])).
% 49.53/49.75 tff(9083,plain,
% 49.53/49.75 (until2p8(s64) | (~xuntil2p9(s63))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9082, 1919, 8730])).
% 49.53/49.75 tff(9084,plain,
% 49.53/49.75 (~xuntil2p9(s63)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9083, 9079])).
% 49.53/49.75 tff(9085,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9086,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9087,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s63) | xuntil2p9(s63) | (~until2p8(s63))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9086, 9085])).
% 49.53/49.75 tff(9088,plain,
% 49.53/49.75 (xuntil2p9(s63) | (~until2p8(s63))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9087, 8715, 6869])).
% 49.53/49.75 tff(9089,plain,
% 49.53/49.75 (~until2p8(s63)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9088, 9084])).
% 49.53/49.75 tff(9090,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9091,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9092,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9091, 9090])).
% 49.53/49.75 tff(9093,plain,
% 49.53/49.75 (until2p8(s63) | (~xuntil2p9(s62))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9092, 1891, 8730])).
% 49.53/49.75 tff(9094,plain,
% 49.53/49.75 (~xuntil2p9(s62)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9093, 9089])).
% 49.53/49.75 tff(9095,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9096,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9097,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s62) | xuntil2p9(s62) | (~until2p8(s62))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9096, 9095])).
% 49.53/49.75 tff(9098,plain,
% 49.53/49.75 (xuntil2p9(s62) | (~until2p8(s62))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9097, 8715, 6877])).
% 49.53/49.75 tff(9099,plain,
% 49.53/49.75 (~until2p8(s62)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9098, 9094])).
% 49.53/49.75 tff(9100,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9101,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9102,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9101, 9100])).
% 49.53/49.75 tff(9103,plain,
% 49.53/49.75 (until2p8(s62) | (~xuntil2p9(s61))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9102, 1860, 8730])).
% 49.53/49.75 tff(9104,plain,
% 49.53/49.75 (~xuntil2p9(s61)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9103, 9099])).
% 49.53/49.75 tff(9105,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9106,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9107,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s61) | xuntil2p9(s61) | (~until2p8(s61))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9106, 9105])).
% 49.53/49.75 tff(9108,plain,
% 49.53/49.75 (xuntil2p9(s61) | (~until2p8(s61))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9107, 8715, 6885])).
% 49.53/49.75 tff(9109,plain,
% 49.53/49.75 (~until2p8(s61)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9108, 9104])).
% 49.53/49.75 tff(9110,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9111,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9112,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9111, 9110])).
% 49.53/49.75 tff(9113,plain,
% 49.53/49.75 (until2p8(s61) | (~xuntil2p9(s60))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9112, 1832, 8730])).
% 49.53/49.75 tff(9114,plain,
% 49.53/49.75 (~xuntil2p9(s60)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9113, 9109])).
% 49.53/49.75 tff(9115,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9116,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9117,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s60) | xuntil2p9(s60) | (~until2p8(s60))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9116, 9115])).
% 49.53/49.75 tff(9118,plain,
% 49.53/49.75 (xuntil2p9(s60) | (~until2p8(s60))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9117, 8715, 6893])).
% 49.53/49.75 tff(9119,plain,
% 49.53/49.75 (~until2p8(s60)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9118, 9114])).
% 49.53/49.75 tff(9120,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9121,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9122,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9121, 9120])).
% 49.53/49.75 tff(9123,plain,
% 49.53/49.75 (until2p8(s60) | (~xuntil2p9(s59))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9122, 1801, 8730])).
% 49.53/49.75 tff(9124,plain,
% 49.53/49.75 (~xuntil2p9(s59)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9123, 9119])).
% 49.53/49.75 tff(9125,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9126,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9127,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9126, 9125])).
% 49.53/49.75 tff(9128,plain,
% 49.53/49.75 (xuntil2p9(s59) | (~until2p8(s59))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9127, 8715, 6901])).
% 49.53/49.75 tff(9129,plain,
% 49.53/49.75 (~until2p8(s59)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9128, 9124])).
% 49.53/49.75 tff(9130,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9131,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9132,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9131, 9130])).
% 49.53/49.75 tff(9133,plain,
% 49.53/49.75 (until2p8(s59) | (~xuntil2p9(s58))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9132, 1773, 8730])).
% 49.53/49.75 tff(9134,plain,
% 49.53/49.75 (~xuntil2p9(s58)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9133, 9129])).
% 49.53/49.75 tff(9135,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9136,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9137,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9136, 9135])).
% 49.53/49.75 tff(9138,plain,
% 49.53/49.75 (xuntil2p9(s58) | (~until2p8(s58))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9137, 8715, 6909])).
% 49.53/49.75 tff(9139,plain,
% 49.53/49.75 (~until2p8(s58)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9138, 9134])).
% 49.53/49.75 tff(9140,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9141,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9142,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9141, 9140])).
% 49.53/49.75 tff(9143,plain,
% 49.53/49.75 (until2p8(s58) | (~xuntil2p9(s57))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9142, 1742, 8730])).
% 49.53/49.75 tff(9144,plain,
% 49.53/49.75 (~xuntil2p9(s57)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9143, 9139])).
% 49.53/49.75 tff(9145,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9146,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9147,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9146, 9145])).
% 49.53/49.75 tff(9148,plain,
% 49.53/49.75 (xuntil2p9(s57) | (~until2p8(s57))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9147, 8715, 6917])).
% 49.53/49.75 tff(9149,plain,
% 49.53/49.75 (~until2p8(s57)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9148, 9144])).
% 49.53/49.75 tff(9150,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9151,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9152,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9151, 9150])).
% 49.53/49.75 tff(9153,plain,
% 49.53/49.75 (until2p8(s57) | (~xuntil2p9(s56))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9152, 1714, 8730])).
% 49.53/49.75 tff(9154,plain,
% 49.53/49.75 (~xuntil2p9(s56)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9153, 9149])).
% 49.53/49.75 tff(9155,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9156,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9157,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9156, 9155])).
% 49.53/49.75 tff(9158,plain,
% 49.53/49.75 (xuntil2p9(s56) | (~until2p8(s56))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9157, 8715, 6925])).
% 49.53/49.75 tff(9159,plain,
% 49.53/49.75 (~until2p8(s56)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9158, 9154])).
% 49.53/49.75 tff(9160,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9161,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9162,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9161, 9160])).
% 49.53/49.75 tff(9163,plain,
% 49.53/49.75 (until2p8(s56) | (~xuntil2p9(s55))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9162, 1683, 8730])).
% 49.53/49.75 tff(9164,plain,
% 49.53/49.75 (~xuntil2p9(s55)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9163, 9159])).
% 49.53/49.75 tff(9165,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9166,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9167,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9166, 9165])).
% 49.53/49.75 tff(9168,plain,
% 49.53/49.75 (xuntil2p9(s55) | (~until2p8(s55))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9167, 8715, 6933])).
% 49.53/49.75 tff(9169,plain,
% 49.53/49.75 (~until2p8(s55)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9168, 9164])).
% 49.53/49.75 tff(9170,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9171,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9172,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9171, 9170])).
% 49.53/49.75 tff(9173,plain,
% 49.53/49.75 (until2p8(s55) | (~xuntil2p9(s54))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9172, 1655, 8730])).
% 49.53/49.75 tff(9174,plain,
% 49.53/49.75 (~xuntil2p9(s54)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9173, 9169])).
% 49.53/49.75 tff(9175,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9176,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9177,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9176, 9175])).
% 49.53/49.75 tff(9178,plain,
% 49.53/49.75 (xuntil2p9(s54) | (~until2p8(s54))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9177, 8715, 6941])).
% 49.53/49.75 tff(9179,plain,
% 49.53/49.75 (~until2p8(s54)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9178, 9174])).
% 49.53/49.75 tff(9180,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9181,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9182,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9181, 9180])).
% 49.53/49.75 tff(9183,plain,
% 49.53/49.75 (until2p8(s54) | (~xuntil2p9(s53))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9182, 1624, 8730])).
% 49.53/49.75 tff(9184,plain,
% 49.53/49.75 (~xuntil2p9(s53)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9183, 9179])).
% 49.53/49.75 tff(9185,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9186,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9187,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9186, 9185])).
% 49.53/49.75 tff(9188,plain,
% 49.53/49.75 (xuntil2p9(s53) | (~until2p8(s53))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9187, 8715, 6949])).
% 49.53/49.75 tff(9189,plain,
% 49.53/49.75 (~until2p8(s53)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9188, 9184])).
% 49.53/49.75 tff(9190,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9191,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9192,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9191, 9190])).
% 49.53/49.75 tff(9193,plain,
% 49.53/49.75 (until2p8(s53) | (~xuntil2p9(s52))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9192, 1596, 8730])).
% 49.53/49.75 tff(9194,plain,
% 49.53/49.75 (~xuntil2p9(s52)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9193, 9189])).
% 49.53/49.75 tff(9195,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9196,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9197,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9196, 9195])).
% 49.53/49.75 tff(9198,plain,
% 49.53/49.75 (xuntil2p9(s52) | (~until2p8(s52))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9197, 8715, 6957])).
% 49.53/49.75 tff(9199,plain,
% 49.53/49.75 (~until2p8(s52)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9198, 9194])).
% 49.53/49.75 tff(9200,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9201,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9202,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9201, 9200])).
% 49.53/49.75 tff(9203,plain,
% 49.53/49.75 (until2p8(s52) | (~xuntil2p9(s51))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9202, 1565, 8730])).
% 49.53/49.75 tff(9204,plain,
% 49.53/49.75 (~xuntil2p9(s51)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9203, 9199])).
% 49.53/49.75 tff(9205,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9206,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9207,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9206, 9205])).
% 49.53/49.75 tff(9208,plain,
% 49.53/49.75 (xuntil2p9(s51) | (~until2p8(s51))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9207, 8715, 6965])).
% 49.53/49.75 tff(9209,plain,
% 49.53/49.75 (~until2p8(s51)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9208, 9204])).
% 49.53/49.75 tff(9210,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9211,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9212,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9211, 9210])).
% 49.53/49.75 tff(9213,plain,
% 49.53/49.75 (until2p8(s51) | (~xuntil2p9(s50))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9212, 1537, 8730])).
% 49.53/49.75 tff(9214,plain,
% 49.53/49.75 (~xuntil2p9(s50)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9213, 9209])).
% 49.53/49.75 tff(9215,plain,
% 49.53/49.75 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9216,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9217,plain,
% 49.53/49.75 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9216, 9215])).
% 49.53/49.75 tff(9218,plain,
% 49.53/49.75 (xuntil2p9(s50) | (~until2p8(s50))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9217, 8715, 6973])).
% 49.53/49.75 tff(9219,plain,
% 49.53/49.75 (~until2p8(s50)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9218, 9214])).
% 49.53/49.75 tff(9220,plain,
% 49.53/49.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 49.53/49.75 inference(rewrite,[status(thm)],[])).
% 49.53/49.75 tff(9221,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 49.53/49.75 inference(quant_inst,[status(thm)],[])).
% 49.53/49.75 tff(9222,plain,
% 49.53/49.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49))),
% 49.53/49.75 inference(modus_ponens,[status(thm)],[9221, 9220])).
% 49.53/49.75 tff(9223,plain,
% 49.53/49.75 (until2p8(s50) | (~xuntil2p9(s49))),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9222, 1506, 8730])).
% 49.53/49.75 tff(9224,plain,
% 49.53/49.75 (~xuntil2p9(s49)),
% 49.53/49.75 inference(unit_resolution,[status(thm)],[9223, 9219])).
% 49.53/49.76 tff(9225,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9226,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9227,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9226, 9225])).
% 49.53/49.76 tff(9228,plain,
% 49.53/49.76 (xuntil2p9(s49) | (~until2p8(s49))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9227, 8715, 6981])).
% 49.53/49.76 tff(9229,plain,
% 49.53/49.76 (~until2p8(s49)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9228, 9224])).
% 49.53/49.76 tff(9230,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9231,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9232,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9231, 9230])).
% 49.53/49.76 tff(9233,plain,
% 49.53/49.76 (until2p8(s49) | (~xuntil2p9(s48))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9232, 1478, 8730])).
% 49.53/49.76 tff(9234,plain,
% 49.53/49.76 (~xuntil2p9(s48)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9233, 9229])).
% 49.53/49.76 tff(9235,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9236,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9237,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9236, 9235])).
% 49.53/49.76 tff(9238,plain,
% 49.53/49.76 (xuntil2p9(s48) | (~until2p8(s48))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9237, 8715, 6989])).
% 49.53/49.76 tff(9239,plain,
% 49.53/49.76 (~until2p8(s48)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9238, 9234])).
% 49.53/49.76 tff(9240,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9241,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9242,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9241, 9240])).
% 49.53/49.76 tff(9243,plain,
% 49.53/49.76 (until2p8(s48) | (~xuntil2p9(s47))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9242, 1447, 8730])).
% 49.53/49.76 tff(9244,plain,
% 49.53/49.76 (~xuntil2p9(s47)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9243, 9239])).
% 49.53/49.76 tff(9245,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9246,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9247,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9246, 9245])).
% 49.53/49.76 tff(9248,plain,
% 49.53/49.76 (xuntil2p9(s47) | (~until2p8(s47))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9247, 8715, 6997])).
% 49.53/49.76 tff(9249,plain,
% 49.53/49.76 (~until2p8(s47)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9248, 9244])).
% 49.53/49.76 tff(9250,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9251,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9252,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9251, 9250])).
% 49.53/49.76 tff(9253,plain,
% 49.53/49.76 (until2p8(s47) | (~xuntil2p9(s46))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9252, 1419, 8730])).
% 49.53/49.76 tff(9254,plain,
% 49.53/49.76 (~xuntil2p9(s46)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9253, 9249])).
% 49.53/49.76 tff(9255,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9256,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9257,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9256, 9255])).
% 49.53/49.76 tff(9258,plain,
% 49.53/49.76 (xuntil2p9(s46) | (~until2p8(s46))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9257, 8715, 7005])).
% 49.53/49.76 tff(9259,plain,
% 49.53/49.76 (~until2p8(s46)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9258, 9254])).
% 49.53/49.76 tff(9260,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9261,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9262,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9261, 9260])).
% 49.53/49.76 tff(9263,plain,
% 49.53/49.76 (until2p8(s46) | (~xuntil2p9(s45))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9262, 1388, 8730])).
% 49.53/49.76 tff(9264,plain,
% 49.53/49.76 (~xuntil2p9(s45)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9263, 9259])).
% 49.53/49.76 tff(9265,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9266,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9267,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9266, 9265])).
% 49.53/49.76 tff(9268,plain,
% 49.53/49.76 (xuntil2p9(s45) | (~until2p8(s45))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9267, 8715, 7013])).
% 49.53/49.76 tff(9269,plain,
% 49.53/49.76 (~until2p8(s45)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9268, 9264])).
% 49.53/49.76 tff(9270,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9271,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9272,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 49.53/49.76 tff(9273,plain,
% 49.53/49.76 (until2p8(s45) | (~xuntil2p9(s44))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9272, 1362, 8730])).
% 49.53/49.76 tff(9274,plain,
% 49.53/49.76 (~xuntil2p9(s44)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9273, 9269])).
% 49.53/49.76 tff(9275,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9276,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9277,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9276, 9275])).
% 49.53/49.76 tff(9278,plain,
% 49.53/49.76 (xuntil2p9(s44) | (~until2p8(s44))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9277, 8715, 7021])).
% 49.53/49.76 tff(9279,plain,
% 49.53/49.76 (~until2p8(s44)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9278, 9274])).
% 49.53/49.76 tff(9280,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9281,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9282,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9281, 9280])).
% 49.53/49.76 tff(9283,plain,
% 49.53/49.76 (until2p8(s44) | (~xuntil2p9(s43))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9282, 1331, 8730])).
% 49.53/49.76 tff(9284,plain,
% 49.53/49.76 (~xuntil2p9(s43)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9283, 9279])).
% 49.53/49.76 tff(9285,plain,
% 49.53/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9286,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 49.53/49.76 inference(quant_inst,[status(thm)],[])).
% 49.53/49.76 tff(9287,plain,
% 49.53/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43))),
% 49.53/49.76 inference(modus_ponens,[status(thm)],[9286, 9285])).
% 49.53/49.76 tff(9288,plain,
% 49.53/49.76 (xuntil2p9(s43) | (~until2p8(s43))),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9287, 8715, 7029])).
% 49.53/49.76 tff(9289,plain,
% 49.53/49.76 (~until2p8(s43)),
% 49.53/49.76 inference(unit_resolution,[status(thm)],[9288, 9284])).
% 49.53/49.76 tff(9290,plain,
% 49.53/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 49.53/49.76 inference(rewrite,[status(thm)],[])).
% 49.53/49.76 tff(9291,plain,
% 49.53/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9292,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9291, 9290])).
% 49.60/49.76 tff(9293,plain,
% 49.60/49.76 (until2p8(s43) | (~xuntil2p9(s42))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9292, 1303, 8730])).
% 49.60/49.76 tff(9294,plain,
% 49.60/49.76 (~xuntil2p9(s42)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9293, 9289])).
% 49.60/49.76 tff(9295,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9296,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9297,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9296, 9295])).
% 49.60/49.76 tff(9298,plain,
% 49.60/49.76 (xuntil2p9(s42) | (~until2p8(s42))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9297, 8715, 7037])).
% 49.60/49.76 tff(9299,plain,
% 49.60/49.76 (~until2p8(s42)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9298, 9294])).
% 49.60/49.76 tff(9300,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9301,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9302,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9301, 9300])).
% 49.60/49.76 tff(9303,plain,
% 49.60/49.76 (until2p8(s42) | (~xuntil2p9(s41))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9302, 1272, 8730])).
% 49.60/49.76 tff(9304,plain,
% 49.60/49.76 (~xuntil2p9(s41)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9303, 9299])).
% 49.60/49.76 tff(9305,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9306,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9307,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9306, 9305])).
% 49.60/49.76 tff(9308,plain,
% 49.60/49.76 (xuntil2p9(s41) | (~until2p8(s41))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9307, 8715, 7045])).
% 49.60/49.76 tff(9309,plain,
% 49.60/49.76 (~until2p8(s41)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9308, 9304])).
% 49.60/49.76 tff(9310,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9311,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9312,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9311, 9310])).
% 49.60/49.76 tff(9313,plain,
% 49.60/49.76 (until2p8(s41) | (~xuntil2p9(s40))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9312, 1244, 8730])).
% 49.60/49.76 tff(9314,plain,
% 49.60/49.76 (~xuntil2p9(s40)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9313, 9309])).
% 49.60/49.76 tff(9315,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9316,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9317,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9316, 9315])).
% 49.60/49.76 tff(9318,plain,
% 49.60/49.76 (xuntil2p9(s40) | (~until2p8(s40))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9317, 8715, 7053])).
% 49.60/49.76 tff(9319,plain,
% 49.60/49.76 (~until2p8(s40)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9318, 9314])).
% 49.60/49.76 tff(9320,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9321,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9322,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9321, 9320])).
% 49.60/49.76 tff(9323,plain,
% 49.60/49.76 (until2p8(s40) | (~xuntil2p9(s39))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9322, 1213, 8730])).
% 49.60/49.76 tff(9324,plain,
% 49.60/49.76 (~xuntil2p9(s39)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9323, 9319])).
% 49.60/49.76 tff(9325,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9326,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9327,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9326, 9325])).
% 49.60/49.76 tff(9328,plain,
% 49.60/49.76 (xuntil2p9(s39) | (~until2p8(s39))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9327, 8715, 7061])).
% 49.60/49.76 tff(9329,plain,
% 49.60/49.76 (~until2p8(s39)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9328, 9324])).
% 49.60/49.76 tff(9330,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9331,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9332,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9331, 9330])).
% 49.60/49.76 tff(9333,plain,
% 49.60/49.76 (until2p8(s39) | (~xuntil2p9(s38))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9332, 1185, 8730])).
% 49.60/49.76 tff(9334,plain,
% 49.60/49.76 (~xuntil2p9(s38)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9333, 9329])).
% 49.60/49.76 tff(9335,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9336,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9337,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9336, 9335])).
% 49.60/49.76 tff(9338,plain,
% 49.60/49.76 (xuntil2p9(s38) | (~until2p8(s38))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9337, 8715, 7069])).
% 49.60/49.76 tff(9339,plain,
% 49.60/49.76 (~until2p8(s38)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9338, 9334])).
% 49.60/49.76 tff(9340,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9341,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9342,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9341, 9340])).
% 49.60/49.76 tff(9343,plain,
% 49.60/49.76 (until2p8(s38) | (~xuntil2p9(s37))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9342, 1154, 8730])).
% 49.60/49.76 tff(9344,plain,
% 49.60/49.76 (~xuntil2p9(s37)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9343, 9339])).
% 49.60/49.76 tff(9345,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9346,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9347,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9346, 9345])).
% 49.60/49.76 tff(9348,plain,
% 49.60/49.76 (xuntil2p9(s37) | (~until2p8(s37))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9347, 8715, 7077])).
% 49.60/49.76 tff(9349,plain,
% 49.60/49.76 (~until2p8(s37)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9348, 9344])).
% 49.60/49.76 tff(9350,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9351,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9352,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9351, 9350])).
% 49.60/49.76 tff(9353,plain,
% 49.60/49.76 (until2p8(s37) | (~xuntil2p9(s36))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9352, 1126, 8730])).
% 49.60/49.76 tff(9354,plain,
% 49.60/49.76 (~xuntil2p9(s36)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9353, 9349])).
% 49.60/49.76 tff(9355,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9356,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9357,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9356, 9355])).
% 49.60/49.76 tff(9358,plain,
% 49.60/49.76 (xuntil2p9(s36) | (~until2p8(s36))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9357, 8715, 7085])).
% 49.60/49.76 tff(9359,plain,
% 49.60/49.76 (~until2p8(s36)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9358, 9354])).
% 49.60/49.76 tff(9360,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9361,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9362,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9361, 9360])).
% 49.60/49.76 tff(9363,plain,
% 49.60/49.76 (until2p8(s36) | (~xuntil2p9(s35))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9362, 1095, 8730])).
% 49.60/49.76 tff(9364,plain,
% 49.60/49.76 (~xuntil2p9(s35)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9363, 9359])).
% 49.60/49.76 tff(9365,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9366,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9367,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9366, 9365])).
% 49.60/49.76 tff(9368,plain,
% 49.60/49.76 (xuntil2p9(s35) | (~until2p8(s35))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9367, 8715, 7093])).
% 49.60/49.76 tff(9369,plain,
% 49.60/49.76 (~until2p8(s35)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9368, 9364])).
% 49.60/49.76 tff(9370,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9371,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9372,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9371, 9370])).
% 49.60/49.76 tff(9373,plain,
% 49.60/49.76 (until2p8(s35) | (~xuntil2p9(s34))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9372, 1067, 8730])).
% 49.60/49.76 tff(9374,plain,
% 49.60/49.76 (~xuntil2p9(s34)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9373, 9369])).
% 49.60/49.76 tff(9375,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9376,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9377,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9376, 9375])).
% 49.60/49.76 tff(9378,plain,
% 49.60/49.76 (xuntil2p9(s34) | (~until2p8(s34))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9377, 8715, 7101])).
% 49.60/49.76 tff(9379,plain,
% 49.60/49.76 (~until2p8(s34)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9378, 9374])).
% 49.60/49.76 tff(9380,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9381,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9382,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9381, 9380])).
% 49.60/49.76 tff(9383,plain,
% 49.60/49.76 (until2p8(s34) | (~xuntil2p9(s33))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9382, 1036, 8730])).
% 49.60/49.76 tff(9384,plain,
% 49.60/49.76 (~xuntil2p9(s33)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9383, 9379])).
% 49.60/49.76 tff(9385,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9386,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9387,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9386, 9385])).
% 49.60/49.76 tff(9388,plain,
% 49.60/49.76 (xuntil2p9(s33) | (~until2p8(s33))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9387, 8715, 7109])).
% 49.60/49.76 tff(9389,plain,
% 49.60/49.76 (~until2p8(s33)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9388, 9384])).
% 49.60/49.76 tff(9390,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9391,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9392,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9391, 9390])).
% 49.60/49.76 tff(9393,plain,
% 49.60/49.76 (until2p8(s33) | (~xuntil2p9(s32))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9392, 1008, 8730])).
% 49.60/49.76 tff(9394,plain,
% 49.60/49.76 (~xuntil2p9(s32)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9393, 9389])).
% 49.60/49.76 tff(9395,plain,
% 49.60/49.76 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9396,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9397,plain,
% 49.60/49.76 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9396, 9395])).
% 49.60/49.76 tff(9398,plain,
% 49.60/49.76 (xuntil2p9(s32) | (~until2p8(s32))),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9397, 8715, 7117])).
% 49.60/49.76 tff(9399,plain,
% 49.60/49.76 (~until2p8(s32)),
% 49.60/49.76 inference(unit_resolution,[status(thm)],[9398, 9394])).
% 49.60/49.76 tff(9400,plain,
% 49.60/49.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 49.60/49.76 inference(rewrite,[status(thm)],[])).
% 49.60/49.76 tff(9401,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 49.60/49.76 inference(quant_inst,[status(thm)],[])).
% 49.60/49.76 tff(9402,plain,
% 49.60/49.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31))),
% 49.60/49.76 inference(modus_ponens,[status(thm)],[9401, 9400])).
% 49.60/49.77 tff(9403,plain,
% 49.60/49.77 (until2p8(s32) | (~xuntil2p9(s31))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9402, 977, 8730])).
% 49.60/49.77 tff(9404,plain,
% 49.60/49.77 (~xuntil2p9(s31)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9403, 9399])).
% 49.60/49.77 tff(9405,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9406,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9407,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9406, 9405])).
% 49.60/49.77 tff(9408,plain,
% 49.60/49.77 (xuntil2p9(s31) | (~until2p8(s31))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9407, 8715, 7125])).
% 49.60/49.77 tff(9409,plain,
% 49.60/49.77 (~until2p8(s31)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9408, 9404])).
% 49.60/49.77 tff(9410,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9411,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9412,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9411, 9410])).
% 49.60/49.77 tff(9413,plain,
% 49.60/49.77 (until2p8(s31) | (~xuntil2p9(s30))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9412, 949, 8730])).
% 49.60/49.77 tff(9414,plain,
% 49.60/49.77 (~xuntil2p9(s30)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9413, 9409])).
% 49.60/49.77 tff(9415,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9416,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9417,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9416, 9415])).
% 49.60/49.77 tff(9418,plain,
% 49.60/49.77 (xuntil2p9(s30) | (~until2p8(s30))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9417, 8715, 7133])).
% 49.60/49.77 tff(9419,plain,
% 49.60/49.77 (~until2p8(s30)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9418, 9414])).
% 49.60/49.77 tff(9420,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9421,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9422,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9421, 9420])).
% 49.60/49.77 tff(9423,plain,
% 49.60/49.77 (until2p8(s30) | (~xuntil2p9(s29))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9422, 918, 8730])).
% 49.60/49.77 tff(9424,plain,
% 49.60/49.77 (~xuntil2p9(s29)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9423, 9419])).
% 49.60/49.77 tff(9425,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9426,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9427,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9426, 9425])).
% 49.60/49.77 tff(9428,plain,
% 49.60/49.77 (xuntil2p9(s29) | (~until2p8(s29))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9427, 8715, 7141])).
% 49.60/49.77 tff(9429,plain,
% 49.60/49.77 (~until2p8(s29)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9428, 9424])).
% 49.60/49.77 tff(9430,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9431,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9432,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9431, 9430])).
% 49.60/49.77 tff(9433,plain,
% 49.60/49.77 (until2p8(s29) | (~xuntil2p9(s28))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9432, 890, 8730])).
% 49.60/49.77 tff(9434,plain,
% 49.60/49.77 (~xuntil2p9(s28)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9433, 9429])).
% 49.60/49.77 tff(9435,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9436,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9437,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9436, 9435])).
% 49.60/49.77 tff(9438,plain,
% 49.60/49.77 (xuntil2p9(s28) | (~until2p8(s28))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9437, 8715, 7149])).
% 49.60/49.77 tff(9439,plain,
% 49.60/49.77 (~until2p8(s28)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9438, 9434])).
% 49.60/49.77 tff(9440,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9441,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9442,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9441, 9440])).
% 49.60/49.77 tff(9443,plain,
% 49.60/49.77 (until2p8(s28) | (~xuntil2p9(s27))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9442, 861, 8730])).
% 49.60/49.77 tff(9444,plain,
% 49.60/49.77 (~xuntil2p9(s27)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9443, 9439])).
% 49.60/49.77 tff(9445,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9446,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9447,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9446, 9445])).
% 49.60/49.77 tff(9448,plain,
% 49.60/49.77 (xuntil2p9(s27) | (~until2p8(s27))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9447, 8715, 7157])).
% 49.60/49.77 tff(9449,plain,
% 49.60/49.77 (~until2p8(s27)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9448, 9444])).
% 49.60/49.77 tff(9450,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9451,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9452,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9451, 9450])).
% 49.60/49.77 tff(9453,plain,
% 49.60/49.77 (until2p8(s27) | (~xuntil2p9(s26))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9452, 833, 8730])).
% 49.60/49.77 tff(9454,plain,
% 49.60/49.77 (~xuntil2p9(s26)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9453, 9449])).
% 49.60/49.77 tff(9455,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9456,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9457,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9456, 9455])).
% 49.60/49.77 tff(9458,plain,
% 49.60/49.77 (xuntil2p9(s26) | (~until2p8(s26))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9457, 8715, 7165])).
% 49.60/49.77 tff(9459,plain,
% 49.60/49.77 (~until2p8(s26)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9458, 9454])).
% 49.60/49.77 tff(9460,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9461,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9462,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9461, 9460])).
% 49.60/49.77 tff(9463,plain,
% 49.60/49.77 (until2p8(s26) | (~xuntil2p9(s25))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9462, 802, 8730])).
% 49.60/49.77 tff(9464,plain,
% 49.60/49.77 (~xuntil2p9(s25)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9463, 9459])).
% 49.60/49.77 tff(9465,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9466,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9467,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9466, 9465])).
% 49.60/49.77 tff(9468,plain,
% 49.60/49.77 (xuntil2p9(s25) | (~until2p8(s25))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9467, 8715, 7173])).
% 49.60/49.77 tff(9469,plain,
% 49.60/49.77 (~until2p8(s25)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9468, 9464])).
% 49.60/49.77 tff(9470,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9471,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9472,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9471, 9470])).
% 49.60/49.77 tff(9473,plain,
% 49.60/49.77 (until2p8(s25) | (~xuntil2p9(s24))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9472, 776, 8730])).
% 49.60/49.77 tff(9474,plain,
% 49.60/49.77 (~xuntil2p9(s24)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9473, 9469])).
% 49.60/49.77 tff(9475,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9476,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9477,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9476, 9475])).
% 49.60/49.77 tff(9478,plain,
% 49.60/49.77 (xuntil2p9(s24) | (~until2p8(s24))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9477, 8715, 7181])).
% 49.60/49.77 tff(9479,plain,
% 49.60/49.77 (~until2p8(s24)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9478, 9474])).
% 49.60/49.77 tff(9480,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9481,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9482,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9481, 9480])).
% 49.60/49.77 tff(9483,plain,
% 49.60/49.77 (until2p8(s24) | (~xuntil2p9(s23))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9482, 745, 8730])).
% 49.60/49.77 tff(9484,plain,
% 49.60/49.77 (~xuntil2p9(s23)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9483, 9479])).
% 49.60/49.77 tff(9485,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9486,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9487,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9486, 9485])).
% 49.60/49.77 tff(9488,plain,
% 49.60/49.77 (xuntil2p9(s23) | (~until2p8(s23))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9487, 8715, 7189])).
% 49.60/49.77 tff(9489,plain,
% 49.60/49.77 (~until2p8(s23)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9488, 9484])).
% 49.60/49.77 tff(9490,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9491,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9492,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9491, 9490])).
% 49.60/49.77 tff(9493,plain,
% 49.60/49.77 (until2p8(s23) | (~xuntil2p9(s22))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9492, 717, 8730])).
% 49.60/49.77 tff(9494,plain,
% 49.60/49.77 (~xuntil2p9(s22)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9493, 9489])).
% 49.60/49.77 tff(9495,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9496,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9497,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9496, 9495])).
% 49.60/49.77 tff(9498,plain,
% 49.60/49.77 (xuntil2p9(s22) | (~until2p8(s22))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9497, 8715, 7197])).
% 49.60/49.77 tff(9499,plain,
% 49.60/49.77 (~until2p8(s22)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9498, 9494])).
% 49.60/49.77 tff(9500,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9501,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9502,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9501, 9500])).
% 49.60/49.77 tff(9503,plain,
% 49.60/49.77 (until2p8(s22) | (~xuntil2p9(s21))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9502, 686, 8730])).
% 49.60/49.77 tff(9504,plain,
% 49.60/49.77 (~xuntil2p9(s21)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9503, 9499])).
% 49.60/49.77 tff(9505,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9506,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9507,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9506, 9505])).
% 49.60/49.77 tff(9508,plain,
% 49.60/49.77 (xuntil2p9(s21) | (~until2p8(s21))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9507, 8715, 7205])).
% 49.60/49.77 tff(9509,plain,
% 49.60/49.77 (~until2p8(s21)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9508, 9504])).
% 49.60/49.77 tff(9510,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9511,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9512,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9511, 9510])).
% 49.60/49.77 tff(9513,plain,
% 49.60/49.77 (until2p8(s21) | (~xuntil2p9(s20))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9512, 658, 8730])).
% 49.60/49.77 tff(9514,plain,
% 49.60/49.77 (~xuntil2p9(s20)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9513, 9509])).
% 49.60/49.77 tff(9515,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9516,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9517,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9516, 9515])).
% 49.60/49.77 tff(9518,plain,
% 49.60/49.77 (xuntil2p9(s20) | (~until2p8(s20))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9517, 8715, 7213])).
% 49.60/49.77 tff(9519,plain,
% 49.60/49.77 (~until2p8(s20)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9518, 9514])).
% 49.60/49.77 tff(9520,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9521,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9522,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9521, 9520])).
% 49.60/49.77 tff(9523,plain,
% 49.60/49.77 (until2p8(s20) | (~xuntil2p9(s19))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9522, 629, 8730])).
% 49.60/49.77 tff(9524,plain,
% 49.60/49.77 (~xuntil2p9(s19)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9523, 9519])).
% 49.60/49.77 tff(9525,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9526,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9527,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9526, 9525])).
% 49.60/49.77 tff(9528,plain,
% 49.60/49.77 (xuntil2p9(s19) | (~until2p8(s19))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9527, 8715, 7221])).
% 49.60/49.77 tff(9529,plain,
% 49.60/49.77 (~until2p8(s19)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9528, 9524])).
% 49.60/49.77 tff(9530,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9531,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9532,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9531, 9530])).
% 49.60/49.77 tff(9533,plain,
% 49.60/49.77 (until2p8(s19) | (~xuntil2p9(s18))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9532, 601, 8730])).
% 49.60/49.77 tff(9534,plain,
% 49.60/49.77 (~xuntil2p9(s18)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9533, 9529])).
% 49.60/49.77 tff(9535,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9536,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9537,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9536, 9535])).
% 49.60/49.77 tff(9538,plain,
% 49.60/49.77 (xuntil2p9(s18) | (~until2p8(s18))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9537, 8715, 7229])).
% 49.60/49.77 tff(9539,plain,
% 49.60/49.77 (~until2p8(s18)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9538, 9534])).
% 49.60/49.77 tff(9540,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9541,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9542,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9541, 9540])).
% 49.60/49.77 tff(9543,plain,
% 49.60/49.77 (until2p8(s18) | (~xuntil2p9(s17))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9542, 570, 8730])).
% 49.60/49.77 tff(9544,plain,
% 49.60/49.77 (~xuntil2p9(s17)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9543, 9539])).
% 49.60/49.77 tff(9545,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9546,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9547,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9546, 9545])).
% 49.60/49.77 tff(9548,plain,
% 49.60/49.77 (xuntil2p9(s17) | (~until2p8(s17))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9547, 8715, 7237])).
% 49.60/49.77 tff(9549,plain,
% 49.60/49.77 (~until2p8(s17)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9548, 9544])).
% 49.60/49.77 tff(9550,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9551,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9552,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9551, 9550])).
% 49.60/49.77 tff(9553,plain,
% 49.60/49.77 (until2p8(s17) | (~xuntil2p9(s16))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9552, 542, 8730])).
% 49.60/49.77 tff(9554,plain,
% 49.60/49.77 (~xuntil2p9(s16)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9553, 9549])).
% 49.60/49.77 tff(9555,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9556,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9557,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9556, 9555])).
% 49.60/49.77 tff(9558,plain,
% 49.60/49.77 (xuntil2p9(s16) | (~until2p8(s16))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9557, 8715, 7245])).
% 49.60/49.77 tff(9559,plain,
% 49.60/49.77 (~until2p8(s16)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9558, 9554])).
% 49.60/49.77 tff(9560,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9561,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9562,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9561, 9560])).
% 49.60/49.77 tff(9563,plain,
% 49.60/49.77 (until2p8(s16) | (~xuntil2p9(s15))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9562, 513, 8730])).
% 49.60/49.77 tff(9564,plain,
% 49.60/49.77 (~xuntil2p9(s15)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9563, 9559])).
% 49.60/49.77 tff(9565,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9566,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9567,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9566, 9565])).
% 49.60/49.77 tff(9568,plain,
% 49.60/49.77 (xuntil2p9(s15) | (~until2p8(s15))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9567, 8715, 7253])).
% 49.60/49.77 tff(9569,plain,
% 49.60/49.77 (~until2p8(s15)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9568, 9564])).
% 49.60/49.77 tff(9570,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9571,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9572,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9571, 9570])).
% 49.60/49.77 tff(9573,plain,
% 49.60/49.77 (until2p8(s15) | (~xuntil2p9(s14))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9572, 485, 8730])).
% 49.60/49.77 tff(9574,plain,
% 49.60/49.77 (~xuntil2p9(s14)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9573, 9569])).
% 49.60/49.77 tff(9575,plain,
% 49.60/49.77 (~always5(s14)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[7261, 7253])).
% 49.60/49.77 tff(9576,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9577,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9578,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9577, 9576])).
% 49.60/49.77 tff(9579,plain,
% 49.60/49.77 (xuntil2p9(s14) | (~until2p8(s14))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9578, 8715, 9575])).
% 49.60/49.77 tff(9580,plain,
% 49.60/49.77 (~until2p8(s14)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9579, 9574])).
% 49.60/49.77 tff(9581,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9582,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9583,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9582, 9581])).
% 49.60/49.77 tff(9584,plain,
% 49.60/49.77 (until2p8(s14) | (~xuntil2p9(s13))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9583, 454, 8730])).
% 49.60/49.77 tff(9585,plain,
% 49.60/49.77 (~xuntil2p9(s13)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9584, 9580])).
% 49.60/49.77 tff(9586,plain,
% 49.60/49.77 (~always5(s13)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[7315, 9575])).
% 49.60/49.77 tff(9587,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9588,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9589,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9588, 9587])).
% 49.60/49.77 tff(9590,plain,
% 49.60/49.77 (xuntil2p9(s13) | (~until2p8(s13))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9589, 8715, 9586])).
% 49.60/49.77 tff(9591,plain,
% 49.60/49.77 (~until2p8(s13)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9590, 9585])).
% 49.60/49.77 tff(9592,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9593,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9594,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9593, 9592])).
% 49.60/49.77 tff(9595,plain,
% 49.60/49.77 (until2p8(s13) | (~xuntil2p9(s12))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9594, 426, 8730])).
% 49.60/49.77 tff(9596,plain,
% 49.60/49.77 (~xuntil2p9(s12)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9595, 9591])).
% 49.60/49.77 tff(9597,plain,
% 49.60/49.77 (~always5(s12)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[7336, 9586])).
% 49.60/49.77 tff(9598,plain,
% 49.60/49.77 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9599,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9600,plain,
% 49.60/49.77 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12))),
% 49.60/49.77 inference(modus_ponens,[status(thm)],[9599, 9598])).
% 49.60/49.77 tff(9601,plain,
% 49.60/49.77 (xuntil2p9(s12) | (~until2p8(s12))),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9600, 8715, 9597])).
% 49.60/49.77 tff(9602,plain,
% 49.60/49.77 (~until2p8(s12)),
% 49.60/49.77 inference(unit_resolution,[status(thm)],[9601, 9596])).
% 49.60/49.77 tff(9603,plain,
% 49.60/49.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 49.60/49.77 inference(rewrite,[status(thm)],[])).
% 49.60/49.77 tff(9604,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 49.60/49.77 inference(quant_inst,[status(thm)],[])).
% 49.60/49.77 tff(9605,plain,
% 49.60/49.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9604, 9603])).
% 49.60/49.78 tff(9606,plain,
% 49.60/49.78 (until2p8(s12) | (~xuntil2p9(s11))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9605, 395, 8730])).
% 49.60/49.78 tff(9607,plain,
% 49.60/49.78 (~xuntil2p9(s11)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9606, 9602])).
% 49.60/49.78 tff(9608,plain,
% 49.60/49.78 (~always5(s11)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7357, 9597])).
% 49.60/49.78 tff(9609,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9610,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9611,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9610, 9609])).
% 49.60/49.78 tff(9612,plain,
% 49.60/49.78 (xuntil2p9(s11) | (~until2p8(s11))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9611, 8715, 9608])).
% 49.60/49.78 tff(9613,plain,
% 49.60/49.78 (~until2p8(s11)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9612, 9607])).
% 49.60/49.78 tff(9614,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9615,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9616,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9615, 9614])).
% 49.60/49.78 tff(9617,plain,
% 49.60/49.78 (until2p8(s11) | (~xuntil2p9(s10))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9616, 367, 8730])).
% 49.60/49.78 tff(9618,plain,
% 49.60/49.78 (~xuntil2p9(s10)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9617, 9613])).
% 49.60/49.78 tff(9619,plain,
% 49.60/49.78 (~always5(s10)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7378, 9608])).
% 49.60/49.78 tff(9620,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9621,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9622,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9621, 9620])).
% 49.60/49.78 tff(9623,plain,
% 49.60/49.78 (xuntil2p9(s10) | (~until2p8(s10))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9622, 8715, 9619])).
% 49.60/49.78 tff(9624,plain,
% 49.60/49.78 (~until2p8(s10)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9623, 9618])).
% 49.60/49.78 tff(9625,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9626,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9627,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9626, 9625])).
% 49.60/49.78 tff(9628,plain,
% 49.60/49.78 (until2p8(s10) | (~xuntil2p9(s9))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9627, 336, 8730])).
% 49.60/49.78 tff(9629,plain,
% 49.60/49.78 (~xuntil2p9(s9)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9628, 9624])).
% 49.60/49.78 tff(9630,plain,
% 49.60/49.78 (~always5(s9)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7399, 9619])).
% 49.60/49.78 tff(9631,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9632,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9633,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9632, 9631])).
% 49.60/49.78 tff(9634,plain,
% 49.60/49.78 (xuntil2p9(s9) | (~until2p8(s9))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9633, 8715, 9630])).
% 49.60/49.78 tff(9635,plain,
% 49.60/49.78 (~until2p8(s9)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9634, 9629])).
% 49.60/49.78 tff(9636,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9637,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9638,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9637, 9636])).
% 49.60/49.78 tff(9639,plain,
% 49.60/49.78 (until2p8(s9) | (~xuntil2p9(s8))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9638, 310, 8730])).
% 49.60/49.78 tff(9640,plain,
% 49.60/49.78 (~xuntil2p9(s8)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9639, 9635])).
% 49.60/49.78 tff(9641,plain,
% 49.60/49.78 (~always5(s8)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7420, 9630])).
% 49.60/49.78 tff(9642,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9643,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9644,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9643, 9642])).
% 49.60/49.78 tff(9645,plain,
% 49.60/49.78 (xuntil2p9(s8) | (~until2p8(s8))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9644, 8715, 9641])).
% 49.60/49.78 tff(9646,plain,
% 49.60/49.78 (~until2p8(s8)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9645, 9640])).
% 49.60/49.78 tff(9647,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9648,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9649,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9648, 9647])).
% 49.60/49.78 tff(9650,plain,
% 49.60/49.78 (until2p8(s8) | (~xuntil2p9(s7))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9649, 281, 8730])).
% 49.60/49.78 tff(9651,plain,
% 49.60/49.78 (~xuntil2p9(s7)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9650, 9646])).
% 49.60/49.78 tff(9652,plain,
% 49.60/49.78 (~always5(s7)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7436, 9641])).
% 49.60/49.78 tff(9653,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9654,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9655,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9654, 9653])).
% 49.60/49.78 tff(9656,plain,
% 49.60/49.78 (xuntil2p9(s7) | (~until2p8(s7))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9655, 8715, 9652])).
% 49.60/49.78 tff(9657,plain,
% 49.60/49.78 (~until2p8(s7)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9656, 9651])).
% 49.60/49.78 tff(9658,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9659,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9660,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9659, 9658])).
% 49.60/49.78 tff(9661,plain,
% 49.60/49.78 (until2p8(s7) | (~xuntil2p9(s6))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9660, 10, 8730])).
% 49.60/49.78 tff(9662,plain,
% 49.60/49.78 (~xuntil2p9(s6)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9661, 9657])).
% 49.60/49.78 tff(9663,plain,
% 49.60/49.78 (~always5(s6)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7444, 9652])).
% 49.60/49.78 tff(9664,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9665,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9666,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9665, 9664])).
% 49.60/49.78 tff(9667,plain,
% 49.60/49.78 (xuntil2p9(s6) | (~until2p8(s6))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9666, 8715, 9663])).
% 49.60/49.78 tff(9668,plain,
% 49.60/49.78 (~until2p8(s6)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9667, 9662])).
% 49.60/49.78 tff(9669,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9670,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9671,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9670, 9669])).
% 49.60/49.78 tff(9672,plain,
% 49.60/49.78 (until2p8(s6) | (~xuntil2p9(s5))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9671, 234, 8730])).
% 49.60/49.78 tff(9673,plain,
% 49.60/49.78 (~xuntil2p9(s5)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9672, 9668])).
% 49.60/49.78 tff(9674,plain,
% 49.60/49.78 (~always5(s5)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7452, 9663])).
% 49.60/49.78 tff(9675,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9676,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9677,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9676, 9675])).
% 49.60/49.78 tff(9678,plain,
% 49.60/49.78 (xuntil2p9(s5) | (~until2p8(s5))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9677, 8715, 9674])).
% 49.60/49.78 tff(9679,plain,
% 49.60/49.78 (~until2p8(s5)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9678, 9673])).
% 49.60/49.78 tff(9680,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9681,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9682,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9681, 9680])).
% 49.60/49.78 tff(9683,plain,
% 49.60/49.78 (until2p8(s5) | (~xuntil2p9(s4))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9682, 206, 8730])).
% 49.60/49.78 tff(9684,plain,
% 49.60/49.78 (~xuntil2p9(s4)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9683, 9679])).
% 49.60/49.78 tff(9685,plain,
% 49.60/49.78 (~always5(s4)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7460, 9674])).
% 49.60/49.78 tff(9686,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9687,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9688,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9687, 9686])).
% 49.60/49.78 tff(9689,plain,
% 49.60/49.78 (xuntil2p9(s4) | (~until2p8(s4))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9688, 8715, 9685])).
% 49.60/49.78 tff(9690,plain,
% 49.60/49.78 (~until2p8(s4)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9689, 9684])).
% 49.60/49.78 tff(9691,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9692,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9693,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9692, 9691])).
% 49.60/49.78 tff(9694,plain,
% 49.60/49.78 (until2p8(s4) | (~xuntil2p9(s3))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9693, 177, 8730])).
% 49.60/49.78 tff(9695,plain,
% 49.60/49.78 (~xuntil2p9(s3)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9694, 9690])).
% 49.60/49.78 tff(9696,plain,
% 49.60/49.78 (~always5(s3)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7468, 9685])).
% 49.60/49.78 tff(9697,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9698,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9699,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9698, 9697])).
% 49.60/49.78 tff(9700,plain,
% 49.60/49.78 (xuntil2p9(s3) | (~until2p8(s3))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9699, 8715, 9696])).
% 49.60/49.78 tff(9701,plain,
% 49.60/49.78 (~until2p8(s3)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9700, 9695])).
% 49.60/49.78 tff(9702,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9703,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9704,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9703, 9702])).
% 49.60/49.78 tff(9705,plain,
% 49.60/49.78 (until2p8(s3) | (~xuntil2p9(s2))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9704, 151, 8730])).
% 49.60/49.78 tff(9706,plain,
% 49.60/49.78 (~xuntil2p9(s2)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9705, 9701])).
% 49.60/49.78 tff(9707,plain,
% 49.60/49.78 (~always5(s2)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[7476, 9696])).
% 49.60/49.78 tff(9708,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9709,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9710,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9709, 9708])).
% 49.60/49.78 tff(9711,plain,
% 49.60/49.78 (xuntil2p9(s2) | (~until2p8(s2))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9710, 8715, 9707])).
% 49.60/49.78 tff(9712,plain,
% 49.60/49.78 (~until2p8(s2)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9711, 9706])).
% 49.60/49.78 tff(9713,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9714,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9715,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9714, 9713])).
% 49.60/49.78 tff(9716,plain,
% 49.60/49.78 (until2p8(s2) | (~xuntil2p9(s1))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9715, 112, 8730])).
% 49.60/49.78 tff(9717,plain,
% 49.60/49.78 (~xuntil2p9(s1)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9716, 9712])).
% 49.60/49.78 tff(9718,assumption,(~always5(s1)), introduced(assumption)).
% 49.60/49.78 tff(9719,plain,
% 49.60/49.78 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9720,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9721,plain,
% 49.60/49.78 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9720, 9719])).
% 49.60/49.78 tff(9722,plain,
% 49.60/49.78 (xuntil2p9(s1) | (~until2p8(s1))),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9721, 8715, 9718])).
% 49.60/49.78 tff(9723,plain,
% 49.60/49.78 (~until2p8(s1)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9722, 9717])).
% 49.60/49.78 tff(9724,plain,
% 49.60/49.78 (^[Y: $i, X: $i] : refl(((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)))),
% 49.60/49.78 inference(bind,[status(th)],[])).
% 49.60/49.78 tff(9725,plain,
% 49.60/49.78 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(quant_intro,[status(thm)],[9724])).
% 49.60/49.78 tff(9726,plain,
% 49.60/49.78 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9727,plain,
% 49.60/49.78 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p8(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~last(X)) | (~trans(X, Y)) | until2p8(Y))), ((((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> (((~last(X)) | (~trans(X, Y)) | until2p8(Y)) | (~xuntil7(X))))), rewrite((((~last(X)) | (~trans(X, Y)) | until2p8(Y)) | (~xuntil7(X))) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))), ((((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))))),
% 49.60/49.78 inference(bind,[status(th)],[])).
% 49.60/49.78 tff(9728,plain,
% 49.60/49.78 (![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(quant_intro,[status(thm)],[9727])).
% 49.60/49.78 tff(9729,axiom,(![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty7')).
% 49.60/49.78 tff(9730,plain,
% 49.60/49.78 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9729, 9728])).
% 49.60/49.78 tff(9731,plain,
% 49.60/49.78 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9730, 9726])).
% 49.60/49.78 tff(9732,plain,(
% 49.60/49.78 ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(skolemize,[status(sab)],[9731])).
% 49.60/49.78 tff(9733,plain,
% 49.60/49.78 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9732, 9725])).
% 49.60/49.78 tff(9734,assumption,(xuntil7(s99)), introduced(assumption)).
% 49.60/49.78 tff(9735,assumption,(~until2p8(s38)), introduced(assumption)).
% 49.60/49.78 tff(9736,assumption,(trans(s99, s38)), introduced(assumption)).
% 49.60/49.78 tff(9737,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9738,plain,
% 49.60/49.78 (((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38)) <=> (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9739,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38))))),
% 49.60/49.78 inference(monotonicity,[status(thm)],[9738])).
% 49.60/49.78 tff(9740,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 49.60/49.78 inference(transitivity,[status(thm)],[9739, 9737])).
% 49.60/49.78 tff(9741,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9742,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9741, 9740])).
% 49.60/49.78 tff(9743,plain,
% 49.60/49.78 ($false),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9742, 8701, 9736, 9733, 9735, 9734])).
% 49.60/49.78 tff(9744,plain,((~trans(s99, s38)) | until2p8(s38) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.78 tff(9745,plain,
% 49.60/49.78 (~trans(s99, s38)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9744, 9339, 8691])).
% 49.60/49.78 tff(9746,assumption,(~until2p8(s86)), introduced(assumption)).
% 49.60/49.78 tff(9747,assumption,(trans(s99, s86)), introduced(assumption)).
% 49.60/49.78 tff(9748,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9749,plain,
% 49.60/49.78 (((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86)) <=> (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9750,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86))))),
% 49.60/49.78 inference(monotonicity,[status(thm)],[9749])).
% 49.60/49.78 tff(9751,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 49.60/49.78 inference(transitivity,[status(thm)],[9750, 9748])).
% 49.60/49.78 tff(9752,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9753,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 49.60/49.78 tff(9754,plain,
% 49.60/49.78 ($false),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9753, 8701, 9747, 9733, 9746, 9734])).
% 49.60/49.78 tff(9755,plain,((~trans(s99, s86)) | until2p8(s86) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.78 tff(9756,plain,
% 49.60/49.78 (~trans(s99, s86)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9755, 8859, 8691])).
% 49.60/49.78 tff(9757,assumption,(~until2p8(s63)), introduced(assumption)).
% 49.60/49.78 tff(9758,assumption,(trans(s99, s63)), introduced(assumption)).
% 49.60/49.78 tff(9759,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9760,plain,
% 49.60/49.78 (((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63)) <=> (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9761,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63))))),
% 49.60/49.78 inference(monotonicity,[status(thm)],[9760])).
% 49.60/49.78 tff(9762,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 49.60/49.78 inference(transitivity,[status(thm)],[9761, 9759])).
% 49.60/49.78 tff(9763,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9764,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9763, 9762])).
% 49.60/49.78 tff(9765,plain,
% 49.60/49.78 ($false),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9764, 8701, 9758, 9733, 9757, 9734])).
% 49.60/49.78 tff(9766,plain,((~trans(s99, s63)) | until2p8(s63) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.78 tff(9767,plain,
% 49.60/49.78 (~trans(s99, s63)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9766, 9089, 8691])).
% 49.60/49.78 tff(9768,assumption,(~until2p8(s36)), introduced(assumption)).
% 49.60/49.78 tff(9769,assumption,(trans(s99, s36)), introduced(assumption)).
% 49.60/49.78 tff(9770,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9771,plain,
% 49.60/49.78 (((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36)) <=> (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9772,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36))))),
% 49.60/49.78 inference(monotonicity,[status(thm)],[9771])).
% 49.60/49.78 tff(9773,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 49.60/49.78 inference(transitivity,[status(thm)],[9772, 9770])).
% 49.60/49.78 tff(9774,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))),
% 49.60/49.78 inference(quant_inst,[status(thm)],[])).
% 49.60/49.78 tff(9775,plain,
% 49.60/49.78 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36))),
% 49.60/49.78 inference(modus_ponens,[status(thm)],[9774, 9773])).
% 49.60/49.78 tff(9776,plain,
% 49.60/49.78 ($false),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9775, 8701, 9769, 9733, 9768, 9734])).
% 49.60/49.78 tff(9777,plain,((~trans(s99, s36)) | until2p8(s36) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.78 tff(9778,plain,
% 49.60/49.78 (~trans(s99, s36)),
% 49.60/49.78 inference(unit_resolution,[status(thm)],[9777, 9359, 8691])).
% 49.60/49.78 tff(9779,assumption,(~until2p8(s42)), introduced(assumption)).
% 49.60/49.78 tff(9780,assumption,(trans(s99, s42)), introduced(assumption)).
% 49.60/49.78 tff(9781,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9782,plain,
% 49.60/49.78 (((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42)) <=> (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 49.60/49.78 inference(rewrite,[status(thm)],[])).
% 49.60/49.78 tff(9783,plain,
% 49.60/49.78 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42))))),
% 49.60/49.78 inference(monotonicity,[status(thm)],[9782])).
% 49.60/49.79 tff(9784,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9783, 9781])).
% 49.60/49.79 tff(9785,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9786,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9785, 9784])).
% 49.60/49.79 tff(9787,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9786, 8701, 9780, 9733, 9779, 9734])).
% 49.60/49.79 tff(9788,plain,((~trans(s99, s42)) | until2p8(s42) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9789,plain,
% 49.60/49.79 (~trans(s99, s42)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9788, 9299, 8691])).
% 49.60/49.79 tff(9790,assumption,(~until2p8(s57)), introduced(assumption)).
% 49.60/49.79 tff(9791,assumption,(trans(s99, s57)), introduced(assumption)).
% 49.60/49.79 tff(9792,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9793,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57)) <=> (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9794,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9793])).
% 49.60/49.79 tff(9795,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9794, 9792])).
% 49.60/49.79 tff(9796,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9797,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9796, 9795])).
% 49.60/49.79 tff(9798,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9797, 8701, 9791, 9733, 9790, 9734])).
% 49.60/49.79 tff(9799,plain,((~trans(s99, s57)) | until2p8(s57) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9800,plain,
% 49.60/49.79 (~trans(s99, s57)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9799, 9149, 8691])).
% 49.60/49.79 tff(9801,assumption,(~until2p8(s49)), introduced(assumption)).
% 49.60/49.79 tff(9802,assumption,(trans(s99, s49)), introduced(assumption)).
% 49.60/49.79 tff(9803,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9804,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49)) <=> (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9805,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9804])).
% 49.60/49.79 tff(9806,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9805, 9803])).
% 49.60/49.79 tff(9807,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9808,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9807, 9806])).
% 49.60/49.79 tff(9809,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9808, 8701, 9802, 9733, 9801, 9734])).
% 49.60/49.79 tff(9810,plain,((~trans(s99, s49)) | until2p8(s49) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9811,plain,
% 49.60/49.79 (~trans(s99, s49)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9810, 9229, 8691])).
% 49.60/49.79 tff(9812,assumption,(~until2p8(s8)), introduced(assumption)).
% 49.60/49.79 tff(9813,assumption,(trans(s99, s8)), introduced(assumption)).
% 49.60/49.79 tff(9814,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9815,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8)) <=> (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9816,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9815])).
% 49.60/49.79 tff(9817,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9816, 9814])).
% 49.60/49.79 tff(9818,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9819,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9818, 9817])).
% 49.60/49.79 tff(9820,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9819, 8701, 9813, 9733, 9812, 9734])).
% 49.60/49.79 tff(9821,plain,((~trans(s99, s8)) | until2p8(s8) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9822,plain,
% 49.60/49.79 (~trans(s99, s8)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9821, 9646, 8691])).
% 49.60/49.79 tff(9823,assumption,(~until2p8(s9)), introduced(assumption)).
% 49.60/49.79 tff(9824,assumption,(trans(s99, s9)), introduced(assumption)).
% 49.60/49.79 tff(9825,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9826,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9)) <=> (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9827,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9826])).
% 49.60/49.79 tff(9828,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9827, 9825])).
% 49.60/49.79 tff(9829,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9830,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9829, 9828])).
% 49.60/49.79 tff(9831,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9830, 8701, 9824, 9733, 9823, 9734])).
% 49.60/49.79 tff(9832,plain,((~trans(s99, s9)) | until2p8(s9) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9833,plain,
% 49.60/49.79 (~trans(s99, s9)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9832, 9635, 8691])).
% 49.60/49.79 tff(9834,assumption,(~until2p8(s10)), introduced(assumption)).
% 49.60/49.79 tff(9835,assumption,(trans(s99, s10)), introduced(assumption)).
% 49.60/49.79 tff(9836,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9837,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10)) <=> (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9838,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9837])).
% 49.60/49.79 tff(9839,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9838, 9836])).
% 49.60/49.79 tff(9840,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9841,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 49.60/49.79 tff(9842,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9841, 8701, 9835, 9733, 9834, 9734])).
% 49.60/49.79 tff(9843,plain,((~trans(s99, s10)) | until2p8(s10) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9844,plain,
% 49.60/49.79 (~trans(s99, s10)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9843, 9624, 8691])).
% 49.60/49.79 tff(9845,assumption,(~until2p8(s5)), introduced(assumption)).
% 49.60/49.79 tff(9846,assumption,(trans(s99, s5)), introduced(assumption)).
% 49.60/49.79 tff(9847,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9848,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5)) <=> (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9849,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9848])).
% 49.60/49.79 tff(9850,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9849, 9847])).
% 49.60/49.79 tff(9851,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9852,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9851, 9850])).
% 49.60/49.79 tff(9853,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9852, 8701, 9846, 9733, 9845, 9734])).
% 49.60/49.79 tff(9854,plain,((~trans(s99, s5)) | until2p8(s5) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9855,plain,
% 49.60/49.79 (~trans(s99, s5)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9854, 9679, 8691])).
% 49.60/49.79 tff(9856,assumption,(~until2p8(s15)), introduced(assumption)).
% 49.60/49.79 tff(9857,assumption,(trans(s99, s15)), introduced(assumption)).
% 49.60/49.79 tff(9858,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9859,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15)) <=> (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9860,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9859])).
% 49.60/49.79 tff(9861,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9860, 9858])).
% 49.60/49.79 tff(9862,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9863,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9862, 9861])).
% 49.60/49.79 tff(9864,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9863, 8701, 9857, 9733, 9856, 9734])).
% 49.60/49.79 tff(9865,plain,((~trans(s99, s15)) | until2p8(s15) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9866,plain,
% 49.60/49.79 (~trans(s99, s15)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9865, 9569, 8691])).
% 49.60/49.79 tff(9867,assumption,(~until2p8(s43)), introduced(assumption)).
% 49.60/49.79 tff(9868,assumption,(trans(s99, s43)), introduced(assumption)).
% 49.60/49.79 tff(9869,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9870,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43)) <=> (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9871,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9870])).
% 49.60/49.79 tff(9872,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9871, 9869])).
% 49.60/49.79 tff(9873,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9874,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9873, 9872])).
% 49.60/49.79 tff(9875,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9874, 8701, 9868, 9733, 9867, 9734])).
% 49.60/49.79 tff(9876,plain,((~trans(s99, s43)) | until2p8(s43) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9877,plain,
% 49.60/49.79 (~trans(s99, s43)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9876, 9289, 8691])).
% 49.60/49.79 tff(9878,assumption,(~until2p8(s47)), introduced(assumption)).
% 49.60/49.79 tff(9879,assumption,(trans(s99, s47)), introduced(assumption)).
% 49.60/49.79 tff(9880,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9881,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47)) <=> (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9882,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9881])).
% 49.60/49.79 tff(9883,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9882, 9880])).
% 49.60/49.79 tff(9884,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9885,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9884, 9883])).
% 49.60/49.79 tff(9886,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9885, 8701, 9879, 9733, 9878, 9734])).
% 49.60/49.79 tff(9887,plain,((~trans(s99, s47)) | until2p8(s47) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9888,plain,
% 49.60/49.79 (~trans(s99, s47)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9887, 9249, 8691])).
% 49.60/49.79 tff(9889,assumption,(~until2p8(s17)), introduced(assumption)).
% 49.60/49.79 tff(9890,assumption,(trans(s99, s17)), introduced(assumption)).
% 49.60/49.79 tff(9891,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9892,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17)) <=> (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9893,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9892])).
% 49.60/49.79 tff(9894,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9893, 9891])).
% 49.60/49.79 tff(9895,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9896,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9895, 9894])).
% 49.60/49.79 tff(9897,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9896, 8701, 9890, 9733, 9889, 9734])).
% 49.60/49.79 tff(9898,plain,((~trans(s99, s17)) | until2p8(s17) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9899,plain,
% 49.60/49.79 (~trans(s99, s17)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9898, 9549, 8691])).
% 49.60/49.79 tff(9900,assumption,(~until2p8(s27)), introduced(assumption)).
% 49.60/49.79 tff(9901,assumption,(trans(s99, s27)), introduced(assumption)).
% 49.60/49.79 tff(9902,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9903,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27)) <=> (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9904,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9903])).
% 49.60/49.79 tff(9905,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9904, 9902])).
% 49.60/49.79 tff(9906,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9907,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9906, 9905])).
% 49.60/49.79 tff(9908,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9907, 8701, 9901, 9733, 9900, 9734])).
% 49.60/49.79 tff(9909,plain,((~trans(s99, s27)) | until2p8(s27) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9910,plain,
% 49.60/49.79 (~trans(s99, s27)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9909, 9449, 8691])).
% 49.60/49.79 tff(9911,assumption,(~until2p8(s76)), introduced(assumption)).
% 49.60/49.79 tff(9912,assumption,(trans(s99, s76)), introduced(assumption)).
% 49.60/49.79 tff(9913,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9914,plain,
% 49.60/49.79 (((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76)) <=> (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 49.60/49.79 inference(rewrite,[status(thm)],[])).
% 49.60/49.79 tff(9915,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76))))),
% 49.60/49.79 inference(monotonicity,[status(thm)],[9914])).
% 49.60/49.79 tff(9916,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 49.60/49.79 inference(transitivity,[status(thm)],[9915, 9913])).
% 49.60/49.79 tff(9917,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))),
% 49.60/49.79 inference(quant_inst,[status(thm)],[])).
% 49.60/49.79 tff(9918,plain,
% 49.60/49.79 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76))),
% 49.60/49.79 inference(modus_ponens,[status(thm)],[9917, 9916])).
% 49.60/49.79 tff(9919,plain,
% 49.60/49.79 ($false),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9918, 8701, 9912, 9733, 9911, 9734])).
% 49.60/49.79 tff(9920,plain,((~trans(s99, s76)) | until2p8(s76) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.79 tff(9921,plain,
% 49.60/49.79 (~trans(s99, s76)),
% 49.60/49.79 inference(unit_resolution,[status(thm)],[9920, 8959, 8691])).
% 49.60/49.79 tff(9922,assumption,(~until2p8(s39)), introduced(assumption)).
% 49.60/49.79 tff(9923,assumption,(trans(s99, s39)), introduced(assumption)).
% 49.60/49.79 tff(9924,plain,
% 49.60/49.79 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9925,plain,
% 49.60/49.80 (((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39)) <=> (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9926,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39))))),
% 49.60/49.80 inference(monotonicity,[status(thm)],[9925])).
% 49.60/49.80 tff(9927,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 49.60/49.80 inference(transitivity,[status(thm)],[9926, 9924])).
% 49.60/49.80 tff(9928,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))),
% 49.60/49.80 inference(quant_inst,[status(thm)],[])).
% 49.60/49.80 tff(9929,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39))),
% 49.60/49.80 inference(modus_ponens,[status(thm)],[9928, 9927])).
% 49.60/49.80 tff(9930,plain,
% 49.60/49.80 ($false),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9929, 8701, 9923, 9733, 9922, 9734])).
% 49.60/49.80 tff(9931,plain,((~trans(s99, s39)) | until2p8(s39) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.80 tff(9932,plain,
% 49.60/49.80 (~trans(s99, s39)),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9931, 9329, 8691])).
% 49.60/49.80 tff(9933,assumption,(~until2p8(s87)), introduced(assumption)).
% 49.60/49.80 tff(9934,assumption,(trans(s99, s87)), introduced(assumption)).
% 49.60/49.80 tff(9935,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9936,plain,
% 49.60/49.80 (((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87)) <=> (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9937,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87))))),
% 49.60/49.80 inference(monotonicity,[status(thm)],[9936])).
% 49.60/49.80 tff(9938,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 49.60/49.80 inference(transitivity,[status(thm)],[9937, 9935])).
% 49.60/49.80 tff(9939,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))),
% 49.60/49.80 inference(quant_inst,[status(thm)],[])).
% 49.60/49.80 tff(9940,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87))),
% 49.60/49.80 inference(modus_ponens,[status(thm)],[9939, 9938])).
% 49.60/49.80 tff(9941,plain,
% 49.60/49.80 ($false),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9940, 8701, 9934, 9733, 9933, 9734])).
% 49.60/49.80 tff(9942,plain,((~trans(s99, s87)) | until2p8(s87) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.80 tff(9943,plain,
% 49.60/49.80 (~trans(s99, s87)),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9942, 8849, 8691])).
% 49.60/49.80 tff(9944,assumption,(~until2p8(s52)), introduced(assumption)).
% 49.60/49.80 tff(9945,assumption,(trans(s99, s52)), introduced(assumption)).
% 49.60/49.80 tff(9946,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9947,plain,
% 49.60/49.80 (((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52)) <=> (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9948,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52))))),
% 49.60/49.80 inference(monotonicity,[status(thm)],[9947])).
% 49.60/49.80 tff(9949,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 49.60/49.80 inference(transitivity,[status(thm)],[9948, 9946])).
% 49.60/49.80 tff(9950,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))),
% 49.60/49.80 inference(quant_inst,[status(thm)],[])).
% 49.60/49.80 tff(9951,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52))),
% 49.60/49.80 inference(modus_ponens,[status(thm)],[9950, 9949])).
% 49.60/49.80 tff(9952,plain,
% 49.60/49.80 ($false),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9951, 8701, 9945, 9733, 9944, 9734])).
% 49.60/49.80 tff(9953,plain,((~trans(s99, s52)) | until2p8(s52) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.60/49.80 tff(9954,plain,
% 49.60/49.80 (~trans(s99, s52)),
% 49.60/49.80 inference(unit_resolution,[status(thm)],[9953, 9199, 8691])).
% 49.60/49.80 tff(9955,assumption,(~until2p8(s13)), introduced(assumption)).
% 49.60/49.80 tff(9956,assumption,(trans(s99, s13)), introduced(assumption)).
% 49.60/49.80 tff(9957,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9958,plain,
% 49.60/49.80 (((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13)) <=> (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 49.60/49.80 inference(rewrite,[status(thm)],[])).
% 49.60/49.80 tff(9959,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13))))),
% 49.60/49.80 inference(monotonicity,[status(thm)],[9958])).
% 49.60/49.80 tff(9960,plain,
% 49.60/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 49.60/49.80 inference(transitivity,[status(thm)],[9959, 9957])).
% 49.60/49.80 tff(9961,plain,
% 49.60/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(9962,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[9961, 9960])).
% 49.63/49.80 tff(9963,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9962, 8701, 9956, 9733, 9955, 9734])).
% 49.63/49.80 tff(9964,plain,((~trans(s99, s13)) | until2p8(s13) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(9965,plain,
% 49.63/49.80 (~trans(s99, s13)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9964, 9591, 8691])).
% 49.63/49.80 tff(9966,assumption,(~until2p8(s68)), introduced(assumption)).
% 49.63/49.80 tff(9967,assumption,(trans(s99, s68)), introduced(assumption)).
% 49.63/49.80 tff(9968,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9969,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68)) <=> (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9970,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[9969])).
% 49.63/49.80 tff(9971,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[9970, 9968])).
% 49.63/49.80 tff(9972,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(9973,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[9972, 9971])).
% 49.63/49.80 tff(9974,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9973, 8701, 9967, 9733, 9966, 9734])).
% 49.63/49.80 tff(9975,plain,((~trans(s99, s68)) | until2p8(s68) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(9976,plain,
% 49.63/49.80 (~trans(s99, s68)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9975, 9039, 8691])).
% 49.63/49.80 tff(9977,assumption,(~until2p8(s44)), introduced(assumption)).
% 49.63/49.80 tff(9978,assumption,(trans(s99, s44)), introduced(assumption)).
% 49.63/49.80 tff(9979,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9980,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44)) <=> (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9981,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[9980])).
% 49.63/49.80 tff(9982,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[9981, 9979])).
% 49.63/49.80 tff(9983,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(9984,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[9983, 9982])).
% 49.63/49.80 tff(9985,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9984, 8701, 9978, 9733, 9977, 9734])).
% 49.63/49.80 tff(9986,plain,((~trans(s99, s44)) | until2p8(s44) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(9987,plain,
% 49.63/49.80 (~trans(s99, s44)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9986, 9279, 8691])).
% 49.63/49.80 tff(9988,assumption,(~until2p8(s55)), introduced(assumption)).
% 49.63/49.80 tff(9989,assumption,(trans(s99, s55)), introduced(assumption)).
% 49.63/49.80 tff(9990,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9991,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55)) <=> (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(9992,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[9991])).
% 49.63/49.80 tff(9993,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[9992, 9990])).
% 49.63/49.80 tff(9994,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(9995,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[9994, 9993])).
% 49.63/49.80 tff(9996,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9995, 8701, 9989, 9733, 9988, 9734])).
% 49.63/49.80 tff(9997,plain,((~trans(s99, s55)) | until2p8(s55) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(9998,plain,
% 49.63/49.80 (~trans(s99, s55)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[9997, 9169, 8691])).
% 49.63/49.80 tff(9999,assumption,(~until2p8(s46)), introduced(assumption)).
% 49.63/49.80 tff(10000,assumption,(trans(s99, s46)), introduced(assumption)).
% 49.63/49.80 tff(10001,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10002,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46)) <=> (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10003,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10002])).
% 49.63/49.80 tff(10004,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10003, 10001])).
% 49.63/49.80 tff(10005,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10006,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10005, 10004])).
% 49.63/49.80 tff(10007,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10006, 8701, 10000, 9733, 9999, 9734])).
% 49.63/49.80 tff(10008,plain,((~trans(s99, s46)) | until2p8(s46) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10009,plain,
% 49.63/49.80 (~trans(s99, s46)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10008, 9259, 8691])).
% 49.63/49.80 tff(10010,assumption,(~until2p8(s18)), introduced(assumption)).
% 49.63/49.80 tff(10011,assumption,(trans(s99, s18)), introduced(assumption)).
% 49.63/49.80 tff(10012,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10013,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18)) <=> (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10014,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10013])).
% 49.63/49.80 tff(10015,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10014, 10012])).
% 49.63/49.80 tff(10016,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10017,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10016, 10015])).
% 49.63/49.80 tff(10018,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10017, 8701, 10011, 9733, 10010, 9734])).
% 49.63/49.80 tff(10019,plain,((~trans(s99, s18)) | until2p8(s18) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10020,plain,
% 49.63/49.80 (~trans(s99, s18)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10019, 9539, 8691])).
% 49.63/49.80 tff(10021,assumption,(~until2p8(s75)), introduced(assumption)).
% 49.63/49.80 tff(10022,assumption,(trans(s99, s75)), introduced(assumption)).
% 49.63/49.80 tff(10023,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10024,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75)) <=> (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10025,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10024])).
% 49.63/49.80 tff(10026,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10025, 10023])).
% 49.63/49.80 tff(10027,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10028,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10027, 10026])).
% 49.63/49.80 tff(10029,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10028, 8701, 10022, 9733, 10021, 9734])).
% 49.63/49.80 tff(10030,plain,((~trans(s99, s75)) | until2p8(s75) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10031,plain,
% 49.63/49.80 (~trans(s99, s75)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10030, 8969, 8691])).
% 49.63/49.80 tff(10032,assumption,(~until2p8(s91)), introduced(assumption)).
% 49.63/49.80 tff(10033,assumption,(trans(s99, s91)), introduced(assumption)).
% 49.63/49.80 tff(10034,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10035,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91)) <=> (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10036,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10035])).
% 49.63/49.80 tff(10037,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10036, 10034])).
% 49.63/49.80 tff(10038,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10039,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10038, 10037])).
% 49.63/49.80 tff(10040,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10039, 8701, 10033, 9733, 10032, 9734])).
% 49.63/49.80 tff(10041,plain,((~trans(s99, s91)) | until2p8(s91) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10042,plain,
% 49.63/49.80 (~trans(s99, s91)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10041, 8809, 8691])).
% 49.63/49.80 tff(10043,assumption,(~until2p8(s3)), introduced(assumption)).
% 49.63/49.80 tff(10044,assumption,(trans(s99, s3)), introduced(assumption)).
% 49.63/49.80 tff(10045,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10046,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3)) <=> (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10047,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10046])).
% 49.63/49.80 tff(10048,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10047, 10045])).
% 49.63/49.80 tff(10049,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10050,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10049, 10048])).
% 49.63/49.80 tff(10051,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10050, 8701, 10044, 9733, 10043, 9734])).
% 49.63/49.80 tff(10052,plain,((~trans(s99, s3)) | until2p8(s3) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10053,plain,
% 49.63/49.80 (~trans(s99, s3)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10052, 9701, 8691])).
% 49.63/49.80 tff(10054,assumption,(~until2p8(s96)), introduced(assumption)).
% 49.63/49.80 tff(10055,assumption,(trans(s99, s96)), introduced(assumption)).
% 49.63/49.80 tff(10056,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10057,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96)) <=> (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10058,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10057])).
% 49.63/49.80 tff(10059,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10058, 10056])).
% 49.63/49.80 tff(10060,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10061,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10060, 10059])).
% 49.63/49.80 tff(10062,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10061, 8701, 10055, 9733, 10054, 9734])).
% 49.63/49.80 tff(10063,plain,((~trans(s99, s96)) | until2p8(s96) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10064,plain,
% 49.63/49.80 (~trans(s99, s96)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10063, 8759, 8691])).
% 49.63/49.80 tff(10065,assumption,(~until2p8(s41)), introduced(assumption)).
% 49.63/49.80 tff(10066,assumption,(trans(s99, s41)), introduced(assumption)).
% 49.63/49.80 tff(10067,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10068,plain,
% 49.63/49.80 (((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41)) <=> (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 49.63/49.80 inference(rewrite,[status(thm)],[])).
% 49.63/49.80 tff(10069,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41))))),
% 49.63/49.80 inference(monotonicity,[status(thm)],[10068])).
% 49.63/49.80 tff(10070,plain,
% 49.63/49.80 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 49.63/49.80 inference(transitivity,[status(thm)],[10069, 10067])).
% 49.63/49.80 tff(10071,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))),
% 49.63/49.80 inference(quant_inst,[status(thm)],[])).
% 49.63/49.80 tff(10072,plain,
% 49.63/49.80 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41))),
% 49.63/49.80 inference(modus_ponens,[status(thm)],[10071, 10070])).
% 49.63/49.80 tff(10073,plain,
% 49.63/49.80 ($false),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10072, 8701, 10066, 9733, 10065, 9734])).
% 49.63/49.80 tff(10074,plain,((~trans(s99, s41)) | until2p8(s41) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.80 tff(10075,plain,
% 49.63/49.80 (~trans(s99, s41)),
% 49.63/49.80 inference(unit_resolution,[status(thm)],[10074, 9309, 8691])).
% 49.63/49.80 tff(10076,assumption,(~until2p8(s48)), introduced(assumption)).
% 49.63/49.81 tff(10077,assumption,(trans(s99, s48)), introduced(assumption)).
% 49.63/49.81 tff(10078,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10079,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48)) <=> (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10080,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10079])).
% 49.63/49.81 tff(10081,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10080, 10078])).
% 49.63/49.81 tff(10082,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10083,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10082, 10081])).
% 49.63/49.81 tff(10084,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10083, 8701, 10077, 9733, 10076, 9734])).
% 49.63/49.81 tff(10085,plain,((~trans(s99, s48)) | until2p8(s48) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10086,plain,
% 49.63/49.81 (~trans(s99, s48)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10085, 9239, 8691])).
% 49.63/49.81 tff(10087,assumption,(~until2p8(s98)), introduced(assumption)).
% 49.63/49.81 tff(10088,assumption,(trans(s99, s98)), introduced(assumption)).
% 49.63/49.81 tff(10089,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10090,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98)) <=> (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10091,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10090])).
% 49.63/49.81 tff(10092,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10091, 10089])).
% 49.63/49.81 tff(10093,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10094,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10093, 10092])).
% 49.63/49.81 tff(10095,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10094, 8701, 10088, 9733, 10087, 9734])).
% 49.63/49.81 tff(10096,plain,((~trans(s99, s98)) | until2p8(s98) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10097,plain,
% 49.63/49.81 (~trans(s99, s98)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10096, 8739, 8691])).
% 49.63/49.81 tff(10098,assumption,(~until2p8(s30)), introduced(assumption)).
% 49.63/49.81 tff(10099,assumption,(trans(s99, s30)), introduced(assumption)).
% 49.63/49.81 tff(10100,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10101,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30)) <=> (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10102,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10101])).
% 49.63/49.81 tff(10103,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10102, 10100])).
% 49.63/49.81 tff(10104,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10105,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10104, 10103])).
% 49.63/49.81 tff(10106,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10105, 8701, 10099, 9733, 10098, 9734])).
% 49.63/49.81 tff(10107,plain,((~trans(s99, s30)) | until2p8(s30) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10108,plain,
% 49.63/49.81 (~trans(s99, s30)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10107, 9419, 8691])).
% 49.63/49.81 tff(10109,assumption,(~until2p8(s51)), introduced(assumption)).
% 49.63/49.81 tff(10110,assumption,(trans(s99, s51)), introduced(assumption)).
% 49.63/49.81 tff(10111,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10112,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51)) <=> (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10113,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10112])).
% 49.63/49.81 tff(10114,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10113, 10111])).
% 49.63/49.81 tff(10115,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10116,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10115, 10114])).
% 49.63/49.81 tff(10117,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10116, 8701, 10110, 9733, 10109, 9734])).
% 49.63/49.81 tff(10118,plain,((~trans(s99, s51)) | until2p8(s51) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10119,plain,
% 49.63/49.81 (~trans(s99, s51)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10118, 9209, 8691])).
% 49.63/49.81 tff(10120,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10121,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10122,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10121, 10120])).
% 49.63/49.81 tff(10123,plain,
% 49.63/49.81 (until2p8(s1) | (~xuntil2p9(s0))),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10122, 66, 8730])).
% 49.63/49.81 tff(10124,plain,
% 49.63/49.81 (~xuntil2p9(s0)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10123, 9723])).
% 49.63/49.81 tff(10125,plain,
% 49.63/49.81 (~always5(s0)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[7492, 9718])).
% 49.63/49.81 tff(10126,plain,
% 49.63/49.81 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10127,plain,
% 49.63/49.81 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10128,plain,
% 49.63/49.81 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10127, 10126])).
% 49.63/49.81 tff(10129,plain,
% 49.63/49.81 (xuntil2p9(s0) | (~until2p8(s0))),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10128, 8715, 10125])).
% 49.63/49.81 tff(10130,plain,
% 49.63/49.81 (~until2p8(s0)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10129, 10124])).
% 49.63/49.81 tff(10131,assumption,(~until2p8(s0)), introduced(assumption)).
% 49.63/49.81 tff(10132,assumption,(trans(s99, s0)), introduced(assumption)).
% 49.63/49.81 tff(10133,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10134,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0)) <=> ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10135,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10134])).
% 49.63/49.81 tff(10136,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10135, 10133])).
% 49.63/49.81 tff(10137,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10138,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10137, 10136])).
% 49.63/49.81 tff(10139,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10138, 8701, 10132, 9733, 9734, 10131])).
% 49.63/49.81 tff(10140,plain,((~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0)), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10141,plain,
% 49.63/49.81 (~trans(s99, s0)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10140, 8691, 10130])).
% 49.63/49.81 tff(10142,assumption,(~until2p8(s28)), introduced(assumption)).
% 49.63/49.81 tff(10143,assumption,(trans(s99, s28)), introduced(assumption)).
% 49.63/49.81 tff(10144,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10145,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28)) <=> (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10146,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10145])).
% 49.63/49.81 tff(10147,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10146, 10144])).
% 49.63/49.81 tff(10148,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10149,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10148, 10147])).
% 49.63/49.81 tff(10150,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10149, 8701, 10143, 9733, 10142, 9734])).
% 49.63/49.81 tff(10151,plain,((~trans(s99, s28)) | until2p8(s28) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10152,plain,
% 49.63/49.81 (~trans(s99, s28)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10151, 9439, 8691])).
% 49.63/49.81 tff(10153,assumption,(~until2p8(s50)), introduced(assumption)).
% 49.63/49.81 tff(10154,assumption,(trans(s99, s50)), introduced(assumption)).
% 49.63/49.81 tff(10155,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10156,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50)) <=> (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10157,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10156])).
% 49.63/49.81 tff(10158,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10157, 10155])).
% 49.63/49.81 tff(10159,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10160,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10159, 10158])).
% 49.63/49.81 tff(10161,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10160, 8701, 10154, 9733, 10153, 9734])).
% 49.63/49.81 tff(10162,plain,((~trans(s99, s50)) | until2p8(s50) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10163,plain,
% 49.63/49.81 (~trans(s99, s50)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10162, 9219, 8691])).
% 49.63/49.81 tff(10164,assumption,(~until2p8(s73)), introduced(assumption)).
% 49.63/49.81 tff(10165,assumption,(trans(s99, s73)), introduced(assumption)).
% 49.63/49.81 tff(10166,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10167,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73)) <=> (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10168,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10167])).
% 49.63/49.81 tff(10169,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10168, 10166])).
% 49.63/49.81 tff(10170,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10171,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10170, 10169])).
% 49.63/49.81 tff(10172,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10171, 8701, 10165, 9733, 10164, 9734])).
% 49.63/49.81 tff(10173,plain,((~trans(s99, s73)) | until2p8(s73) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10174,plain,
% 49.63/49.81 (~trans(s99, s73)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10173, 8989, 8691])).
% 49.63/49.81 tff(10175,assumption,(~until2p8(s54)), introduced(assumption)).
% 49.63/49.81 tff(10176,assumption,(trans(s99, s54)), introduced(assumption)).
% 49.63/49.81 tff(10177,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10178,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54)) <=> (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10179,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10178])).
% 49.63/49.81 tff(10180,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10179, 10177])).
% 49.63/49.81 tff(10181,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10182,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10181, 10180])).
% 49.63/49.81 tff(10183,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10182, 8701, 10176, 9733, 10175, 9734])).
% 49.63/49.81 tff(10184,plain,((~trans(s99, s54)) | until2p8(s54) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10185,plain,
% 49.63/49.81 (~trans(s99, s54)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10184, 9179, 8691])).
% 49.63/49.81 tff(10186,assumption,(~until2p8(s99)), introduced(assumption)).
% 49.63/49.81 tff(10187,assumption,(trans(s99, s99)), introduced(assumption)).
% 49.63/49.81 tff(10188,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10189,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99)) <=> (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10190,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10189])).
% 49.63/49.81 tff(10191,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10190, 10188])).
% 49.63/49.81 tff(10192,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10193,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10192, 10191])).
% 49.63/49.81 tff(10194,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10193, 8701, 10187, 9733, 10186, 9734])).
% 49.63/49.81 tff(10195,plain,((~trans(s99, s99)) | until2p8(s99) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10196,plain,
% 49.63/49.81 (~trans(s99, s99)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10195, 8720, 8691])).
% 49.63/49.81 tff(10197,assumption,(~until2p8(s72)), introduced(assumption)).
% 49.63/49.81 tff(10198,assumption,(trans(s99, s72)), introduced(assumption)).
% 49.63/49.81 tff(10199,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10200,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72)) <=> (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10201,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10200])).
% 49.63/49.81 tff(10202,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10201, 10199])).
% 49.63/49.81 tff(10203,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10204,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10203, 10202])).
% 49.63/49.81 tff(10205,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10204, 8701, 10198, 9733, 10197, 9734])).
% 49.63/49.81 tff(10206,plain,((~trans(s99, s72)) | until2p8(s72) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10207,plain,
% 49.63/49.81 (~trans(s99, s72)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10206, 8999, 8691])).
% 49.63/49.81 tff(10208,assumption,(~until2p8(s24)), introduced(assumption)).
% 49.63/49.81 tff(10209,assumption,(trans(s99, s24)), introduced(assumption)).
% 49.63/49.81 tff(10210,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10211,plain,
% 49.63/49.81 (((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24)) <=> (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 49.63/49.81 inference(rewrite,[status(thm)],[])).
% 49.63/49.81 tff(10212,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24))))),
% 49.63/49.81 inference(monotonicity,[status(thm)],[10211])).
% 49.63/49.81 tff(10213,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 49.63/49.81 inference(transitivity,[status(thm)],[10212, 10210])).
% 49.63/49.81 tff(10214,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))),
% 49.63/49.81 inference(quant_inst,[status(thm)],[])).
% 49.63/49.81 tff(10215,plain,
% 49.63/49.81 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24))),
% 49.63/49.81 inference(modus_ponens,[status(thm)],[10214, 10213])).
% 49.63/49.81 tff(10216,plain,
% 49.63/49.81 ($false),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10215, 8701, 10209, 9733, 10208, 9734])).
% 49.63/49.81 tff(10217,plain,((~trans(s99, s24)) | until2p8(s24) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.81 tff(10218,plain,
% 49.63/49.81 (~trans(s99, s24)),
% 49.63/49.81 inference(unit_resolution,[status(thm)],[10217, 9479, 8691])).
% 49.63/49.81 tff(10219,assumption,(~until2p8(s84)), introduced(assumption)).
% 49.63/49.81 tff(10220,assumption,(trans(s99, s84)), introduced(assumption)).
% 49.63/49.81 tff(10221,plain,
% 49.63/49.81 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10222,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84)) <=> (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10223,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10222])).
% 49.63/49.82 tff(10224,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10223, 10221])).
% 49.63/49.82 tff(10225,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10226,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10225, 10224])).
% 49.63/49.82 tff(10227,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10226, 8701, 10220, 9733, 10219, 9734])).
% 49.63/49.82 tff(10228,plain,((~trans(s99, s84)) | until2p8(s84) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10229,plain,
% 49.63/49.82 (~trans(s99, s84)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10228, 8879, 8691])).
% 49.63/49.82 tff(10230,assumption,(~until2p8(s66)), introduced(assumption)).
% 49.63/49.82 tff(10231,assumption,(trans(s99, s66)), introduced(assumption)).
% 49.63/49.82 tff(10232,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10233,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66)) <=> (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10234,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10233])).
% 49.63/49.82 tff(10235,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10234, 10232])).
% 49.63/49.82 tff(10236,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10237,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10236, 10235])).
% 49.63/49.82 tff(10238,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10237, 8701, 10231, 9733, 10230, 9734])).
% 49.63/49.82 tff(10239,plain,((~trans(s99, s66)) | until2p8(s66) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10240,plain,
% 49.63/49.82 (~trans(s99, s66)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10239, 9059, 8691])).
% 49.63/49.82 tff(10241,assumption,(~until2p8(s37)), introduced(assumption)).
% 49.63/49.82 tff(10242,assumption,(trans(s99, s37)), introduced(assumption)).
% 49.63/49.82 tff(10243,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10244,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37)) <=> (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10245,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10244])).
% 49.63/49.82 tff(10246,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10245, 10243])).
% 49.63/49.82 tff(10247,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10248,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10247, 10246])).
% 49.63/49.82 tff(10249,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10248, 8701, 10242, 9733, 10241, 9734])).
% 49.63/49.82 tff(10250,plain,((~trans(s99, s37)) | until2p8(s37) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10251,plain,
% 49.63/49.82 (~trans(s99, s37)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10250, 9349, 8691])).
% 49.63/49.82 tff(10252,assumption,(~until2p8(s11)), introduced(assumption)).
% 49.63/49.82 tff(10253,assumption,(trans(s99, s11)), introduced(assumption)).
% 49.63/49.82 tff(10254,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10255,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11)) <=> (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10256,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10255])).
% 49.63/49.82 tff(10257,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10256, 10254])).
% 49.63/49.82 tff(10258,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10259,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10258, 10257])).
% 49.63/49.82 tff(10260,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10259, 8701, 10253, 9733, 10252, 9734])).
% 49.63/49.82 tff(10261,plain,((~trans(s99, s11)) | until2p8(s11) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10262,plain,
% 49.63/49.82 (~trans(s99, s11)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10261, 9613, 8691])).
% 49.63/49.82 tff(10263,assumption,(~until2p8(s88)), introduced(assumption)).
% 49.63/49.82 tff(10264,assumption,(trans(s99, s88)), introduced(assumption)).
% 49.63/49.82 tff(10265,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10266,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88)) <=> (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10267,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10266])).
% 49.63/49.82 tff(10268,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10267, 10265])).
% 49.63/49.82 tff(10269,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10270,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10269, 10268])).
% 49.63/49.82 tff(10271,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10270, 8701, 10264, 9733, 10263, 9734])).
% 49.63/49.82 tff(10272,plain,((~trans(s99, s88)) | until2p8(s88) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10273,plain,
% 49.63/49.82 (~trans(s99, s88)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10272, 8839, 8691])).
% 49.63/49.82 tff(10274,assumption,(~until2p8(s74)), introduced(assumption)).
% 49.63/49.82 tff(10275,assumption,(trans(s99, s74)), introduced(assumption)).
% 49.63/49.82 tff(10276,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10277,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74)) <=> (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10278,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10277])).
% 49.63/49.82 tff(10279,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10278, 10276])).
% 49.63/49.82 tff(10280,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10281,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10280, 10279])).
% 49.63/49.82 tff(10282,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10281, 8701, 10275, 9733, 10274, 9734])).
% 49.63/49.82 tff(10283,plain,((~trans(s99, s74)) | until2p8(s74) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10284,plain,
% 49.63/49.82 (~trans(s99, s74)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10283, 8979, 8691])).
% 49.63/49.82 tff(10285,assumption,(~until2p8(s32)), introduced(assumption)).
% 49.63/49.82 tff(10286,assumption,(trans(s99, s32)), introduced(assumption)).
% 49.63/49.82 tff(10287,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10288,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32)) <=> (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10289,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10288])).
% 49.63/49.82 tff(10290,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10289, 10287])).
% 49.63/49.82 tff(10291,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10292,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10291, 10290])).
% 49.63/49.82 tff(10293,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10292, 8701, 10286, 9733, 10285, 9734])).
% 49.63/49.82 tff(10294,plain,((~trans(s99, s32)) | until2p8(s32) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10295,plain,
% 49.63/49.82 (~trans(s99, s32)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10294, 9399, 8691])).
% 49.63/49.82 tff(10296,assumption,(~until2p8(s4)), introduced(assumption)).
% 49.63/49.82 tff(10297,assumption,(trans(s99, s4)), introduced(assumption)).
% 49.63/49.82 tff(10298,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10299,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4)) <=> (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10300,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10299])).
% 49.63/49.82 tff(10301,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10300, 10298])).
% 49.63/49.82 tff(10302,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10303,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10302, 10301])).
% 49.63/49.82 tff(10304,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10303, 8701, 10297, 9733, 10296, 9734])).
% 49.63/49.82 tff(10305,plain,((~trans(s99, s4)) | until2p8(s4) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10306,plain,
% 49.63/49.82 (~trans(s99, s4)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10305, 9690, 8691])).
% 49.63/49.82 tff(10307,assumption,(~until2p8(s97)), introduced(assumption)).
% 49.63/49.82 tff(10308,assumption,(trans(s99, s97)), introduced(assumption)).
% 49.63/49.82 tff(10309,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10310,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97)) <=> (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10311,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10310])).
% 49.63/49.82 tff(10312,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10311, 10309])).
% 49.63/49.82 tff(10313,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10314,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10313, 10312])).
% 49.63/49.82 tff(10315,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10314, 8701, 10308, 9733, 10307, 9734])).
% 49.63/49.82 tff(10316,plain,((~trans(s99, s97)) | until2p8(s97) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10317,plain,
% 49.63/49.82 (~trans(s99, s97)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10316, 8749, 8691])).
% 49.63/49.82 tff(10318,assumption,(~until2p8(s34)), introduced(assumption)).
% 49.63/49.82 tff(10319,assumption,(trans(s99, s34)), introduced(assumption)).
% 49.63/49.82 tff(10320,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10321,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34)) <=> (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10322,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10321])).
% 49.63/49.82 tff(10323,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10322, 10320])).
% 49.63/49.82 tff(10324,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10325,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10324, 10323])).
% 49.63/49.82 tff(10326,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10325, 8701, 10319, 9733, 10318, 9734])).
% 49.63/49.82 tff(10327,plain,((~trans(s99, s34)) | until2p8(s34) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10328,plain,
% 49.63/49.82 (~trans(s99, s34)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10327, 9379, 8691])).
% 49.63/49.82 tff(10329,assumption,(~until2p8(s71)), introduced(assumption)).
% 49.63/49.82 tff(10330,assumption,(trans(s99, s71)), introduced(assumption)).
% 49.63/49.82 tff(10331,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10332,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71)) <=> (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10333,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10332])).
% 49.63/49.82 tff(10334,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10333, 10331])).
% 49.63/49.82 tff(10335,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10336,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10335, 10334])).
% 49.63/49.82 tff(10337,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10336, 8701, 10330, 9733, 10329, 9734])).
% 49.63/49.82 tff(10338,plain,((~trans(s99, s71)) | until2p8(s71) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10339,plain,
% 49.63/49.82 (~trans(s99, s71)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10338, 9009, 8691])).
% 49.63/49.82 tff(10340,assumption,(~until2p8(s19)), introduced(assumption)).
% 49.63/49.82 tff(10341,assumption,(trans(s99, s19)), introduced(assumption)).
% 49.63/49.82 tff(10342,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10343,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19)) <=> (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10344,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10343])).
% 49.63/49.82 tff(10345,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10344, 10342])).
% 49.63/49.82 tff(10346,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))),
% 49.63/49.82 inference(quant_inst,[status(thm)],[])).
% 49.63/49.82 tff(10347,plain,
% 49.63/49.82 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19))),
% 49.63/49.82 inference(modus_ponens,[status(thm)],[10346, 10345])).
% 49.63/49.82 tff(10348,plain,
% 49.63/49.82 ($false),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10347, 8701, 10341, 9733, 10340, 9734])).
% 49.63/49.82 tff(10349,plain,((~trans(s99, s19)) | until2p8(s19) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.82 tff(10350,plain,
% 49.63/49.82 (~trans(s99, s19)),
% 49.63/49.82 inference(unit_resolution,[status(thm)],[10349, 9529, 8691])).
% 49.63/49.82 tff(10351,assumption,(~until2p8(s26)), introduced(assumption)).
% 49.63/49.82 tff(10352,assumption,(trans(s99, s26)), introduced(assumption)).
% 49.63/49.82 tff(10353,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10354,plain,
% 49.63/49.82 (((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26)) <=> (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 49.63/49.82 inference(rewrite,[status(thm)],[])).
% 49.63/49.82 tff(10355,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26))))),
% 49.63/49.82 inference(monotonicity,[status(thm)],[10354])).
% 49.63/49.82 tff(10356,plain,
% 49.63/49.82 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 49.63/49.82 inference(transitivity,[status(thm)],[10355, 10353])).
% 49.63/49.83 tff(10357,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10358,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10357, 10356])).
% 49.63/49.83 tff(10359,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10358, 8701, 10352, 9733, 10351, 9734])).
% 49.63/49.83 tff(10360,plain,((~trans(s99, s26)) | until2p8(s26) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10361,plain,
% 49.63/49.83 (~trans(s99, s26)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10360, 9459, 8691])).
% 49.63/49.83 tff(10362,assumption,(~until2p8(s12)), introduced(assumption)).
% 49.63/49.83 tff(10363,assumption,(trans(s99, s12)), introduced(assumption)).
% 49.63/49.83 tff(10364,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10365,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12)) <=> (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10366,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10365])).
% 49.63/49.83 tff(10367,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10366, 10364])).
% 49.63/49.83 tff(10368,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10369,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10368, 10367])).
% 49.63/49.83 tff(10370,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10369, 8701, 10363, 9733, 10362, 9734])).
% 49.63/49.83 tff(10371,plain,((~trans(s99, s12)) | until2p8(s12) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10372,plain,
% 49.63/49.83 (~trans(s99, s12)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10371, 9602, 8691])).
% 49.63/49.83 tff(10373,assumption,(~until2p8(s85)), introduced(assumption)).
% 49.63/49.83 tff(10374,assumption,(trans(s99, s85)), introduced(assumption)).
% 49.63/49.83 tff(10375,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10376,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85)) <=> (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10377,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10376])).
% 49.63/49.83 tff(10378,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10377, 10375])).
% 49.63/49.83 tff(10379,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10380,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10379, 10378])).
% 49.63/49.83 tff(10381,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10380, 8701, 10374, 9733, 10373, 9734])).
% 49.63/49.83 tff(10382,plain,((~trans(s99, s85)) | until2p8(s85) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10383,plain,
% 49.63/49.83 (~trans(s99, s85)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10382, 8869, 8691])).
% 49.63/49.83 tff(10384,assumption,(~until2p8(s45)), introduced(assumption)).
% 49.63/49.83 tff(10385,assumption,(trans(s99, s45)), introduced(assumption)).
% 49.63/49.83 tff(10386,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10387,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45)) <=> (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10388,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10387])).
% 49.63/49.83 tff(10389,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10388, 10386])).
% 49.63/49.83 tff(10390,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10391,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10390, 10389])).
% 49.63/49.83 tff(10392,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10391, 8701, 10385, 9733, 10384, 9734])).
% 49.63/49.83 tff(10393,plain,((~trans(s99, s45)) | until2p8(s45) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10394,plain,
% 49.63/49.83 (~trans(s99, s45)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10393, 9269, 8691])).
% 49.63/49.83 tff(10395,assumption,(~until2p8(s81)), introduced(assumption)).
% 49.63/49.83 tff(10396,assumption,(trans(s99, s81)), introduced(assumption)).
% 49.63/49.83 tff(10397,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10398,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81)) <=> (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10399,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10398])).
% 49.63/49.83 tff(10400,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10399, 10397])).
% 49.63/49.83 tff(10401,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10402,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10401, 10400])).
% 49.63/49.83 tff(10403,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10402, 8701, 10396, 9733, 10395, 9734])).
% 49.63/49.83 tff(10404,plain,((~trans(s99, s81)) | until2p8(s81) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10405,plain,
% 49.63/49.83 (~trans(s99, s81)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10404, 8909, 8691])).
% 49.63/49.83 tff(10406,assumption,(~until2p8(s62)), introduced(assumption)).
% 49.63/49.83 tff(10407,assumption,(trans(s99, s62)), introduced(assumption)).
% 49.63/49.83 tff(10408,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10409,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62)) <=> (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10410,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10409])).
% 49.63/49.83 tff(10411,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10410, 10408])).
% 49.63/49.83 tff(10412,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10413,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10412, 10411])).
% 49.63/49.83 tff(10414,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10413, 8701, 10407, 9733, 10406, 9734])).
% 49.63/49.83 tff(10415,plain,((~trans(s99, s62)) | until2p8(s62) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10416,plain,
% 49.63/49.83 (~trans(s99, s62)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10415, 9099, 8691])).
% 49.63/49.83 tff(10417,assumption,(~until2p8(s60)), introduced(assumption)).
% 49.63/49.83 tff(10418,assumption,(trans(s99, s60)), introduced(assumption)).
% 49.63/49.83 tff(10419,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10420,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60)) <=> (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10421,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10420])).
% 49.63/49.83 tff(10422,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10421, 10419])).
% 49.63/49.83 tff(10423,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10424,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10423, 10422])).
% 49.63/49.83 tff(10425,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10424, 8701, 10418, 9733, 10417, 9734])).
% 49.63/49.83 tff(10426,plain,((~trans(s99, s60)) | until2p8(s60) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10427,plain,
% 49.63/49.83 (~trans(s99, s60)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10426, 9119, 8691])).
% 49.63/49.83 tff(10428,assumption,(~until2p8(s82)), introduced(assumption)).
% 49.63/49.83 tff(10429,assumption,(trans(s99, s82)), introduced(assumption)).
% 49.63/49.83 tff(10430,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10431,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82)) <=> (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10432,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10431])).
% 49.63/49.83 tff(10433,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10432, 10430])).
% 49.63/49.83 tff(10434,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10435,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10434, 10433])).
% 49.63/49.83 tff(10436,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10435, 8701, 10429, 9733, 10428, 9734])).
% 49.63/49.83 tff(10437,plain,((~trans(s99, s82)) | until2p8(s82) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10438,plain,
% 49.63/49.83 (~trans(s99, s82)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10437, 8899, 8691])).
% 49.63/49.83 tff(10439,assumption,(~until2p8(s25)), introduced(assumption)).
% 49.63/49.83 tff(10440,assumption,(trans(s99, s25)), introduced(assumption)).
% 49.63/49.83 tff(10441,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10442,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25)) <=> (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10443,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10442])).
% 49.63/49.83 tff(10444,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10443, 10441])).
% 49.63/49.83 tff(10445,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10446,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10445, 10444])).
% 49.63/49.83 tff(10447,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10446, 8701, 10440, 9733, 10439, 9734])).
% 49.63/49.83 tff(10448,plain,((~trans(s99, s25)) | until2p8(s25) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10449,plain,
% 49.63/49.83 (~trans(s99, s25)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10448, 9469, 8691])).
% 49.63/49.83 tff(10450,assumption,(~until2p8(s7)), introduced(assumption)).
% 49.63/49.83 tff(10451,assumption,(trans(s99, s7)), introduced(assumption)).
% 49.63/49.83 tff(10452,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10453,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7)) <=> (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10454,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10453])).
% 49.63/49.83 tff(10455,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10454, 10452])).
% 49.63/49.83 tff(10456,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10457,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10456, 10455])).
% 49.63/49.83 tff(10458,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10457, 8701, 10451, 9733, 10450, 9734])).
% 49.63/49.83 tff(10459,plain,((~trans(s99, s7)) | until2p8(s7) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10460,plain,
% 49.63/49.83 (~trans(s99, s7)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10459, 9657, 8691])).
% 49.63/49.83 tff(10461,assumption,(~until2p8(s65)), introduced(assumption)).
% 49.63/49.83 tff(10462,assumption,(trans(s99, s65)), introduced(assumption)).
% 49.63/49.83 tff(10463,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10464,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65)) <=> (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10465,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10464])).
% 49.63/49.83 tff(10466,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10465, 10463])).
% 49.63/49.83 tff(10467,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10468,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10467, 10466])).
% 49.63/49.83 tff(10469,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10468, 8701, 10462, 9733, 10461, 9734])).
% 49.63/49.83 tff(10470,plain,((~trans(s99, s65)) | until2p8(s65) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10471,plain,
% 49.63/49.83 (~trans(s99, s65)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10470, 9069, 8691])).
% 49.63/49.83 tff(10472,assumption,(~until2p8(s58)), introduced(assumption)).
% 49.63/49.83 tff(10473,assumption,(trans(s99, s58)), introduced(assumption)).
% 49.63/49.83 tff(10474,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10475,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58)) <=> (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10476,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10475])).
% 49.63/49.83 tff(10477,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10476, 10474])).
% 49.63/49.83 tff(10478,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10479,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10478, 10477])).
% 49.63/49.83 tff(10480,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10479, 8701, 10473, 9733, 10472, 9734])).
% 49.63/49.83 tff(10481,plain,((~trans(s99, s58)) | until2p8(s58) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10482,plain,
% 49.63/49.83 (~trans(s99, s58)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10481, 9139, 8691])).
% 49.63/49.83 tff(10483,assumption,(~until2p8(s64)), introduced(assumption)).
% 49.63/49.83 tff(10484,assumption,(trans(s99, s64)), introduced(assumption)).
% 49.63/49.83 tff(10485,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10486,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64)) <=> (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10487,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10486])).
% 49.63/49.83 tff(10488,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10487, 10485])).
% 49.63/49.83 tff(10489,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10490,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10489, 10488])).
% 49.63/49.83 tff(10491,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10490, 8701, 10484, 9733, 10483, 9734])).
% 49.63/49.83 tff(10492,plain,((~trans(s99, s64)) | until2p8(s64) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10493,plain,
% 49.63/49.83 (~trans(s99, s64)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10492, 9079, 8691])).
% 49.63/49.83 tff(10494,assumption,(~until2p8(s14)), introduced(assumption)).
% 49.63/49.83 tff(10495,assumption,(trans(s99, s14)), introduced(assumption)).
% 49.63/49.83 tff(10496,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10497,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14)) <=> (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10498,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10497])).
% 49.63/49.83 tff(10499,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10498, 10496])).
% 49.63/49.83 tff(10500,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10501,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10500, 10499])).
% 49.63/49.83 tff(10502,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10501, 8701, 10495, 9733, 10494, 9734])).
% 49.63/49.83 tff(10503,plain,((~trans(s99, s14)) | until2p8(s14) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.83 tff(10504,plain,
% 49.63/49.83 (~trans(s99, s14)),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10503, 9580, 8691])).
% 49.63/49.83 tff(10505,assumption,(~until2p8(s29)), introduced(assumption)).
% 49.63/49.83 tff(10506,assumption,(trans(s99, s29)), introduced(assumption)).
% 49.63/49.83 tff(10507,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10508,plain,
% 49.63/49.83 (((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29)) <=> (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 49.63/49.83 inference(rewrite,[status(thm)],[])).
% 49.63/49.83 tff(10509,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29))))),
% 49.63/49.83 inference(monotonicity,[status(thm)],[10508])).
% 49.63/49.83 tff(10510,plain,
% 49.63/49.83 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 49.63/49.83 inference(transitivity,[status(thm)],[10509, 10507])).
% 49.63/49.83 tff(10511,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))),
% 49.63/49.83 inference(quant_inst,[status(thm)],[])).
% 49.63/49.83 tff(10512,plain,
% 49.63/49.83 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29))),
% 49.63/49.83 inference(modus_ponens,[status(thm)],[10511, 10510])).
% 49.63/49.83 tff(10513,plain,
% 49.63/49.83 ($false),
% 49.63/49.83 inference(unit_resolution,[status(thm)],[10512, 8701, 10506, 9733, 10505, 9734])).
% 49.63/49.83 tff(10514,plain,((~trans(s99, s29)) | until2p8(s29) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10515,plain,
% 49.63/49.84 (~trans(s99, s29)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10514, 9429, 8691])).
% 49.63/49.84 tff(10516,assumption,(~until2p8(s79)), introduced(assumption)).
% 49.63/49.84 tff(10517,assumption,(trans(s99, s79)), introduced(assumption)).
% 49.63/49.84 tff(10518,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10519,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79)) <=> (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10520,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10519])).
% 49.63/49.84 tff(10521,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10520, 10518])).
% 49.63/49.84 tff(10522,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10523,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10522, 10521])).
% 49.63/49.84 tff(10524,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10523, 8701, 10517, 9733, 10516, 9734])).
% 49.63/49.84 tff(10525,plain,((~trans(s99, s79)) | until2p8(s79) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10526,plain,
% 49.63/49.84 (~trans(s99, s79)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10525, 8929, 8691])).
% 49.63/49.84 tff(10527,assumption,(~until2p8(s6)), introduced(assumption)).
% 49.63/49.84 tff(10528,assumption,(trans(s99, s6)), introduced(assumption)).
% 49.63/49.84 tff(10529,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10530,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6)) <=> (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10531,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10530])).
% 49.63/49.84 tff(10532,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10531, 10529])).
% 49.63/49.84 tff(10533,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10534,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10533, 10532])).
% 49.63/49.84 tff(10535,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10534, 8701, 10528, 9733, 10527, 9734])).
% 49.63/49.84 tff(10536,plain,((~trans(s99, s6)) | until2p8(s6) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10537,plain,
% 49.63/49.84 (~trans(s99, s6)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10536, 9668, 8691])).
% 49.63/49.84 tff(10538,assumption,(~until2p8(s67)), introduced(assumption)).
% 49.63/49.84 tff(10539,assumption,(trans(s99, s67)), introduced(assumption)).
% 49.63/49.84 tff(10540,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10541,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67)) <=> (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10542,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10541])).
% 49.63/49.84 tff(10543,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10542, 10540])).
% 49.63/49.84 tff(10544,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10545,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10544, 10543])).
% 49.63/49.84 tff(10546,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10545, 8701, 10539, 9733, 10538, 9734])).
% 49.63/49.84 tff(10547,plain,((~trans(s99, s67)) | until2p8(s67) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10548,plain,
% 49.63/49.84 (~trans(s99, s67)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10547, 9049, 8691])).
% 49.63/49.84 tff(10549,assumption,(~until2p8(s80)), introduced(assumption)).
% 49.63/49.84 tff(10550,assumption,(trans(s99, s80)), introduced(assumption)).
% 49.63/49.84 tff(10551,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10552,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80)) <=> (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10553,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10552])).
% 49.63/49.84 tff(10554,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10553, 10551])).
% 49.63/49.84 tff(10555,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10556,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10555, 10554])).
% 49.63/49.84 tff(10557,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10556, 8701, 10550, 9733, 10549, 9734])).
% 49.63/49.84 tff(10558,plain,((~trans(s99, s80)) | until2p8(s80) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10559,plain,
% 49.63/49.84 (~trans(s99, s80)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10558, 8919, 8691])).
% 49.63/49.84 tff(10560,assumption,(~until2p8(s16)), introduced(assumption)).
% 49.63/49.84 tff(10561,assumption,(trans(s99, s16)), introduced(assumption)).
% 49.63/49.84 tff(10562,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10563,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16)) <=> (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10564,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10563])).
% 49.63/49.84 tff(10565,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10564, 10562])).
% 49.63/49.84 tff(10566,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10567,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 49.63/49.84 tff(10568,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10567, 8701, 10561, 9733, 10560, 9734])).
% 49.63/49.84 tff(10569,plain,((~trans(s99, s16)) | until2p8(s16) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10570,plain,
% 49.63/49.84 (~trans(s99, s16)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10569, 9559, 8691])).
% 49.63/49.84 tff(10571,assumption,(~until2p8(s56)), introduced(assumption)).
% 49.63/49.84 tff(10572,assumption,(trans(s99, s56)), introduced(assumption)).
% 49.63/49.84 tff(10573,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10574,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56)) <=> (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10575,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10574])).
% 49.63/49.84 tff(10576,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10575, 10573])).
% 49.63/49.84 tff(10577,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10578,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10577, 10576])).
% 49.63/49.84 tff(10579,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10578, 8701, 10572, 9733, 10571, 9734])).
% 49.63/49.84 tff(10580,plain,((~trans(s99, s56)) | until2p8(s56) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10581,plain,
% 49.63/49.84 (~trans(s99, s56)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10580, 9159, 8691])).
% 49.63/49.84 tff(10582,assumption,(~until2p8(s53)), introduced(assumption)).
% 49.63/49.84 tff(10583,assumption,(trans(s99, s53)), introduced(assumption)).
% 49.63/49.84 tff(10584,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10585,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53)) <=> (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10586,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10585])).
% 49.63/49.84 tff(10587,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10586, 10584])).
% 49.63/49.84 tff(10588,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10589,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10588, 10587])).
% 49.63/49.84 tff(10590,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10589, 8701, 10583, 9733, 10582, 9734])).
% 49.63/49.84 tff(10591,plain,((~trans(s99, s53)) | until2p8(s53) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10592,plain,
% 49.63/49.84 (~trans(s99, s53)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10591, 9189, 8691])).
% 49.63/49.84 tff(10593,assumption,(~until2p8(s40)), introduced(assumption)).
% 49.63/49.84 tff(10594,assumption,(trans(s99, s40)), introduced(assumption)).
% 49.63/49.84 tff(10595,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10596,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40)) <=> (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10597,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10596])).
% 49.63/49.84 tff(10598,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10597, 10595])).
% 49.63/49.84 tff(10599,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10600,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10599, 10598])).
% 49.63/49.84 tff(10601,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10600, 8701, 10594, 9733, 10593, 9734])).
% 49.63/49.84 tff(10602,plain,((~trans(s99, s40)) | until2p8(s40) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10603,plain,
% 49.63/49.84 (~trans(s99, s40)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10602, 9319, 8691])).
% 49.63/49.84 tff(10604,assumption,(~until2p8(s20)), introduced(assumption)).
% 49.63/49.84 tff(10605,assumption,(trans(s99, s20)), introduced(assumption)).
% 49.63/49.84 tff(10606,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10607,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20)) <=> (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10608,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10607])).
% 49.63/49.84 tff(10609,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10608, 10606])).
% 49.63/49.84 tff(10610,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10611,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10610, 10609])).
% 49.63/49.84 tff(10612,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10611, 8701, 10605, 9733, 10604, 9734])).
% 49.63/49.84 tff(10613,plain,((~trans(s99, s20)) | until2p8(s20) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10614,plain,
% 49.63/49.84 (~trans(s99, s20)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10613, 9519, 8691])).
% 49.63/49.84 tff(10615,assumption,(~until2p8(s69)), introduced(assumption)).
% 49.63/49.84 tff(10616,assumption,(trans(s99, s69)), introduced(assumption)).
% 49.63/49.84 tff(10617,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10618,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69)) <=> (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10619,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10618])).
% 49.63/49.84 tff(10620,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10619, 10617])).
% 49.63/49.84 tff(10621,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10622,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 49.63/49.84 tff(10623,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10622, 8701, 10616, 9733, 10615, 9734])).
% 49.63/49.84 tff(10624,plain,((~trans(s99, s69)) | until2p8(s69) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10625,plain,
% 49.63/49.84 (~trans(s99, s69)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10624, 9029, 8691])).
% 49.63/49.84 tff(10626,assumption,(~until2p8(s22)), introduced(assumption)).
% 49.63/49.84 tff(10627,assumption,(trans(s99, s22)), introduced(assumption)).
% 49.63/49.84 tff(10628,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10629,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22)) <=> (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10630,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10629])).
% 49.63/49.84 tff(10631,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10630, 10628])).
% 49.63/49.84 tff(10632,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10633,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10632, 10631])).
% 49.63/49.84 tff(10634,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10633, 8701, 10627, 9733, 10626, 9734])).
% 49.63/49.84 tff(10635,plain,((~trans(s99, s22)) | until2p8(s22) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10636,plain,
% 49.63/49.84 (~trans(s99, s22)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10635, 9499, 8691])).
% 49.63/49.84 tff(10637,assumption,(~until2p8(s23)), introduced(assumption)).
% 49.63/49.84 tff(10638,assumption,(trans(s99, s23)), introduced(assumption)).
% 49.63/49.84 tff(10639,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10640,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23)) <=> (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10641,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23))))),
% 49.63/49.84 inference(monotonicity,[status(thm)],[10640])).
% 49.63/49.84 tff(10642,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 49.63/49.84 inference(transitivity,[status(thm)],[10641, 10639])).
% 49.63/49.84 tff(10643,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))),
% 49.63/49.84 inference(quant_inst,[status(thm)],[])).
% 49.63/49.84 tff(10644,plain,
% 49.63/49.84 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23))),
% 49.63/49.84 inference(modus_ponens,[status(thm)],[10643, 10642])).
% 49.63/49.84 tff(10645,plain,
% 49.63/49.84 ($false),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10644, 8701, 10638, 9733, 10637, 9734])).
% 49.63/49.84 tff(10646,plain,((~trans(s99, s23)) | until2p8(s23) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.84 tff(10647,plain,
% 49.63/49.84 (~trans(s99, s23)),
% 49.63/49.84 inference(unit_resolution,[status(thm)],[10646, 9489, 8691])).
% 49.63/49.84 tff(10648,assumption,(~until2p8(s59)), introduced(assumption)).
% 49.63/49.84 tff(10649,assumption,(trans(s99, s59)), introduced(assumption)).
% 49.63/49.84 tff(10650,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10651,plain,
% 49.63/49.84 (((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59)) <=> (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 49.63/49.84 inference(rewrite,[status(thm)],[])).
% 49.63/49.84 tff(10652,plain,
% 49.63/49.84 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59))))),
% 49.63/49.85 inference(monotonicity,[status(thm)],[10651])).
% 49.63/49.85 tff(10653,plain,
% 49.63/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 49.63/49.85 inference(transitivity,[status(thm)],[10652, 10650])).
% 49.63/49.85 tff(10654,plain,
% 49.63/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))),
% 49.63/49.85 inference(quant_inst,[status(thm)],[])).
% 49.63/49.85 tff(10655,plain,
% 49.63/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59))),
% 49.63/49.85 inference(modus_ponens,[status(thm)],[10654, 10653])).
% 49.63/49.85 tff(10656,plain,
% 49.63/49.85 ($false),
% 49.63/49.85 inference(unit_resolution,[status(thm)],[10655, 8701, 10649, 9733, 10648, 9734])).
% 49.63/49.85 tff(10657,plain,((~trans(s99, s59)) | until2p8(s59) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.85 tff(10658,plain,
% 49.63/49.85 (~trans(s99, s59)),
% 49.63/49.85 inference(unit_resolution,[status(thm)],[10657, 9129, 8691])).
% 49.63/49.85 tff(10659,assumption,(~until2p8(s93)), introduced(assumption)).
% 49.63/49.85 tff(10660,assumption,(trans(s99, s93)), introduced(assumption)).
% 49.63/49.85 tff(10661,plain,
% 49.63/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 49.63/49.85 inference(rewrite,[status(thm)],[])).
% 49.63/49.85 tff(10662,plain,
% 49.63/49.85 (((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93)) <=> (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 49.63/49.85 inference(rewrite,[status(thm)],[])).
% 49.63/49.85 tff(10663,plain,
% 49.63/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93))))),
% 49.63/49.85 inference(monotonicity,[status(thm)],[10662])).
% 49.63/49.85 tff(10664,plain,
% 49.63/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 49.63/49.85 inference(transitivity,[status(thm)],[10663, 10661])).
% 49.63/49.85 tff(10665,plain,
% 49.63/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))),
% 49.63/49.85 inference(quant_inst,[status(thm)],[])).
% 49.63/49.85 tff(10666,plain,
% 49.63/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93))),
% 49.63/49.85 inference(modus_ponens,[status(thm)],[10665, 10664])).
% 49.63/49.85 tff(10667,plain,
% 49.63/49.85 ($false),
% 49.63/49.85 inference(unit_resolution,[status(thm)],[10666, 8701, 10660, 9733, 10659, 9734])).
% 49.63/49.85 tff(10668,plain,((~trans(s99, s93)) | until2p8(s93) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.63/49.85 tff(10669,plain,
% 49.63/49.85 (~trans(s99, s93)),
% 49.63/49.85 inference(unit_resolution,[status(thm)],[10668, 8789, 8691])).
% 49.63/49.85 tff(10670,assumption,(~until2p8(s2)), introduced(assumption)).
% 49.63/49.85 tff(10671,assumption,(trans(s99, s2)), introduced(assumption)).
% 49.63/49.85 tff(10672,plain,
% 49.63/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 49.63/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10673,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2)) <=> (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10674,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10673])).
% 49.68/49.85 tff(10675,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10674, 10672])).
% 49.68/49.85 tff(10676,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10677,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10676, 10675])).
% 49.68/49.85 tff(10678,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10677, 8701, 10671, 9733, 10670, 9734])).
% 49.68/49.85 tff(10679,plain,((~trans(s99, s2)) | until2p8(s2) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10680,plain,
% 49.68/49.85 (~trans(s99, s2)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10679, 9712, 8691])).
% 49.68/49.85 tff(10681,assumption,(~until2p8(s92)), introduced(assumption)).
% 49.68/49.85 tff(10682,assumption,(trans(s99, s92)), introduced(assumption)).
% 49.68/49.85 tff(10683,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10684,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92)) <=> (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10685,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10684])).
% 49.68/49.85 tff(10686,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10685, 10683])).
% 49.68/49.85 tff(10687,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10688,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 49.68/49.85 tff(10689,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10688, 8701, 10682, 9733, 10681, 9734])).
% 49.68/49.85 tff(10690,plain,((~trans(s99, s92)) | until2p8(s92) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10691,plain,
% 49.68/49.85 (~trans(s99, s92)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10690, 8799, 8691])).
% 49.68/49.85 tff(10692,assumption,(~until2p8(s95)), introduced(assumption)).
% 49.68/49.85 tff(10693,assumption,(trans(s99, s95)), introduced(assumption)).
% 49.68/49.85 tff(10694,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10695,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95)) <=> (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10696,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10695])).
% 49.68/49.85 tff(10697,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10696, 10694])).
% 49.68/49.85 tff(10698,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10699,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10698, 10697])).
% 49.68/49.85 tff(10700,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10699, 8701, 10693, 9733, 10692, 9734])).
% 49.68/49.85 tff(10701,plain,((~trans(s99, s95)) | until2p8(s95) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10702,plain,
% 49.68/49.85 (~trans(s99, s95)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10701, 8769, 8691])).
% 49.68/49.85 tff(10703,assumption,(~until2p8(s61)), introduced(assumption)).
% 49.68/49.85 tff(10704,assumption,(trans(s99, s61)), introduced(assumption)).
% 49.68/49.85 tff(10705,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10706,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61)) <=> (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10707,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10706])).
% 49.68/49.85 tff(10708,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10707, 10705])).
% 49.68/49.85 tff(10709,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10710,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10709, 10708])).
% 49.68/49.85 tff(10711,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10710, 8701, 10704, 9733, 10703, 9734])).
% 49.68/49.85 tff(10712,plain,((~trans(s99, s61)) | until2p8(s61) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10713,plain,
% 49.68/49.85 (~trans(s99, s61)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10712, 9109, 8691])).
% 49.68/49.85 tff(10714,assumption,(~until2p8(s78)), introduced(assumption)).
% 49.68/49.85 tff(10715,assumption,(trans(s99, s78)), introduced(assumption)).
% 49.68/49.85 tff(10716,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10717,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78)) <=> (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10718,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10717])).
% 49.68/49.85 tff(10719,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10718, 10716])).
% 49.68/49.85 tff(10720,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10721,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10720, 10719])).
% 49.68/49.85 tff(10722,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10721, 8701, 10715, 9733, 10714, 9734])).
% 49.68/49.85 tff(10723,plain,((~trans(s99, s78)) | until2p8(s78) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10724,plain,
% 49.68/49.85 (~trans(s99, s78)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10723, 8939, 8691])).
% 49.68/49.85 tff(10725,assumption,(~until2p8(s89)), introduced(assumption)).
% 49.68/49.85 tff(10726,assumption,(trans(s99, s89)), introduced(assumption)).
% 49.68/49.85 tff(10727,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10728,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89)) <=> (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10729,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10728])).
% 49.68/49.85 tff(10730,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10729, 10727])).
% 49.68/49.85 tff(10731,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10732,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10731, 10730])).
% 49.68/49.85 tff(10733,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10732, 8701, 10726, 9733, 10725, 9734])).
% 49.68/49.85 tff(10734,plain,((~trans(s99, s89)) | until2p8(s89) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10735,plain,
% 49.68/49.85 (~trans(s99, s89)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10734, 8829, 8691])).
% 49.68/49.85 tff(10736,assumption,(~until2p8(s83)), introduced(assumption)).
% 49.68/49.85 tff(10737,assumption,(trans(s99, s83)), introduced(assumption)).
% 49.68/49.85 tff(10738,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10739,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83)) <=> (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10740,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10739])).
% 49.68/49.85 tff(10741,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10740, 10738])).
% 49.68/49.85 tff(10742,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10743,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10742, 10741])).
% 49.68/49.85 tff(10744,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10743, 8701, 10737, 9733, 10736, 9734])).
% 49.68/49.85 tff(10745,plain,((~trans(s99, s83)) | until2p8(s83) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10746,plain,
% 49.68/49.85 (~trans(s99, s83)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10745, 8889, 8691])).
% 49.68/49.85 tff(10747,assumption,(~until2p8(s90)), introduced(assumption)).
% 49.68/49.85 tff(10748,assumption,(trans(s99, s90)), introduced(assumption)).
% 49.68/49.85 tff(10749,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10750,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90)) <=> (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10751,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10750])).
% 49.68/49.85 tff(10752,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10751, 10749])).
% 49.68/49.85 tff(10753,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10754,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10753, 10752])).
% 49.68/49.85 tff(10755,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10754, 8701, 10748, 9733, 10747, 9734])).
% 49.68/49.85 tff(10756,plain,((~trans(s99, s90)) | until2p8(s90) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10757,plain,
% 49.68/49.85 (~trans(s99, s90)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10756, 8819, 8691])).
% 49.68/49.85 tff(10758,assumption,(~until2p8(s21)), introduced(assumption)).
% 49.68/49.85 tff(10759,assumption,(trans(s99, s21)), introduced(assumption)).
% 49.68/49.85 tff(10760,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10761,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21)) <=> (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10762,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10761])).
% 49.68/49.85 tff(10763,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10762, 10760])).
% 49.68/49.85 tff(10764,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10765,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10764, 10763])).
% 49.68/49.85 tff(10766,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10765, 8701, 10759, 9733, 10758, 9734])).
% 49.68/49.85 tff(10767,plain,((~trans(s99, s21)) | until2p8(s21) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10768,plain,
% 49.68/49.85 (~trans(s99, s21)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10767, 9509, 8691])).
% 49.68/49.85 tff(10769,assumption,(~until2p8(s94)), introduced(assumption)).
% 49.68/49.85 tff(10770,assumption,(trans(s99, s94)), introduced(assumption)).
% 49.68/49.85 tff(10771,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10772,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94)) <=> (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10773,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10772])).
% 49.68/49.85 tff(10774,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10773, 10771])).
% 49.68/49.85 tff(10775,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10776,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10775, 10774])).
% 49.68/49.85 tff(10777,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10776, 8701, 10770, 9733, 10769, 9734])).
% 49.68/49.85 tff(10778,plain,((~trans(s99, s94)) | until2p8(s94) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.85 tff(10779,plain,
% 49.68/49.85 (~trans(s99, s94)),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10778, 8779, 8691])).
% 49.68/49.85 tff(10780,assumption,(~until2p8(s33)), introduced(assumption)).
% 49.68/49.85 tff(10781,assumption,(trans(s99, s33)), introduced(assumption)).
% 49.68/49.85 tff(10782,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10783,plain,
% 49.68/49.85 (((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33)) <=> (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 49.68/49.85 inference(rewrite,[status(thm)],[])).
% 49.68/49.85 tff(10784,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33))))),
% 49.68/49.85 inference(monotonicity,[status(thm)],[10783])).
% 49.68/49.85 tff(10785,plain,
% 49.68/49.85 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 49.68/49.85 inference(transitivity,[status(thm)],[10784, 10782])).
% 49.68/49.85 tff(10786,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))),
% 49.68/49.85 inference(quant_inst,[status(thm)],[])).
% 49.68/49.85 tff(10787,plain,
% 49.68/49.85 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33))),
% 49.68/49.85 inference(modus_ponens,[status(thm)],[10786, 10785])).
% 49.68/49.85 tff(10788,plain,
% 49.68/49.85 ($false),
% 49.68/49.85 inference(unit_resolution,[status(thm)],[10787, 8701, 10781, 9733, 10780, 9734])).
% 49.68/49.85 tff(10789,plain,((~trans(s99, s33)) | until2p8(s33) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.86 tff(10790,plain,
% 49.68/49.86 (~trans(s99, s33)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10789, 9389, 8691])).
% 49.68/49.86 tff(10791,assumption,(~until2p8(s77)), introduced(assumption)).
% 49.68/49.86 tff(10792,assumption,(trans(s99, s77)), introduced(assumption)).
% 49.68/49.86 tff(10793,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10794,plain,
% 49.68/49.86 (((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77)) <=> (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10795,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77))))),
% 49.68/49.86 inference(monotonicity,[status(thm)],[10794])).
% 49.68/49.86 tff(10796,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 49.68/49.86 inference(transitivity,[status(thm)],[10795, 10793])).
% 49.68/49.86 tff(10797,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10798,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10797, 10796])).
% 49.68/49.86 tff(10799,plain,
% 49.68/49.86 ($false),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10798, 8701, 10792, 9733, 10791, 9734])).
% 49.68/49.86 tff(10800,plain,((~trans(s99, s77)) | until2p8(s77) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.86 tff(10801,plain,
% 49.68/49.86 (~trans(s99, s77)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10800, 8949, 8691])).
% 49.68/49.86 tff(10802,assumption,(~until2p8(s35)), introduced(assumption)).
% 49.68/49.86 tff(10803,assumption,(trans(s99, s35)), introduced(assumption)).
% 49.68/49.86 tff(10804,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10805,plain,
% 49.68/49.86 (((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35)) <=> (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10806,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35))))),
% 49.68/49.86 inference(monotonicity,[status(thm)],[10805])).
% 49.68/49.86 tff(10807,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 49.68/49.86 inference(transitivity,[status(thm)],[10806, 10804])).
% 49.68/49.86 tff(10808,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10809,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10808, 10807])).
% 49.68/49.86 tff(10810,plain,
% 49.68/49.86 ($false),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10809, 8701, 10803, 9733, 10802, 9734])).
% 49.68/49.86 tff(10811,plain,((~trans(s99, s35)) | until2p8(s35) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.86 tff(10812,plain,
% 49.68/49.86 (~trans(s99, s35)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10811, 9369, 8691])).
% 49.68/49.86 tff(10813,assumption,(~until2p8(s31)), introduced(assumption)).
% 49.68/49.86 tff(10814,assumption,(trans(s99, s31)), introduced(assumption)).
% 49.68/49.86 tff(10815,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10816,plain,
% 49.68/49.86 (((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31)) <=> (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10817,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31))))),
% 49.68/49.86 inference(monotonicity,[status(thm)],[10816])).
% 49.68/49.86 tff(10818,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 49.68/49.86 inference(transitivity,[status(thm)],[10817, 10815])).
% 49.68/49.86 tff(10819,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10820,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10819, 10818])).
% 49.68/49.86 tff(10821,plain,
% 49.68/49.86 ($false),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10820, 8701, 10814, 9733, 10813, 9734])).
% 49.68/49.86 tff(10822,plain,((~trans(s99, s31)) | until2p8(s31) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.86 tff(10823,plain,
% 49.68/49.86 (~trans(s99, s31)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10822, 9409, 8691])).
% 49.68/49.86 tff(10824,assumption,(~until2p8(s70)), introduced(assumption)).
% 49.68/49.86 tff(10825,assumption,(trans(s99, s70)), introduced(assumption)).
% 49.68/49.86 tff(10826,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10827,plain,
% 49.68/49.86 (((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70)) <=> (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10828,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70))))),
% 49.68/49.86 inference(monotonicity,[status(thm)],[10827])).
% 49.68/49.86 tff(10829,plain,
% 49.68/49.86 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 49.68/49.86 inference(transitivity,[status(thm)],[10828, 10826])).
% 49.68/49.86 tff(10830,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10831,plain,
% 49.68/49.86 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10830, 10829])).
% 49.68/49.86 tff(10832,plain,
% 49.68/49.86 ($false),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10831, 8701, 10825, 9733, 10824, 9734])).
% 49.68/49.86 tff(10833,plain,((~trans(s99, s70)) | until2p8(s70) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 49.68/49.86 tff(10834,plain,
% 49.68/49.86 (~trans(s99, s70)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10833, 9019, 8691])).
% 49.68/49.86 tff(10835,assumption,(~loop), introduced(assumption)).
% 49.68/49.86 tff(10836,plain,
% 49.68/49.86 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 49.68/49.86 inference(bind,[status(th)],[])).
% 49.68/49.86 tff(10837,plain,
% 49.68/49.86 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(quant_intro,[status(thm)],[10836])).
% 49.68/49.86 tff(10838,plain,
% 49.68/49.86 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10839,plain,
% 49.68/49.86 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 49.68/49.86 inference(bind,[status(th)],[])).
% 49.68/49.86 tff(10840,plain,
% 49.68/49.86 (![X: $i] : ((loop | (~last(X))) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(quant_intro,[status(thm)],[10839])).
% 49.68/49.86 tff(10841,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty6')).
% 49.68/49.86 tff(10842,plain,
% 49.68/49.86 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10841, 10840])).
% 49.68/49.86 tff(10843,plain,
% 49.68/49.86 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10842, 10838])).
% 49.68/49.86 tff(10844,plain,(
% 49.68/49.86 ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(skolemize,[status(sab)],[10843])).
% 49.68/49.86 tff(10845,plain,
% 49.68/49.86 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10844, 10837])).
% 49.68/49.86 tff(10846,plain,
% 49.68/49.86 (((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s99)) | (~xuntil7(s99)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s99)) | (~xuntil7(s99)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10847,plain,
% 49.68/49.86 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s99)) | (~xuntil7(s99)))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10848,plain,
% 49.68/49.86 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s99)) | (~xuntil7(s99))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10847, 10846])).
% 49.68/49.86 tff(10849,plain,
% 49.68/49.86 (loop | (~xuntil7(s99))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10848, 8701, 10845])).
% 49.68/49.86 tff(10850,plain,
% 49.68/49.86 (~xuntil7(s99)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10849, 10835])).
% 49.68/49.86 tff(10851,plain,
% 49.68/49.86 (^[X: $i] : refl((loop | (~always5(X)) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 49.68/49.86 inference(bind,[status(th)],[])).
% 49.68/49.86 tff(10852,plain,
% 49.68/49.86 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(quant_intro,[status(thm)],[10851])).
% 49.68/49.86 tff(10853,plain,
% 49.68/49.86 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10854,plain,
% 49.68/49.86 (^[X: $i] : rewrite(((loop | (~always5(X))) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 49.68/49.86 inference(bind,[status(th)],[])).
% 49.68/49.86 tff(10855,plain,
% 49.68/49.86 (![X: $i] : ((loop | (~always5(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(quant_intro,[status(thm)],[10854])).
% 49.68/49.86 tff(10856,axiom,(![X: $i] : ((loop | (~always5(X))) | (~last(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty3')).
% 49.68/49.86 tff(10857,plain,
% 49.68/49.86 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10856, 10855])).
% 49.68/49.86 tff(10858,plain,
% 49.68/49.86 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10857, 10853])).
% 49.68/49.86 tff(10859,plain,(
% 49.68/49.86 ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(skolemize,[status(sab)],[10858])).
% 49.68/49.86 tff(10860,plain,
% 49.68/49.86 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10859, 10852])).
% 49.68/49.86 tff(10861,plain,
% 49.68/49.86 (((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s99)) | (~last(s99)))) <=> ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s99)) | (~last(s99)))),
% 49.68/49.86 inference(rewrite,[status(thm)],[])).
% 49.68/49.86 tff(10862,plain,
% 49.68/49.86 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s99)) | (~last(s99)))),
% 49.68/49.86 inference(quant_inst,[status(thm)],[])).
% 49.68/49.86 tff(10863,plain,
% 49.68/49.86 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s99)) | (~last(s99))),
% 49.68/49.86 inference(modus_ponens,[status(thm)],[10862, 10861])).
% 49.68/49.86 tff(10864,plain,
% 49.68/49.86 (loop | (~always5(s99))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10863, 8701, 10860])).
% 49.68/49.86 tff(10865,plain,
% 49.68/49.86 (~always5(s99)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10864, 10835])).
% 49.68/49.86 tff(10866,plain,
% 49.68/49.86 (~until6(s99)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8690, 7273, 10865, 10850])).
% 49.68/49.86 tff(10867,plain,
% 49.68/49.86 (~xuntil7(s98)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8683, 10866])).
% 49.68/49.86 tff(10868,plain,
% 49.68/49.86 (~always5(s98)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6602, 10865])).
% 49.68/49.86 tff(10869,plain,
% 49.68/49.86 (xuntil7(s98) | (~until6(s98))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8677, 7273, 10868])).
% 49.68/49.86 tff(10870,plain,
% 49.68/49.86 (~until6(s98)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10869, 10867])).
% 49.68/49.86 tff(10871,plain,
% 49.68/49.86 (~xuntil7(s97)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8670, 10870])).
% 49.68/49.86 tff(10872,plain,
% 49.68/49.86 (~always5(s97)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6610, 10868])).
% 49.68/49.86 tff(10873,plain,
% 49.68/49.86 (xuntil7(s97) | (~until6(s97))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8664, 7273, 10872])).
% 49.68/49.86 tff(10874,plain,
% 49.68/49.86 (~until6(s97)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10873, 10871])).
% 49.68/49.86 tff(10875,plain,
% 49.68/49.86 (~xuntil7(s96)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8657, 10874])).
% 49.68/49.86 tff(10876,plain,
% 49.68/49.86 (~always5(s96)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6347, 10872])).
% 49.68/49.86 tff(10877,plain,
% 49.68/49.86 (xuntil7(s96) | (~until6(s96))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8651, 7273, 10876])).
% 49.68/49.86 tff(10878,plain,
% 49.68/49.86 (~until6(s96)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10877, 10875])).
% 49.68/49.86 tff(10879,plain,
% 49.68/49.86 (~xuntil7(s95)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8644, 10878])).
% 49.68/49.86 tff(10880,plain,
% 49.68/49.86 (~always5(s95)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6339, 10876])).
% 49.68/49.86 tff(10881,plain,
% 49.68/49.86 (xuntil7(s95) | (~until6(s95))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8638, 7273, 10880])).
% 49.68/49.86 tff(10882,plain,
% 49.68/49.86 (~until6(s95)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10881, 10879])).
% 49.68/49.86 tff(10883,plain,
% 49.68/49.86 (~xuntil7(s94)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8631, 10882])).
% 49.68/49.86 tff(10884,plain,
% 49.68/49.86 (~always5(s94)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6620, 10880])).
% 49.68/49.86 tff(10885,plain,
% 49.68/49.86 (xuntil7(s94) | (~until6(s94))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8625, 7273, 10884])).
% 49.68/49.86 tff(10886,plain,
% 49.68/49.86 (~until6(s94)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10885, 10883])).
% 49.68/49.86 tff(10887,plain,
% 49.68/49.86 (~xuntil7(s93)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8618, 10886])).
% 49.68/49.86 tff(10888,plain,
% 49.68/49.86 (~always5(s93)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6628, 10884])).
% 49.68/49.86 tff(10889,plain,
% 49.68/49.86 (xuntil7(s93) | (~until6(s93))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8612, 7273, 10888])).
% 49.68/49.86 tff(10890,plain,
% 49.68/49.86 (~until6(s93)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10889, 10887])).
% 49.68/49.86 tff(10891,plain,
% 49.68/49.86 (~xuntil7(s92)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8605, 10890])).
% 49.68/49.86 tff(10892,plain,
% 49.68/49.86 (~always5(s92)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6636, 10888])).
% 49.68/49.86 tff(10893,plain,
% 49.68/49.86 (xuntil7(s92) | (~until6(s92))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8599, 7273, 10892])).
% 49.68/49.86 tff(10894,plain,
% 49.68/49.86 (~until6(s92)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10893, 10891])).
% 49.68/49.86 tff(10895,plain,
% 49.68/49.86 (~xuntil7(s91)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8592, 10894])).
% 49.68/49.86 tff(10896,plain,
% 49.68/49.86 (~always5(s91)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6644, 10892])).
% 49.68/49.86 tff(10897,plain,
% 49.68/49.86 (xuntil7(s91) | (~until6(s91))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8586, 7273, 10896])).
% 49.68/49.86 tff(10898,plain,
% 49.68/49.86 (~until6(s91)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10897, 10895])).
% 49.68/49.86 tff(10899,plain,
% 49.68/49.86 (~xuntil7(s90)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8579, 10898])).
% 49.68/49.86 tff(10900,plain,
% 49.68/49.86 (~always5(s90)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6652, 10896])).
% 49.68/49.86 tff(10901,plain,
% 49.68/49.86 (xuntil7(s90) | (~until6(s90))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8573, 7273, 10900])).
% 49.68/49.86 tff(10902,plain,
% 49.68/49.86 (~until6(s90)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10901, 10899])).
% 49.68/49.86 tff(10903,plain,
% 49.68/49.86 (~xuntil7(s89)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8566, 10902])).
% 49.68/49.86 tff(10904,plain,
% 49.68/49.86 (~always5(s89)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6660, 10900])).
% 49.68/49.86 tff(10905,plain,
% 49.68/49.86 (xuntil7(s89) | (~until6(s89))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8560, 7273, 10904])).
% 49.68/49.86 tff(10906,plain,
% 49.68/49.86 (~until6(s89)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10905, 10903])).
% 49.68/49.86 tff(10907,plain,
% 49.68/49.86 (~xuntil7(s88)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8553, 10906])).
% 49.68/49.86 tff(10908,plain,
% 49.68/49.86 (~always5(s88)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6668, 10904])).
% 49.68/49.86 tff(10909,plain,
% 49.68/49.86 (xuntil7(s88) | (~until6(s88))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8547, 7273, 10908])).
% 49.68/49.86 tff(10910,plain,
% 49.68/49.86 (~until6(s88)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10909, 10907])).
% 49.68/49.86 tff(10911,plain,
% 49.68/49.86 (~xuntil7(s87)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8540, 10910])).
% 49.68/49.86 tff(10912,plain,
% 49.68/49.86 (~always5(s87)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6676, 10908])).
% 49.68/49.86 tff(10913,plain,
% 49.68/49.86 (xuntil7(s87) | (~until6(s87))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8534, 7273, 10912])).
% 49.68/49.86 tff(10914,plain,
% 49.68/49.86 (~until6(s87)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10913, 10911])).
% 49.68/49.86 tff(10915,plain,
% 49.68/49.86 (~xuntil7(s86)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8527, 10914])).
% 49.68/49.86 tff(10916,plain,
% 49.68/49.86 (~always5(s86)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6684, 10912])).
% 49.68/49.86 tff(10917,plain,
% 49.68/49.86 (xuntil7(s86) | (~until6(s86))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8521, 7273, 10916])).
% 49.68/49.86 tff(10918,plain,
% 49.68/49.86 (~until6(s86)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10917, 10915])).
% 49.68/49.86 tff(10919,plain,
% 49.68/49.86 (~xuntil7(s85)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8514, 10918])).
% 49.68/49.86 tff(10920,plain,
% 49.68/49.86 (~always5(s85)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6692, 10916])).
% 49.68/49.86 tff(10921,plain,
% 49.68/49.86 (xuntil7(s85) | (~until6(s85))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8508, 7273, 10920])).
% 49.68/49.86 tff(10922,plain,
% 49.68/49.86 (~until6(s85)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10921, 10919])).
% 49.68/49.86 tff(10923,plain,
% 49.68/49.86 (~xuntil7(s84)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8501, 10922])).
% 49.68/49.86 tff(10924,plain,
% 49.68/49.86 (~always5(s84)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6700, 10920])).
% 49.68/49.86 tff(10925,plain,
% 49.68/49.86 (xuntil7(s84) | (~until6(s84))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8495, 7273, 10924])).
% 49.68/49.86 tff(10926,plain,
% 49.68/49.86 (~until6(s84)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10925, 10923])).
% 49.68/49.86 tff(10927,plain,
% 49.68/49.86 (~xuntil7(s83)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8488, 10926])).
% 49.68/49.86 tff(10928,plain,
% 49.68/49.86 (~always5(s83)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6708, 10924])).
% 49.68/49.86 tff(10929,plain,
% 49.68/49.86 (xuntil7(s83) | (~until6(s83))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8482, 7273, 10928])).
% 49.68/49.86 tff(10930,plain,
% 49.68/49.86 (~until6(s83)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10929, 10927])).
% 49.68/49.86 tff(10931,plain,
% 49.68/49.86 (~xuntil7(s82)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8475, 10930])).
% 49.68/49.86 tff(10932,plain,
% 49.68/49.86 (~always5(s82)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6716, 10928])).
% 49.68/49.86 tff(10933,plain,
% 49.68/49.86 (xuntil7(s82) | (~until6(s82))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8469, 7273, 10932])).
% 49.68/49.86 tff(10934,plain,
% 49.68/49.86 (~until6(s82)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10933, 10931])).
% 49.68/49.86 tff(10935,plain,
% 49.68/49.86 (~xuntil7(s81)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8462, 10934])).
% 49.68/49.86 tff(10936,plain,
% 49.68/49.86 (~always5(s81)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6724, 10932])).
% 49.68/49.86 tff(10937,plain,
% 49.68/49.86 (xuntil7(s81) | (~until6(s81))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8456, 7273, 10936])).
% 49.68/49.86 tff(10938,plain,
% 49.68/49.86 (~until6(s81)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10937, 10935])).
% 49.68/49.86 tff(10939,plain,
% 49.68/49.86 (~xuntil7(s80)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8449, 10938])).
% 49.68/49.86 tff(10940,plain,
% 49.68/49.86 (~always5(s80)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6732, 10936])).
% 49.68/49.86 tff(10941,plain,
% 49.68/49.86 (xuntil7(s80) | (~until6(s80))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8443, 7273, 10940])).
% 49.68/49.86 tff(10942,plain,
% 49.68/49.86 (~until6(s80)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10941, 10939])).
% 49.68/49.86 tff(10943,plain,
% 49.68/49.86 (~xuntil7(s79)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8436, 10942])).
% 49.68/49.86 tff(10944,plain,
% 49.68/49.86 (~always5(s79)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6740, 10940])).
% 49.68/49.86 tff(10945,plain,
% 49.68/49.86 (xuntil7(s79) | (~until6(s79))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8430, 7273, 10944])).
% 49.68/49.86 tff(10946,plain,
% 49.68/49.86 (~until6(s79)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10945, 10943])).
% 49.68/49.86 tff(10947,plain,
% 49.68/49.86 (~xuntil7(s78)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8423, 10946])).
% 49.68/49.86 tff(10948,plain,
% 49.68/49.86 (~always5(s78)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6748, 10944])).
% 49.68/49.86 tff(10949,plain,
% 49.68/49.86 (xuntil7(s78) | (~until6(s78))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8417, 7273, 10948])).
% 49.68/49.86 tff(10950,plain,
% 49.68/49.86 (~until6(s78)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10949, 10947])).
% 49.68/49.86 tff(10951,plain,
% 49.68/49.86 (~xuntil7(s77)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8410, 10950])).
% 49.68/49.86 tff(10952,plain,
% 49.68/49.86 (~always5(s77)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6756, 10948])).
% 49.68/49.86 tff(10953,plain,
% 49.68/49.86 (xuntil7(s77) | (~until6(s77))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8404, 7273, 10952])).
% 49.68/49.86 tff(10954,plain,
% 49.68/49.86 (~until6(s77)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10953, 10951])).
% 49.68/49.86 tff(10955,plain,
% 49.68/49.86 (~xuntil7(s76)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8397, 10954])).
% 49.68/49.86 tff(10956,plain,
% 49.68/49.86 (~always5(s76)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6764, 10952])).
% 49.68/49.86 tff(10957,plain,
% 49.68/49.86 (xuntil7(s76) | (~until6(s76))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8391, 7273, 10956])).
% 49.68/49.86 tff(10958,plain,
% 49.68/49.86 (~until6(s76)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10957, 10955])).
% 49.68/49.86 tff(10959,plain,
% 49.68/49.86 (~xuntil7(s75)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8384, 10958])).
% 49.68/49.86 tff(10960,plain,
% 49.68/49.86 (~always5(s75)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6772, 10956])).
% 49.68/49.86 tff(10961,plain,
% 49.68/49.86 (xuntil7(s75) | (~until6(s75))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8378, 7273, 10960])).
% 49.68/49.86 tff(10962,plain,
% 49.68/49.86 (~until6(s75)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10961, 10959])).
% 49.68/49.86 tff(10963,plain,
% 49.68/49.86 (~xuntil7(s74)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8371, 10962])).
% 49.68/49.86 tff(10964,plain,
% 49.68/49.86 (~always5(s74)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6780, 10960])).
% 49.68/49.86 tff(10965,plain,
% 49.68/49.86 (xuntil7(s74) | (~until6(s74))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8365, 7273, 10964])).
% 49.68/49.86 tff(10966,plain,
% 49.68/49.86 (~until6(s74)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10965, 10963])).
% 49.68/49.86 tff(10967,plain,
% 49.68/49.86 (~xuntil7(s73)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8358, 10966])).
% 49.68/49.86 tff(10968,plain,
% 49.68/49.86 (~always5(s73)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6788, 10964])).
% 49.68/49.86 tff(10969,plain,
% 49.68/49.86 (xuntil7(s73) | (~until6(s73))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8352, 7273, 10968])).
% 49.68/49.86 tff(10970,plain,
% 49.68/49.86 (~until6(s73)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10969, 10967])).
% 49.68/49.86 tff(10971,plain,
% 49.68/49.86 (~xuntil7(s72)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8345, 10970])).
% 49.68/49.86 tff(10972,plain,
% 49.68/49.86 (~always5(s72)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6796, 10968])).
% 49.68/49.86 tff(10973,plain,
% 49.68/49.86 (xuntil7(s72) | (~until6(s72))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8339, 7273, 10972])).
% 49.68/49.86 tff(10974,plain,
% 49.68/49.86 (~until6(s72)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10973, 10971])).
% 49.68/49.86 tff(10975,plain,
% 49.68/49.86 (~xuntil7(s71)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8332, 10974])).
% 49.68/49.86 tff(10976,plain,
% 49.68/49.86 (~always5(s71)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6804, 10972])).
% 49.68/49.86 tff(10977,plain,
% 49.68/49.86 (xuntil7(s71) | (~until6(s71))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8326, 7273, 10976])).
% 49.68/49.86 tff(10978,plain,
% 49.68/49.86 (~until6(s71)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10977, 10975])).
% 49.68/49.86 tff(10979,plain,
% 49.68/49.86 (~xuntil7(s70)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8319, 10978])).
% 49.68/49.86 tff(10980,plain,
% 49.68/49.86 (~always5(s70)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6812, 10976])).
% 49.68/49.86 tff(10981,plain,
% 49.68/49.86 (xuntil7(s70) | (~until6(s70))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8313, 7273, 10980])).
% 49.68/49.86 tff(10982,plain,
% 49.68/49.86 (~until6(s70)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10981, 10979])).
% 49.68/49.86 tff(10983,plain,
% 49.68/49.86 (~xuntil7(s69)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8306, 10982])).
% 49.68/49.86 tff(10984,plain,
% 49.68/49.86 (~always5(s69)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6820, 10980])).
% 49.68/49.86 tff(10985,plain,
% 49.68/49.86 (xuntil7(s69) | (~until6(s69))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8300, 7273, 10984])).
% 49.68/49.86 tff(10986,plain,
% 49.68/49.86 (~until6(s69)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10985, 10983])).
% 49.68/49.86 tff(10987,plain,
% 49.68/49.86 (~xuntil7(s68)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8293, 10986])).
% 49.68/49.86 tff(10988,plain,
% 49.68/49.86 (~always5(s68)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6828, 10984])).
% 49.68/49.86 tff(10989,plain,
% 49.68/49.86 (xuntil7(s68) | (~until6(s68))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8287, 7273, 10988])).
% 49.68/49.86 tff(10990,plain,
% 49.68/49.86 (~until6(s68)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10989, 10987])).
% 49.68/49.86 tff(10991,plain,
% 49.68/49.86 (~xuntil7(s67)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8280, 10990])).
% 49.68/49.86 tff(10992,plain,
% 49.68/49.86 (~always5(s67)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6836, 10988])).
% 49.68/49.86 tff(10993,plain,
% 49.68/49.86 (xuntil7(s67) | (~until6(s67))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8274, 7273, 10992])).
% 49.68/49.86 tff(10994,plain,
% 49.68/49.86 (~until6(s67)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10993, 10991])).
% 49.68/49.86 tff(10995,plain,
% 49.68/49.86 (~xuntil7(s66)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8267, 10994])).
% 49.68/49.86 tff(10996,plain,
% 49.68/49.86 (~always5(s66)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6844, 10992])).
% 49.68/49.86 tff(10997,plain,
% 49.68/49.86 (xuntil7(s66) | (~until6(s66))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8261, 7273, 10996])).
% 49.68/49.86 tff(10998,plain,
% 49.68/49.86 (~until6(s66)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[10997, 10995])).
% 49.68/49.86 tff(10999,plain,
% 49.68/49.86 (~xuntil7(s65)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8254, 10998])).
% 49.68/49.86 tff(11000,plain,
% 49.68/49.86 (~always5(s65)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6852, 10996])).
% 49.68/49.86 tff(11001,plain,
% 49.68/49.86 (xuntil7(s65) | (~until6(s65))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8248, 7273, 11000])).
% 49.68/49.86 tff(11002,plain,
% 49.68/49.86 (~until6(s65)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11001, 10999])).
% 49.68/49.86 tff(11003,plain,
% 49.68/49.86 (~xuntil7(s64)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8241, 11002])).
% 49.68/49.86 tff(11004,plain,
% 49.68/49.86 (~always5(s64)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6860, 11000])).
% 49.68/49.86 tff(11005,plain,
% 49.68/49.86 (xuntil7(s64) | (~until6(s64))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8235, 7273, 11004])).
% 49.68/49.86 tff(11006,plain,
% 49.68/49.86 (~until6(s64)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11005, 11003])).
% 49.68/49.86 tff(11007,plain,
% 49.68/49.86 (~xuntil7(s63)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8228, 11006])).
% 49.68/49.86 tff(11008,plain,
% 49.68/49.86 (~always5(s63)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6868, 11004])).
% 49.68/49.86 tff(11009,plain,
% 49.68/49.86 (xuntil7(s63) | (~until6(s63))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8222, 7273, 11008])).
% 49.68/49.86 tff(11010,plain,
% 49.68/49.86 (~until6(s63)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11009, 11007])).
% 49.68/49.86 tff(11011,plain,
% 49.68/49.86 (~xuntil7(s62)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8215, 11010])).
% 49.68/49.86 tff(11012,plain,
% 49.68/49.86 (~always5(s62)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6876, 11008])).
% 49.68/49.86 tff(11013,plain,
% 49.68/49.86 (xuntil7(s62) | (~until6(s62))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8209, 7273, 11012])).
% 49.68/49.86 tff(11014,plain,
% 49.68/49.86 (~until6(s62)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11013, 11011])).
% 49.68/49.86 tff(11015,plain,
% 49.68/49.86 (~xuntil7(s61)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8202, 11014])).
% 49.68/49.86 tff(11016,plain,
% 49.68/49.86 (~always5(s61)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6884, 11012])).
% 49.68/49.86 tff(11017,plain,
% 49.68/49.86 (xuntil7(s61) | (~until6(s61))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8196, 7273, 11016])).
% 49.68/49.86 tff(11018,plain,
% 49.68/49.86 (~until6(s61)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11017, 11015])).
% 49.68/49.86 tff(11019,plain,
% 49.68/49.86 (~xuntil7(s60)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8189, 11018])).
% 49.68/49.86 tff(11020,plain,
% 49.68/49.86 (~always5(s60)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6892, 11016])).
% 49.68/49.86 tff(11021,plain,
% 49.68/49.86 (xuntil7(s60) | (~until6(s60))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8183, 7273, 11020])).
% 49.68/49.86 tff(11022,plain,
% 49.68/49.86 (~until6(s60)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11021, 11019])).
% 49.68/49.86 tff(11023,plain,
% 49.68/49.86 (~xuntil7(s59)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8176, 11022])).
% 49.68/49.86 tff(11024,plain,
% 49.68/49.86 (~always5(s59)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6900, 11020])).
% 49.68/49.86 tff(11025,plain,
% 49.68/49.86 (xuntil7(s59) | (~until6(s59))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8170, 7273, 11024])).
% 49.68/49.86 tff(11026,plain,
% 49.68/49.86 (~until6(s59)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11025, 11023])).
% 49.68/49.86 tff(11027,plain,
% 49.68/49.86 (~xuntil7(s58)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8163, 11026])).
% 49.68/49.86 tff(11028,plain,
% 49.68/49.86 (~always5(s58)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6908, 11024])).
% 49.68/49.86 tff(11029,plain,
% 49.68/49.86 (xuntil7(s58) | (~until6(s58))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8157, 7273, 11028])).
% 49.68/49.86 tff(11030,plain,
% 49.68/49.86 (~until6(s58)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11029, 11027])).
% 49.68/49.86 tff(11031,plain,
% 49.68/49.86 (~xuntil7(s57)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8150, 11030])).
% 49.68/49.86 tff(11032,plain,
% 49.68/49.86 (~always5(s57)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6916, 11028])).
% 49.68/49.86 tff(11033,plain,
% 49.68/49.86 (xuntil7(s57) | (~until6(s57))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8144, 7273, 11032])).
% 49.68/49.86 tff(11034,plain,
% 49.68/49.86 (~until6(s57)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11033, 11031])).
% 49.68/49.86 tff(11035,plain,
% 49.68/49.86 (~xuntil7(s56)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8137, 11034])).
% 49.68/49.86 tff(11036,plain,
% 49.68/49.86 (~always5(s56)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6924, 11032])).
% 49.68/49.86 tff(11037,plain,
% 49.68/49.86 (xuntil7(s56) | (~until6(s56))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8131, 7273, 11036])).
% 49.68/49.86 tff(11038,plain,
% 49.68/49.86 (~until6(s56)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11037, 11035])).
% 49.68/49.86 tff(11039,plain,
% 49.68/49.86 (~xuntil7(s55)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8124, 11038])).
% 49.68/49.86 tff(11040,plain,
% 49.68/49.86 (~always5(s55)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6932, 11036])).
% 49.68/49.86 tff(11041,plain,
% 49.68/49.86 (xuntil7(s55) | (~until6(s55))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8118, 7273, 11040])).
% 49.68/49.86 tff(11042,plain,
% 49.68/49.86 (~until6(s55)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11041, 11039])).
% 49.68/49.86 tff(11043,plain,
% 49.68/49.86 (~xuntil7(s54)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8111, 11042])).
% 49.68/49.86 tff(11044,plain,
% 49.68/49.86 (~always5(s54)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6940, 11040])).
% 49.68/49.86 tff(11045,plain,
% 49.68/49.86 (xuntil7(s54) | (~until6(s54))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8105, 7273, 11044])).
% 49.68/49.86 tff(11046,plain,
% 49.68/49.86 (~until6(s54)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11045, 11043])).
% 49.68/49.86 tff(11047,plain,
% 49.68/49.86 (~xuntil7(s53)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8098, 11046])).
% 49.68/49.86 tff(11048,plain,
% 49.68/49.86 (~always5(s53)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6948, 11044])).
% 49.68/49.86 tff(11049,plain,
% 49.68/49.86 (xuntil7(s53) | (~until6(s53))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8092, 7273, 11048])).
% 49.68/49.86 tff(11050,plain,
% 49.68/49.86 (~until6(s53)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11049, 11047])).
% 49.68/49.86 tff(11051,plain,
% 49.68/49.86 (~xuntil7(s52)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8085, 11050])).
% 49.68/49.86 tff(11052,plain,
% 49.68/49.86 (~always5(s52)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6956, 11048])).
% 49.68/49.86 tff(11053,plain,
% 49.68/49.86 (xuntil7(s52) | (~until6(s52))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8079, 7273, 11052])).
% 49.68/49.86 tff(11054,plain,
% 49.68/49.86 (~until6(s52)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11053, 11051])).
% 49.68/49.86 tff(11055,plain,
% 49.68/49.86 (~xuntil7(s51)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8072, 11054])).
% 49.68/49.86 tff(11056,plain,
% 49.68/49.86 (~always5(s51)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6964, 11052])).
% 49.68/49.86 tff(11057,plain,
% 49.68/49.86 (xuntil7(s51) | (~until6(s51))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[8066, 7273, 11056])).
% 49.68/49.86 tff(11058,plain,
% 49.68/49.86 (~until6(s51)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11057, 11055])).
% 49.68/49.86 tff(11059,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[8059, 11058])).
% 49.68/49.86 tff(11060,plain,
% 49.68/49.86 (~always5(s50)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6972, 11056])).
% 49.68/49.86 tff(11061,plain,
% 49.68/49.86 (~always5(s49)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[6980, 11060])).
% 49.68/49.86 tff(11062,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[6988, 11061])).
% 49.68/49.86 tff(11063,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[6996, 11062])).
% 49.68/49.86 tff(11064,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7004, 11063])).
% 49.68/49.86 tff(11065,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7012, 11064])).
% 49.68/49.86 tff(11066,plain,
% 49.68/49.86 (~always5(s44)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7020, 11065])).
% 49.68/49.86 tff(11067,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7028, 11066])).
% 49.68/49.86 tff(11068,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7036, 11067])).
% 49.68/49.86 tff(11069,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7044, 11068])).
% 49.68/49.86 tff(11070,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7052, 11069])).
% 49.68/49.86 tff(11071,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7060, 11070])).
% 49.68/49.86 tff(11072,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7068, 11071])).
% 49.68/49.86 tff(11073,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7076, 11072])).
% 49.68/49.86 tff(11074,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7084, 11073])).
% 49.68/49.86 tff(11075,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7092, 11074])).
% 49.68/49.86 tff(11076,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7100, 11075])).
% 49.68/49.86 tff(11077,plain,
% 49.68/49.86 (~always5(s33)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7108, 11076])).
% 49.68/49.86 tff(11078,plain,
% 49.68/49.86 (~always5(s32)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7116, 11077])).
% 49.68/49.86 tff(11079,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7124, 11078])).
% 49.68/49.86 tff(11080,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7132, 11079])).
% 49.68/49.86 tff(11081,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7140, 11080])).
% 49.68/49.86 tff(11082,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7148, 11081])).
% 49.68/49.86 tff(11083,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7156, 11082])).
% 49.68/49.86 tff(11084,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7164, 11083])).
% 49.68/49.86 tff(11085,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7172, 11084])).
% 49.68/49.86 tff(11086,plain,
% 49.68/49.86 (~always5(s24)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7180, 11085])).
% 49.68/49.86 tff(11087,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7188, 11086])).
% 49.68/49.86 tff(11088,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7196, 11087])).
% 49.68/49.86 tff(11089,plain,
% 49.68/49.86 (~always5(s21)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7204, 11088])).
% 49.68/49.86 tff(11090,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7212, 11089])).
% 49.68/49.86 tff(11091,plain,
% 49.68/49.86 (~always5(s19)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7220, 11090])).
% 49.68/49.86 tff(11092,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7228, 11091])).
% 49.68/49.86 tff(11093,plain,
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% 49.68/49.86 inference(unit_resolution,[status(thm)],[7236, 11092])).
% 49.68/49.86 tff(11094,plain,
% 49.68/49.86 (~always5(s16)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7244, 11093])).
% 49.68/49.86 tff(11095,plain,
% 49.68/49.86 (~always5(s15)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7252, 11094])).
% 49.68/49.86 tff(11096,plain,
% 49.68/49.86 (~always5(s14)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7261, 11095])).
% 49.68/49.86 tff(11097,plain,
% 49.68/49.86 (~always5(s13)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7315, 11096])).
% 49.68/49.86 tff(11098,plain,
% 49.68/49.86 (~always5(s12)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7336, 11097])).
% 49.68/49.86 tff(11099,plain,
% 49.68/49.86 (~always5(s11)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7357, 11098])).
% 49.68/49.86 tff(11100,plain,
% 49.68/49.86 (~always5(s10)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7378, 11099])).
% 49.68/49.86 tff(11101,plain,
% 49.68/49.86 (~always5(s9)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7399, 11100])).
% 49.68/49.86 tff(11102,plain,
% 49.68/49.86 (~always5(s8)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7420, 11101])).
% 49.68/49.86 tff(11103,plain,
% 49.68/49.86 (~always5(s7)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7436, 11102])).
% 49.68/49.86 tff(11104,plain,
% 49.68/49.86 (~always5(s6)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7444, 11103])).
% 49.68/49.86 tff(11105,plain,
% 49.68/49.86 (~always5(s5)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7452, 11104])).
% 49.68/49.86 tff(11106,plain,
% 49.68/49.86 (~always5(s4)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7460, 11105])).
% 49.68/49.86 tff(11107,plain,
% 49.68/49.86 (~always5(s3)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7468, 11106])).
% 49.68/49.86 tff(11108,plain,
% 49.68/49.86 (~always5(s2)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7476, 11107])).
% 49.68/49.86 tff(11109,plain,
% 49.68/49.86 (~always5(s1)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7484, 11108])).
% 49.68/49.86 tff(11110,plain,
% 49.68/49.86 (~always5(s0)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7492, 11109])).
% 49.68/49.86 tff(11111,plain,
% 49.68/49.86 (xuntil7(s0)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7503, 11110])).
% 49.68/49.86 tff(11112,plain,
% 49.68/49.86 (until6(s1)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7508, 11111])).
% 49.68/49.86 tff(11113,plain,
% 49.68/49.86 (xuntil7(s1)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7515, 7273, 11112, 11109])).
% 49.68/49.86 tff(11114,plain,
% 49.68/49.86 (until6(s2)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7520, 11113])).
% 49.68/49.86 tff(11115,plain,
% 49.68/49.86 (xuntil7(s2) | (~until6(s2))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7527, 7273, 11108])).
% 49.68/49.86 tff(11116,plain,
% 49.68/49.86 (xuntil7(s2)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11115, 11114])).
% 49.68/49.86 tff(11117,plain,
% 49.68/49.86 (until6(s3)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7533, 11116])).
% 49.68/49.86 tff(11118,plain,
% 49.68/49.86 (xuntil7(s3) | (~until6(s3))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7540, 7273, 11107])).
% 49.68/49.86 tff(11119,plain,
% 49.68/49.86 (xuntil7(s3)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11118, 11117])).
% 49.68/49.86 tff(11120,plain,
% 49.68/49.86 (until6(s4)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7546, 11119])).
% 49.68/49.86 tff(11121,plain,
% 49.68/49.86 (xuntil7(s4) | (~until6(s4))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7553, 7273, 11106])).
% 49.68/49.86 tff(11122,plain,
% 49.68/49.86 (xuntil7(s4)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11121, 11120])).
% 49.68/49.86 tff(11123,plain,
% 49.68/49.86 (until6(s5)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7559, 11122])).
% 49.68/49.86 tff(11124,plain,
% 49.68/49.86 (xuntil7(s5) | (~until6(s5))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7566, 7273, 11105])).
% 49.68/49.86 tff(11125,plain,
% 49.68/49.86 (xuntil7(s5)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11124, 11123])).
% 49.68/49.86 tff(11126,plain,
% 49.68/49.86 (until6(s6)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7572, 11125])).
% 49.68/49.86 tff(11127,plain,
% 49.68/49.86 (xuntil7(s6) | (~until6(s6))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7579, 7273, 11104])).
% 49.68/49.86 tff(11128,plain,
% 49.68/49.86 (xuntil7(s6)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11127, 11126])).
% 49.68/49.86 tff(11129,plain,
% 49.68/49.86 (until6(s7)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7585, 11128])).
% 49.68/49.86 tff(11130,plain,
% 49.68/49.86 (xuntil7(s7) | (~until6(s7))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7592, 7273, 11103])).
% 49.68/49.86 tff(11131,plain,
% 49.68/49.86 (xuntil7(s7)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11130, 11129])).
% 49.68/49.86 tff(11132,plain,
% 49.68/49.86 (until6(s8)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7598, 11131])).
% 49.68/49.86 tff(11133,plain,
% 49.68/49.86 (xuntil7(s8) | (~until6(s8))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7427, 7273, 11102])).
% 49.68/49.86 tff(11134,plain,
% 49.68/49.86 (xuntil7(s8)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11133, 11132])).
% 49.68/49.86 tff(11135,plain,
% 49.68/49.86 (until6(s9)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7412, 11134])).
% 49.68/49.86 tff(11136,plain,
% 49.68/49.86 (xuntil7(s9) | (~until6(s9))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7406, 7273, 11101])).
% 49.68/49.86 tff(11137,plain,
% 49.68/49.86 (xuntil7(s9)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11136, 11135])).
% 49.68/49.86 tff(11138,plain,
% 49.68/49.86 (until6(s10)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7391, 11137])).
% 49.68/49.86 tff(11139,plain,
% 49.68/49.86 (xuntil7(s10) | (~until6(s10))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7385, 7273, 11100])).
% 49.68/49.86 tff(11140,plain,
% 49.68/49.86 (xuntil7(s10)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11139, 11138])).
% 49.68/49.86 tff(11141,plain,
% 49.68/49.86 (until6(s11)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7370, 11140])).
% 49.68/49.86 tff(11142,plain,
% 49.68/49.86 (xuntil7(s11) | (~until6(s11))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7364, 7273, 11099])).
% 49.68/49.86 tff(11143,plain,
% 49.68/49.86 (xuntil7(s11)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11142, 11141])).
% 49.68/49.86 tff(11144,plain,
% 49.68/49.86 (until6(s12)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7349, 11143])).
% 49.68/49.86 tff(11145,plain,
% 49.68/49.86 (xuntil7(s12) | (~until6(s12))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7343, 7273, 11098])).
% 49.68/49.86 tff(11146,plain,
% 49.68/49.86 (xuntil7(s12)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11145, 11144])).
% 49.68/49.86 tff(11147,plain,
% 49.68/49.86 (until6(s13)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7328, 11146])).
% 49.68/49.86 tff(11148,plain,
% 49.68/49.86 (xuntil7(s13) | (~until6(s13))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7322, 7273, 11097])).
% 49.68/49.86 tff(11149,plain,
% 49.68/49.86 (xuntil7(s13)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11148, 11147])).
% 49.68/49.86 tff(11150,plain,
% 49.68/49.86 (until6(s14)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7307, 11149])).
% 49.68/49.86 tff(11151,plain,
% 49.68/49.86 (xuntil7(s14) | (~until6(s14))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7302, 7273, 11096])).
% 49.68/49.86 tff(11152,plain,
% 49.68/49.86 (xuntil7(s14)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11151, 11150])).
% 49.68/49.86 tff(11153,plain,
% 49.68/49.86 (until6(s15)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7295, 11152])).
% 49.68/49.86 tff(11154,plain,
% 49.68/49.86 (xuntil7(s15) | (~until6(s15))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7279, 7273, 11095])).
% 49.68/49.86 tff(11155,plain,
% 49.68/49.86 (xuntil7(s15)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11154, 11153])).
% 49.68/49.86 tff(11156,plain,
% 49.68/49.86 (until6(s16)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7605, 11155])).
% 49.68/49.86 tff(11157,plain,
% 49.68/49.86 (xuntil7(s16) | (~until6(s16))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7612, 7273, 11094])).
% 49.68/49.86 tff(11158,plain,
% 49.68/49.86 (xuntil7(s16)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11157, 11156])).
% 49.68/49.86 tff(11159,plain,
% 49.68/49.86 (until6(s17)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7617, 11158])).
% 49.68/49.86 tff(11160,plain,
% 49.68/49.86 (xuntil7(s17) | (~until6(s17))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7624, 7273, 11093])).
% 49.68/49.86 tff(11161,plain,
% 49.68/49.86 (xuntil7(s17)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11160, 11159])).
% 49.68/49.86 tff(11162,plain,
% 49.68/49.86 (until6(s18)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7630, 11161])).
% 49.68/49.86 tff(11163,plain,
% 49.68/49.86 (xuntil7(s18) | (~until6(s18))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7637, 7273, 11092])).
% 49.68/49.86 tff(11164,plain,
% 49.68/49.86 (xuntil7(s18)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11163, 11162])).
% 49.68/49.86 tff(11165,plain,
% 49.68/49.86 (until6(s19)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7643, 11164])).
% 49.68/49.86 tff(11166,plain,
% 49.68/49.86 (xuntil7(s19) | (~until6(s19))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7650, 7273, 11091])).
% 49.68/49.86 tff(11167,plain,
% 49.68/49.86 (xuntil7(s19)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11166, 11165])).
% 49.68/49.86 tff(11168,plain,
% 49.68/49.86 (until6(s20)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7656, 11167])).
% 49.68/49.86 tff(11169,plain,
% 49.68/49.86 (xuntil7(s20) | (~until6(s20))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7663, 7273, 11090])).
% 49.68/49.86 tff(11170,plain,
% 49.68/49.86 (xuntil7(s20)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11169, 11168])).
% 49.68/49.86 tff(11171,plain,
% 49.68/49.86 (until6(s21)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7669, 11170])).
% 49.68/49.86 tff(11172,plain,
% 49.68/49.86 (xuntil7(s21) | (~until6(s21))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7676, 7273, 11089])).
% 49.68/49.86 tff(11173,plain,
% 49.68/49.86 (xuntil7(s21)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11172, 11171])).
% 49.68/49.86 tff(11174,plain,
% 49.68/49.86 (until6(s22)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7682, 11173])).
% 49.68/49.86 tff(11175,plain,
% 49.68/49.86 (xuntil7(s22) | (~until6(s22))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7689, 7273, 11088])).
% 49.68/49.86 tff(11176,plain,
% 49.68/49.86 (xuntil7(s22)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11175, 11174])).
% 49.68/49.86 tff(11177,plain,
% 49.68/49.86 (until6(s23)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7695, 11176])).
% 49.68/49.86 tff(11178,plain,
% 49.68/49.86 (xuntil7(s23) | (~until6(s23))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7702, 7273, 11087])).
% 49.68/49.86 tff(11179,plain,
% 49.68/49.86 (xuntil7(s23)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11178, 11177])).
% 49.68/49.86 tff(11180,plain,
% 49.68/49.86 (until6(s24)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7708, 11179])).
% 49.68/49.86 tff(11181,plain,
% 49.68/49.86 (xuntil7(s24) | (~until6(s24))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7715, 7273, 11086])).
% 49.68/49.86 tff(11182,plain,
% 49.68/49.86 (xuntil7(s24)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11181, 11180])).
% 49.68/49.86 tff(11183,plain,
% 49.68/49.86 (until6(s25)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7721, 11182])).
% 49.68/49.86 tff(11184,plain,
% 49.68/49.86 (xuntil7(s25) | (~until6(s25))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7728, 7273, 11085])).
% 49.68/49.86 tff(11185,plain,
% 49.68/49.86 (xuntil7(s25)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11184, 11183])).
% 49.68/49.86 tff(11186,plain,
% 49.68/49.86 (until6(s26)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7734, 11185])).
% 49.68/49.86 tff(11187,plain,
% 49.68/49.86 (xuntil7(s26) | (~until6(s26))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7741, 7273, 11084])).
% 49.68/49.86 tff(11188,plain,
% 49.68/49.86 (xuntil7(s26)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11187, 11186])).
% 49.68/49.86 tff(11189,plain,
% 49.68/49.86 (until6(s27)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7747, 11188])).
% 49.68/49.86 tff(11190,plain,
% 49.68/49.86 (xuntil7(s27) | (~until6(s27))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7754, 7273, 11083])).
% 49.68/49.86 tff(11191,plain,
% 49.68/49.86 (xuntil7(s27)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11190, 11189])).
% 49.68/49.86 tff(11192,plain,
% 49.68/49.86 (until6(s28)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7760, 11191])).
% 49.68/49.86 tff(11193,plain,
% 49.68/49.86 (xuntil7(s28) | (~until6(s28))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7767, 7273, 11082])).
% 49.68/49.86 tff(11194,plain,
% 49.68/49.86 (xuntil7(s28)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11193, 11192])).
% 49.68/49.86 tff(11195,plain,
% 49.68/49.86 (until6(s29)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7773, 11194])).
% 49.68/49.86 tff(11196,plain,
% 49.68/49.86 (xuntil7(s29) | (~until6(s29))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7780, 7273, 11081])).
% 49.68/49.86 tff(11197,plain,
% 49.68/49.86 (xuntil7(s29)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11196, 11195])).
% 49.68/49.86 tff(11198,plain,
% 49.68/49.86 (until6(s30)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7786, 11197])).
% 49.68/49.86 tff(11199,plain,
% 49.68/49.86 (xuntil7(s30) | (~until6(s30))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7793, 7273, 11080])).
% 49.68/49.86 tff(11200,plain,
% 49.68/49.86 (xuntil7(s30)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11199, 11198])).
% 49.68/49.86 tff(11201,plain,
% 49.68/49.86 (until6(s31)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7799, 11200])).
% 49.68/49.86 tff(11202,plain,
% 49.68/49.86 (xuntil7(s31) | (~until6(s31))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7806, 7273, 11079])).
% 49.68/49.86 tff(11203,plain,
% 49.68/49.86 (xuntil7(s31)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11202, 11201])).
% 49.68/49.86 tff(11204,plain,
% 49.68/49.86 (until6(s32)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7812, 11203])).
% 49.68/49.86 tff(11205,plain,
% 49.68/49.86 (xuntil7(s32) | (~until6(s32))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7819, 7273, 11078])).
% 49.68/49.86 tff(11206,plain,
% 49.68/49.86 (xuntil7(s32)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11205, 11204])).
% 49.68/49.86 tff(11207,plain,
% 49.68/49.86 (until6(s33)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7825, 11206])).
% 49.68/49.86 tff(11208,plain,
% 49.68/49.86 (xuntil7(s33) | (~until6(s33))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7832, 7273, 11077])).
% 49.68/49.86 tff(11209,plain,
% 49.68/49.86 (xuntil7(s33)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11208, 11207])).
% 49.68/49.86 tff(11210,plain,
% 49.68/49.86 (until6(s34)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7838, 11209])).
% 49.68/49.86 tff(11211,plain,
% 49.68/49.86 (xuntil7(s34) | (~until6(s34))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7845, 7273, 11076])).
% 49.68/49.86 tff(11212,plain,
% 49.68/49.86 (xuntil7(s34)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11211, 11210])).
% 49.68/49.86 tff(11213,plain,
% 49.68/49.86 (until6(s35)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7851, 11212])).
% 49.68/49.86 tff(11214,plain,
% 49.68/49.86 (xuntil7(s35) | (~until6(s35))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7858, 7273, 11075])).
% 49.68/49.86 tff(11215,plain,
% 49.68/49.86 (xuntil7(s35)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11214, 11213])).
% 49.68/49.86 tff(11216,plain,
% 49.68/49.86 (until6(s36)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7864, 11215])).
% 49.68/49.86 tff(11217,plain,
% 49.68/49.86 (xuntil7(s36) | (~until6(s36))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7871, 7273, 11074])).
% 49.68/49.86 tff(11218,plain,
% 49.68/49.86 (xuntil7(s36)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11217, 11216])).
% 49.68/49.86 tff(11219,plain,
% 49.68/49.86 (until6(s37)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7877, 11218])).
% 49.68/49.86 tff(11220,plain,
% 49.68/49.86 (xuntil7(s37) | (~until6(s37))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7884, 7273, 11073])).
% 49.68/49.86 tff(11221,plain,
% 49.68/49.86 (xuntil7(s37)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11220, 11219])).
% 49.68/49.86 tff(11222,plain,
% 49.68/49.86 (until6(s38)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7890, 11221])).
% 49.68/49.86 tff(11223,plain,
% 49.68/49.86 (xuntil7(s38) | (~until6(s38))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7897, 7273, 11072])).
% 49.68/49.86 tff(11224,plain,
% 49.68/49.86 (xuntil7(s38)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11223, 11222])).
% 49.68/49.86 tff(11225,plain,
% 49.68/49.86 (until6(s39)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7903, 11224])).
% 49.68/49.86 tff(11226,plain,
% 49.68/49.86 (xuntil7(s39) | (~until6(s39))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7910, 7273, 11071])).
% 49.68/49.86 tff(11227,plain,
% 49.68/49.86 (xuntil7(s39)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11226, 11225])).
% 49.68/49.86 tff(11228,plain,
% 49.68/49.86 (until6(s40)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7916, 11227])).
% 49.68/49.86 tff(11229,plain,
% 49.68/49.86 (xuntil7(s40) | (~until6(s40))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7923, 7273, 11070])).
% 49.68/49.86 tff(11230,plain,
% 49.68/49.86 (xuntil7(s40)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11229, 11228])).
% 49.68/49.86 tff(11231,plain,
% 49.68/49.86 (until6(s41)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7929, 11230])).
% 49.68/49.86 tff(11232,plain,
% 49.68/49.86 (xuntil7(s41) | (~until6(s41))),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[7936, 7273, 11069])).
% 49.68/49.86 tff(11233,plain,
% 49.68/49.86 (xuntil7(s41)),
% 49.68/49.86 inference(unit_resolution,[status(thm)],[11232, 11231])).
% 49.68/49.86 tff(11234,plain,
% 49.68/49.87 (until6(s42)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7942, 11233])).
% 49.68/49.87 tff(11235,plain,
% 49.68/49.87 (xuntil7(s42) | (~until6(s42))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7949, 7273, 11068])).
% 49.68/49.87 tff(11236,plain,
% 49.68/49.87 (xuntil7(s42)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11235, 11234])).
% 49.68/49.87 tff(11237,plain,
% 49.68/49.87 (until6(s43)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7955, 11236])).
% 49.68/49.87 tff(11238,plain,
% 49.68/49.87 (xuntil7(s43) | (~until6(s43))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7962, 7273, 11067])).
% 49.68/49.87 tff(11239,plain,
% 49.68/49.87 (xuntil7(s43)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11238, 11237])).
% 49.68/49.87 tff(11240,plain,
% 49.68/49.87 (until6(s44)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7968, 11239])).
% 49.68/49.87 tff(11241,plain,
% 49.68/49.87 (xuntil7(s44) | (~until6(s44))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7975, 7273, 11066])).
% 49.68/49.87 tff(11242,plain,
% 49.68/49.87 (xuntil7(s44)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11241, 11240])).
% 49.68/49.87 tff(11243,plain,
% 49.68/49.87 (until6(s45)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7981, 11242])).
% 49.68/49.87 tff(11244,plain,
% 49.68/49.87 (xuntil7(s45) | (~until6(s45))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7988, 7273, 11065])).
% 49.68/49.87 tff(11245,plain,
% 49.68/49.87 (xuntil7(s45)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11244, 11243])).
% 49.68/49.87 tff(11246,plain,
% 49.68/49.87 (until6(s46)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[7994, 11245])).
% 49.68/49.87 tff(11247,plain,
% 49.68/49.87 (xuntil7(s46) | (~until6(s46))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8001, 7273, 11064])).
% 49.68/49.87 tff(11248,plain,
% 49.68/49.87 (xuntil7(s46)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11247, 11246])).
% 49.68/49.87 tff(11249,plain,
% 49.68/49.87 (until6(s47)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8007, 11248])).
% 49.68/49.87 tff(11250,plain,
% 49.68/49.87 (xuntil7(s47) | (~until6(s47))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8014, 7273, 11063])).
% 49.68/49.87 tff(11251,plain,
% 49.68/49.87 (xuntil7(s47)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11250, 11249])).
% 49.68/49.87 tff(11252,plain,
% 49.68/49.87 (until6(s48)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8020, 11251])).
% 49.68/49.87 tff(11253,plain,
% 49.68/49.87 (xuntil7(s48) | (~until6(s48))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8027, 7273, 11062])).
% 49.68/49.87 tff(11254,plain,
% 49.68/49.87 (xuntil7(s48)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11253, 11252])).
% 49.68/49.87 tff(11255,plain,
% 49.68/49.87 (until6(s49)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8033, 11254])).
% 49.68/49.87 tff(11256,plain,
% 49.68/49.87 (xuntil7(s49) | (~until6(s49))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8040, 7273, 11061])).
% 49.68/49.87 tff(11257,plain,
% 49.68/49.87 (xuntil7(s49)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11256, 11255])).
% 49.68/49.87 tff(11258,plain,
% 49.68/49.87 (until6(s50)),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8046, 11257])).
% 49.68/49.87 tff(11259,plain,
% 49.68/49.87 (xuntil7(s50) | (~until6(s50))),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[8053, 7273, 11060])).
% 49.68/49.87 tff(11260,plain,
% 49.68/49.87 ($false),
% 49.68/49.87 inference(unit_resolution,[status(thm)],[11259, 11258, 11059])).
% 49.68/49.87 tff(11261,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 49.68/49.87 tff(11262,plain,
% 49.68/49.87 (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 49.68/49.87 inference(rewrite,[status(thm)],[])).
% 49.68/49.87 tff(11263,plain,
% 49.68/49.87 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 49.68/49.87 inference(rewrite,[status(thm)],[])).
% 49.68/49.87 tff(11264,plain,
% 49.68/49.87 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 49.68/49.88 inference(rewrite,[status(thm)],[])).
% 49.68/49.88 tff(11265,plain,
% 49.68/49.88 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 49.68/49.88 inference(rewrite,[status(thm)],[])).
% 49.68/49.88 tff(11266,plain,
% 49.68/49.88 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 49.68/49.88 inference(rewrite,[status(thm)],[])).
% 49.68/49.88 tff(11267,plain,
% 49.68/49.88 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 49.68/49.89 inference(rewrite,[status(thm)],[])).
% 49.68/49.89 tff(11268,plain,
% 49.68/49.89 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 49.68/49.89 inference(rewrite,[status(thm)],[])).
% 49.68/49.89 tff(11269,plain,
% 49.68/49.89 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 49.68/49.89 inference(rewrite,[status(thm)],[])).
% 49.68/49.89 tff(11270,plain,
% 49.68/49.89 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 49.68/49.90 inference(rewrite,[status(thm)],[])).
% 49.68/49.90 tff(11271,plain,
% 49.68/49.90 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 49.68/49.90 inference(rewrite,[status(thm)],[])).
% 49.68/49.90 tff(11272,plain,
% 49.68/49.90 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 49.68/49.90 inference(rewrite,[status(thm)],[])).
% 49.68/49.90 tff(11273,plain,
% 49.68/49.90 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 49.68/49.90 inference(rewrite,[status(thm)],[])).
% 49.68/49.90 tff(11274,plain,
% 49.68/49.90 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 49.68/49.91 inference(rewrite,[status(thm)],[])).
% 49.68/49.91 tff(11275,plain,
% 49.68/49.91 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 49.68/49.91 inference(rewrite,[status(thm)],[])).
% 49.68/49.91 tff(11276,plain,
% 49.68/49.91 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 49.68/49.91 inference(rewrite,[status(thm)],[])).
% 49.68/49.91 tff(11277,plain,
% 49.68/49.91 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 49.68/49.91 inference(rewrite,[status(thm)],[])).
% 49.68/49.91 tff(11278,plain,
% 49.68/49.91 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 49.68/49.92 inference(rewrite,[status(thm)],[])).
% 49.68/49.92 tff(11279,plain,
% 49.68/49.92 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 49.68/49.92 inference(rewrite,[status(thm)],[])).
% 49.68/49.92 tff(11280,plain,
% 49.68/49.92 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 49.68/49.92 inference(rewrite,[status(thm)],[])).
% 49.68/49.92 tff(11281,plain,
% 49.68/49.92 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 49.68/49.92 inference(rewrite,[status(thm)],[])).
% 49.68/49.92 tff(11282,plain,
% 49.68/49.92 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 49.68/49.93 inference(rewrite,[status(thm)],[])).
% 49.68/49.93 tff(11283,plain,
% 49.68/49.93 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 49.68/49.93 inference(rewrite,[status(thm)],[])).
% 49.68/49.93 tff(11284,plain,
% 49.68/49.93 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 49.68/49.93 inference(rewrite,[status(thm)],[])).
% 49.68/49.93 tff(11285,plain,
% 49.68/49.93 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 49.68/49.93 inference(rewrite,[status(thm)],[])).
% 49.68/49.93 tff(11286,plain,
% 49.68/49.93 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 49.68/49.94 inference(rewrite,[status(thm)],[])).
% 49.68/49.94 tff(11287,plain,
% 49.68/49.94 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 49.68/49.94 inference(rewrite,[status(thm)],[])).
% 49.68/49.94 tff(11288,plain,
% 49.68/49.94 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 49.68/49.94 inference(rewrite,[status(thm)],[])).
% 49.68/49.94 tff(11289,plain,
% 49.68/49.94 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 49.68/49.94 inference(rewrite,[status(thm)],[])).
% 49.68/49.94 tff(11290,plain,
% 49.68/49.94 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 49.78/49.95 inference(rewrite,[status(thm)],[])).
% 49.78/49.95 tff(11291,plain,
% 49.78/49.95 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 49.78/49.95 inference(rewrite,[status(thm)],[])).
% 49.78/49.95 tff(11292,plain,
% 49.78/49.95 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 49.78/49.95 inference(rewrite,[status(thm)],[])).
% 49.78/49.95 tff(11293,plain,
% 49.78/49.95 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 49.78/49.95 inference(rewrite,[status(thm)],[])).
% 49.78/49.95 tff(11294,plain,
% 49.78/49.95 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 49.78/49.95 inference(rewrite,[status(thm)],[])).
% 49.78/49.95 tff(11295,plain,
% 49.78/49.95 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 49.78/49.96 inference(rewrite,[status(thm)],[])).
% 49.78/49.96 tff(11296,plain,
% 49.78/49.96 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 49.78/49.96 inference(rewrite,[status(thm)],[])).
% 49.78/49.96 tff(11297,plain,
% 49.78/49.96 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 49.78/49.96 inference(rewrite,[status(thm)],[])).
% 49.78/49.96 tff(11298,plain,
% 49.78/49.96 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 49.78/49.96 inference(rewrite,[status(thm)],[])).
% 49.78/49.96 tff(11299,plain,
% 49.78/49.96 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 49.78/49.96 inference(rewrite,[status(thm)],[])).
% 49.78/49.96 tff(11300,plain,
% 49.78/49.96 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11301,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11302,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11303,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11304,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11305,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 49.78/49.97 inference(rewrite,[status(thm)],[])).
% 49.78/49.97 tff(11306,plain,
% 49.78/49.97 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11307,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11308,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11309,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11310,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11311,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 49.78/49.98 inference(rewrite,[status(thm)],[])).
% 49.78/49.98 tff(11312,plain,
% 49.78/49.98 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11313,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11314,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11315,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11316,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11317,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 49.78/49.99 inference(rewrite,[status(thm)],[])).
% 49.78/49.99 tff(11318,plain,
% 49.78/49.99 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11319,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11320,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11321,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11322,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11323,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11324,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11325,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 49.78/50.00 inference(rewrite,[status(thm)],[])).
% 49.78/50.00 tff(11326,plain,
% 49.78/50.00 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 49.78/50.01 inference(rewrite,[status(thm)],[])).
% 49.78/50.01 tff(11327,plain,
% 49.78/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 49.78/50.01 inference(rewrite,[status(thm)],[])).
% 49.78/50.01 tff(11328,plain,
% 49.78/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 49.78/50.01 inference(rewrite,[status(thm)],[])).
% 49.78/50.01 tff(11329,plain,
% 49.78/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 49.78/50.01 inference(rewrite,[status(thm)],[])).
% 49.78/50.01 tff(11330,plain,
% 49.78/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11331,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11332,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11333,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11334,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11335,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11336,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 49.85/50.01 inference(rewrite,[status(thm)],[])).
% 49.85/50.01 tff(11337,plain,
% 49.85/50.01 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11338,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11339,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11340,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11341,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11342,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11343,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11344,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11345,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11346,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11347,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11348,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11349,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11350,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11351,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11352,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11353,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11354,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11355,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11356,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11357,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11358,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11359,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11360,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11361,plain,
% 49.85/50.02 ((((~loop) | trans(s99, s0)) | trans(s99, s1)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1))),
% 49.85/50.02 inference(rewrite,[status(thm)],[])).
% 49.85/50.02 tff(11362,plain,
% 49.85/50.02 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2))),
% 49.85/50.02 inference(monotonicity,[status(thm)],[11361])).
% 49.85/50.02 tff(11363,plain,
% 49.85/50.02 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 49.85/50.02 inference(transitivity,[status(thm)],[11362, 11360])).
% 49.85/50.02 tff(11364,plain,
% 49.85/50.02 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3))),
% 49.85/50.02 inference(monotonicity,[status(thm)],[11363])).
% 49.85/50.02 tff(11365,plain,
% 49.85/50.02 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 49.85/50.02 inference(transitivity,[status(thm)],[11364, 11359])).
% 49.85/50.02 tff(11366,plain,
% 49.85/50.02 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11365])).
% 49.85/50.03 tff(11367,plain,
% 49.85/50.03 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11366, 11358])).
% 49.85/50.03 tff(11368,plain,
% 49.85/50.03 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11367])).
% 49.85/50.03 tff(11369,plain,
% 49.85/50.03 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11368, 11357])).
% 49.85/50.03 tff(11370,plain,
% 49.85/50.03 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11369])).
% 49.85/50.03 tff(11371,plain,
% 49.85/50.03 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11370, 11356])).
% 49.85/50.03 tff(11372,plain,
% 49.85/50.03 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11371])).
% 49.85/50.03 tff(11373,plain,
% 49.85/50.03 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11372, 11355])).
% 49.85/50.03 tff(11374,plain,
% 49.85/50.03 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11373])).
% 49.85/50.03 tff(11375,plain,
% 49.85/50.03 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11374, 11354])).
% 49.85/50.03 tff(11376,plain,
% 49.85/50.03 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11375])).
% 49.85/50.03 tff(11377,plain,
% 49.85/50.03 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11376, 11353])).
% 49.85/50.03 tff(11378,plain,
% 49.85/50.03 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11377])).
% 49.85/50.03 tff(11379,plain,
% 49.85/50.03 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11378, 11352])).
% 49.85/50.03 tff(11380,plain,
% 49.85/50.03 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11379])).
% 49.85/50.03 tff(11381,plain,
% 49.85/50.03 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11380, 11351])).
% 49.85/50.03 tff(11382,plain,
% 49.85/50.03 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11381])).
% 49.85/50.03 tff(11383,plain,
% 49.85/50.03 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11382, 11350])).
% 49.85/50.03 tff(11384,plain,
% 49.85/50.03 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11383])).
% 49.85/50.03 tff(11385,plain,
% 49.85/50.03 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11384, 11349])).
% 49.85/50.03 tff(11386,plain,
% 49.85/50.03 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11385])).
% 49.85/50.03 tff(11387,plain,
% 49.85/50.03 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11386, 11348])).
% 49.85/50.03 tff(11388,plain,
% 49.85/50.03 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11387])).
% 49.85/50.03 tff(11389,plain,
% 49.85/50.03 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11388, 11347])).
% 49.85/50.03 tff(11390,plain,
% 49.85/50.03 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16))),
% 49.85/50.03 inference(monotonicity,[status(thm)],[11389])).
% 49.85/50.03 tff(11391,plain,
% 49.85/50.03 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 49.85/50.03 inference(transitivity,[status(thm)],[11390, 11346])).
% 49.85/50.03 tff(11392,plain,
% 49.85/50.03 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11391])).
% 49.85/50.04 tff(11393,plain,
% 49.85/50.04 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11392, 11345])).
% 49.85/50.04 tff(11394,plain,
% 49.85/50.04 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11393])).
% 49.85/50.04 tff(11395,plain,
% 49.85/50.04 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11394, 11344])).
% 49.85/50.04 tff(11396,plain,
% 49.85/50.04 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11395])).
% 49.85/50.04 tff(11397,plain,
% 49.85/50.04 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11396, 11343])).
% 49.85/50.04 tff(11398,plain,
% 49.85/50.04 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11397])).
% 49.85/50.04 tff(11399,plain,
% 49.85/50.04 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11398, 11342])).
% 49.85/50.04 tff(11400,plain,
% 49.85/50.04 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11399])).
% 49.85/50.04 tff(11401,plain,
% 49.85/50.04 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11400, 11341])).
% 49.85/50.04 tff(11402,plain,
% 49.85/50.04 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11401])).
% 49.85/50.04 tff(11403,plain,
% 49.85/50.04 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11402, 11340])).
% 49.85/50.04 tff(11404,plain,
% 49.85/50.04 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23))),
% 49.85/50.04 inference(monotonicity,[status(thm)],[11403])).
% 49.85/50.04 tff(11405,plain,
% 49.85/50.04 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 49.85/50.04 inference(transitivity,[status(thm)],[11404, 11339])).
% 49.85/50.04 tff(11406,plain,
% 49.85/50.04 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11405])).
% 49.85/50.05 tff(11407,plain,
% 49.85/50.05 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 49.85/50.05 inference(transitivity,[status(thm)],[11406, 11338])).
% 49.85/50.05 tff(11408,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11407])).
% 49.85/50.05 tff(11409,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 49.85/50.05 inference(transitivity,[status(thm)],[11408, 11337])).
% 49.85/50.05 tff(11410,plain,
% 49.85/50.05 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11409])).
% 49.85/50.05 tff(11411,plain,
% 49.85/50.05 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 49.85/50.05 inference(transitivity,[status(thm)],[11410, 11336])).
% 49.85/50.05 tff(11412,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11411])).
% 49.85/50.05 tff(11413,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 49.85/50.05 inference(transitivity,[status(thm)],[11412, 11335])).
% 49.85/50.05 tff(11414,plain,
% 49.85/50.05 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11413])).
% 49.85/50.05 tff(11415,plain,
% 49.85/50.05 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 49.85/50.05 inference(transitivity,[status(thm)],[11414, 11334])).
% 49.85/50.05 tff(11416,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29))),
% 49.85/50.05 inference(monotonicity,[status(thm)],[11415])).
% 49.85/50.05 tff(11417,plain,
% 49.85/50.05 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 49.85/50.06 inference(transitivity,[status(thm)],[11416, 11333])).
% 49.85/50.06 tff(11418,plain,
% 49.85/50.06 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30))),
% 49.85/50.06 inference(monotonicity,[status(thm)],[11417])).
% 49.85/50.06 tff(11419,plain,
% 49.85/50.06 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 49.85/50.06 inference(transitivity,[status(thm)],[11418, 11332])).
% 49.85/50.06 tff(11420,plain,
% 49.85/50.06 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31))),
% 49.85/50.06 inference(monotonicity,[status(thm)],[11419])).
% 49.85/50.06 tff(11421,plain,
% 49.85/50.06 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 49.85/50.06 inference(transitivity,[status(thm)],[11420, 11331])).
% 49.85/50.06 tff(11422,plain,
% 49.85/50.06 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32))),
% 49.85/50.06 inference(monotonicity,[status(thm)],[11421])).
% 49.85/50.06 tff(11423,plain,
% 49.85/50.06 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 49.90/50.06 inference(transitivity,[status(thm)],[11422, 11330])).
% 49.90/50.06 tff(11424,plain,
% 49.90/50.06 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33))),
% 49.90/50.06 inference(monotonicity,[status(thm)],[11423])).
% 49.90/50.06 tff(11425,plain,
% 49.90/50.06 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 49.90/50.06 inference(transitivity,[status(thm)],[11424, 11329])).
% 49.90/50.06 tff(11426,plain,
% 49.90/50.06 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34))),
% 49.90/50.07 inference(monotonicity,[status(thm)],[11425])).
% 49.90/50.07 tff(11427,plain,
% 49.90/50.07 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 49.90/50.07 inference(transitivity,[status(thm)],[11426, 11328])).
% 49.90/50.07 tff(11428,plain,
% 49.90/50.07 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35))),
% 49.90/50.07 inference(monotonicity,[status(thm)],[11427])).
% 49.90/50.07 tff(11429,plain,
% 49.90/50.07 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 49.90/50.07 inference(transitivity,[status(thm)],[11428, 11327])).
% 49.90/50.07 tff(11430,plain,
% 49.90/50.07 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36))),
% 49.90/50.07 inference(monotonicity,[status(thm)],[11429])).
% 49.90/50.07 tff(11431,plain,
% 49.90/50.07 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 49.90/50.07 inference(transitivity,[status(thm)],[11430, 11326])).
% 49.90/50.07 tff(11432,plain,
% 49.90/50.07 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37))),
% 49.90/50.07 inference(monotonicity,[status(thm)],[11431])).
% 49.90/50.07 tff(11433,plain,
% 49.90/50.07 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 49.90/50.07 inference(transitivity,[status(thm)],[11432, 11325])).
% 49.90/50.07 tff(11434,plain,
% 49.90/50.07 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38))),
% 49.90/50.08 inference(monotonicity,[status(thm)],[11433])).
% 49.90/50.08 tff(11435,plain,
% 49.90/50.08 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 49.90/50.08 inference(transitivity,[status(thm)],[11434, 11324])).
% 49.90/50.08 tff(11436,plain,
% 49.90/50.08 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39))),
% 49.90/50.08 inference(monotonicity,[status(thm)],[11435])).
% 49.90/50.08 tff(11437,plain,
% 49.90/50.08 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 49.90/50.08 inference(transitivity,[status(thm)],[11436, 11323])).
% 49.90/50.08 tff(11438,plain,
% 49.90/50.08 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40))),
% 49.90/50.08 inference(monotonicity,[status(thm)],[11437])).
% 49.90/50.08 tff(11439,plain,
% 49.90/50.08 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 49.90/50.08 inference(transitivity,[status(thm)],[11438, 11322])).
% 49.90/50.08 tff(11440,plain,
% 49.90/50.08 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41))),
% 49.90/50.08 inference(monotonicity,[status(thm)],[11439])).
% 49.90/50.08 tff(11441,plain,
% 49.90/50.08 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 49.90/50.08 inference(transitivity,[status(thm)],[11440, 11321])).
% 49.90/50.08 tff(11442,plain,
% 49.90/50.08 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42))),
% 49.90/50.08 inference(monotonicity,[status(thm)],[11441])).
% 49.90/50.08 tff(11443,plain,
% 49.90/50.08 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 49.90/50.08 inference(transitivity,[status(thm)],[11442, 11320])).
% 49.90/50.08 tff(11444,plain,
% 49.90/50.08 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43))),
% 49.90/50.09 inference(monotonicity,[status(thm)],[11443])).
% 49.90/50.09 tff(11445,plain,
% 49.90/50.09 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 49.90/50.09 inference(transitivity,[status(thm)],[11444, 11319])).
% 49.90/50.09 tff(11446,plain,
% 49.90/50.09 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44))),
% 49.90/50.09 inference(monotonicity,[status(thm)],[11445])).
% 49.90/50.09 tff(11447,plain,
% 49.90/50.09 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 49.90/50.09 inference(transitivity,[status(thm)],[11446, 11318])).
% 49.90/50.09 tff(11448,plain,
% 49.90/50.09 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45))),
% 49.90/50.09 inference(monotonicity,[status(thm)],[11447])).
% 49.90/50.09 tff(11449,plain,
% 49.90/50.09 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 49.90/50.09 inference(transitivity,[status(thm)],[11448, 11317])).
% 49.90/50.09 tff(11450,plain,
% 49.90/50.09 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46))),
% 49.90/50.09 inference(monotonicity,[status(thm)],[11449])).
% 49.90/50.09 tff(11451,plain,
% 49.90/50.09 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 49.90/50.10 inference(transitivity,[status(thm)],[11450, 11316])).
% 49.90/50.10 tff(11452,plain,
% 49.90/50.10 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47))),
% 49.90/50.10 inference(monotonicity,[status(thm)],[11451])).
% 49.90/50.10 tff(11453,plain,
% 49.90/50.10 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 49.90/50.10 inference(transitivity,[status(thm)],[11452, 11315])).
% 49.90/50.10 tff(11454,plain,
% 49.90/50.10 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48))),
% 49.90/50.10 inference(monotonicity,[status(thm)],[11453])).
% 49.90/50.10 tff(11455,plain,
% 49.90/50.10 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 49.90/50.10 inference(transitivity,[status(thm)],[11454, 11314])).
% 49.90/50.10 tff(11456,plain,
% 49.90/50.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49))),
% 49.90/50.10 inference(monotonicity,[status(thm)],[11455])).
% 49.90/50.10 tff(11457,plain,
% 49.90/50.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 49.90/50.11 inference(transitivity,[status(thm)],[11456, 11313])).
% 49.90/50.11 tff(11458,plain,
% 49.90/50.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50))),
% 49.90/50.11 inference(monotonicity,[status(thm)],[11457])).
% 49.90/50.11 tff(11459,plain,
% 49.90/50.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 49.90/50.11 inference(transitivity,[status(thm)],[11458, 11312])).
% 49.90/50.11 tff(11460,plain,
% 49.90/50.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51))),
% 49.90/50.11 inference(monotonicity,[status(thm)],[11459])).
% 49.90/50.11 tff(11461,plain,
% 49.90/50.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 49.90/50.11 inference(transitivity,[status(thm)],[11460, 11311])).
% 49.90/50.11 tff(11462,plain,
% 49.90/50.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52))),
% 49.90/50.11 inference(monotonicity,[status(thm)],[11461])).
% 49.90/50.11 tff(11463,plain,
% 49.90/50.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 49.90/50.12 inference(transitivity,[status(thm)],[11462, 11310])).
% 49.90/50.12 tff(11464,plain,
% 49.90/50.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53))),
% 49.90/50.12 inference(monotonicity,[status(thm)],[11463])).
% 49.90/50.12 tff(11465,plain,
% 49.90/50.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 49.90/50.12 inference(transitivity,[status(thm)],[11464, 11309])).
% 49.90/50.12 tff(11466,plain,
% 49.90/50.12 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54))),
% 49.90/50.12 inference(monotonicity,[status(thm)],[11465])).
% 49.90/50.12 tff(11467,plain,
% 49.90/50.12 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 49.90/50.12 inference(transitivity,[status(thm)],[11466, 11308])).
% 49.90/50.12 tff(11468,plain,
% 49.90/50.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55))),
% 49.90/50.12 inference(monotonicity,[status(thm)],[11467])).
% 49.90/50.12 tff(11469,plain,
% 49.90/50.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 49.90/50.13 inference(transitivity,[status(thm)],[11468, 11307])).
% 49.90/50.13 tff(11470,plain,
% 49.90/50.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56))),
% 49.90/50.13 inference(monotonicity,[status(thm)],[11469])).
% 49.90/50.13 tff(11471,plain,
% 49.90/50.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 49.90/50.13 inference(transitivity,[status(thm)],[11470, 11306])).
% 49.90/50.13 tff(11472,plain,
% 49.90/50.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57))),
% 49.90/50.13 inference(monotonicity,[status(thm)],[11471])).
% 49.90/50.13 tff(11473,plain,
% 49.90/50.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 49.90/50.13 inference(transitivity,[status(thm)],[11472, 11305])).
% 49.90/50.13 tff(11474,plain,
% 49.90/50.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58))),
% 49.90/50.13 inference(monotonicity,[status(thm)],[11473])).
% 49.90/50.13 tff(11475,plain,
% 49.90/50.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 49.90/50.13 inference(transitivity,[status(thm)],[11474, 11304])).
% 49.90/50.13 tff(11476,plain,
% 49.90/50.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59))),
% 49.90/50.14 inference(monotonicity,[status(thm)],[11475])).
% 49.90/50.14 tff(11477,plain,
% 49.90/50.14 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 49.90/50.14 inference(transitivity,[status(thm)],[11476, 11303])).
% 49.90/50.14 tff(11478,plain,
% 49.90/50.14 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60))),
% 49.90/50.14 inference(monotonicity,[status(thm)],[11477])).
% 49.90/50.14 tff(11479,plain,
% 49.90/50.14 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 49.90/50.14 inference(transitivity,[status(thm)],[11478, 11302])).
% 49.90/50.14 tff(11480,plain,
% 49.90/50.14 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61))),
% 49.90/50.14 inference(monotonicity,[status(thm)],[11479])).
% 49.90/50.14 tff(11481,plain,
% 49.90/50.14 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 49.98/50.15 inference(transitivity,[status(thm)],[11480, 11301])).
% 49.98/50.15 tff(11482,plain,
% 49.98/50.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62))),
% 49.98/50.15 inference(monotonicity,[status(thm)],[11481])).
% 49.98/50.15 tff(11483,plain,
% 49.98/50.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 49.98/50.15 inference(transitivity,[status(thm)],[11482, 11300])).
% 49.98/50.15 tff(11484,plain,
% 49.98/50.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63))),
% 49.98/50.15 inference(monotonicity,[status(thm)],[11483])).
% 49.98/50.15 tff(11485,plain,
% 49.98/50.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 49.98/50.16 inference(transitivity,[status(thm)],[11484, 11299])).
% 49.98/50.16 tff(11486,plain,
% 49.98/50.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64))),
% 49.98/50.16 inference(monotonicity,[status(thm)],[11485])).
% 49.98/50.16 tff(11487,plain,
% 49.98/50.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 49.98/50.16 inference(transitivity,[status(thm)],[11486, 11298])).
% 49.98/50.16 tff(11488,plain,
% 49.98/50.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65))),
% 49.98/50.16 inference(monotonicity,[status(thm)],[11487])).
% 49.98/50.16 tff(11489,plain,
% 49.98/50.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 49.98/50.16 inference(transitivity,[status(thm)],[11488, 11297])).
% 49.98/50.16 tff(11490,plain,
% 49.98/50.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66))),
% 49.98/50.16 inference(monotonicity,[status(thm)],[11489])).
% 49.98/50.16 tff(11491,plain,
% 49.98/50.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 49.98/50.17 inference(transitivity,[status(thm)],[11490, 11296])).
% 49.98/50.17 tff(11492,plain,
% 49.98/50.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67))),
% 49.98/50.17 inference(monotonicity,[status(thm)],[11491])).
% 49.98/50.17 tff(11493,plain,
% 49.98/50.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 49.98/50.17 inference(transitivity,[status(thm)],[11492, 11295])).
% 49.98/50.17 tff(11494,plain,
% 49.98/50.17 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68))),
% 49.98/50.17 inference(monotonicity,[status(thm)],[11493])).
% 49.98/50.17 tff(11495,plain,
% 49.98/50.17 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 49.98/50.17 inference(transitivity,[status(thm)],[11494, 11294])).
% 49.98/50.17 tff(11496,plain,
% 49.98/50.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69))),
% 49.98/50.18 inference(monotonicity,[status(thm)],[11495])).
% 49.98/50.18 tff(11497,plain,
% 49.98/50.18 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 49.98/50.18 inference(transitivity,[status(thm)],[11496, 11293])).
% 49.98/50.18 tff(11498,plain,
% 49.98/50.18 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70))),
% 49.98/50.18 inference(monotonicity,[status(thm)],[11497])).
% 49.98/50.18 tff(11499,plain,
% 49.98/50.18 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 50.02/50.18 inference(transitivity,[status(thm)],[11498, 11292])).
% 50.02/50.18 tff(11500,plain,
% 50.02/50.18 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71))),
% 50.02/50.19 inference(monotonicity,[status(thm)],[11499])).
% 50.02/50.19 tff(11501,plain,
% 50.02/50.19 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 50.02/50.19 inference(transitivity,[status(thm)],[11500, 11291])).
% 50.02/50.19 tff(11502,plain,
% 50.02/50.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72))),
% 50.02/50.19 inference(monotonicity,[status(thm)],[11501])).
% 50.02/50.19 tff(11503,plain,
% 50.02/50.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 50.02/50.19 inference(transitivity,[status(thm)],[11502, 11290])).
% 50.02/50.19 tff(11504,plain,
% 50.02/50.19 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73))),
% 50.02/50.20 inference(monotonicity,[status(thm)],[11503])).
% 50.02/50.20 tff(11505,plain,
% 50.02/50.20 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 50.02/50.20 inference(transitivity,[status(thm)],[11504, 11289])).
% 50.02/50.20 tff(11506,plain,
% 50.02/50.20 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74))),
% 50.02/50.20 inference(monotonicity,[status(thm)],[11505])).
% 50.02/50.20 tff(11507,plain,
% 50.02/50.20 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 50.02/50.20 inference(transitivity,[status(thm)],[11506, 11288])).
% 50.02/50.20 tff(11508,plain,
% 50.02/50.20 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75))),
% 50.02/50.20 inference(monotonicity,[status(thm)],[11507])).
% 50.02/50.21 tff(11509,plain,
% 50.02/50.21 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 50.02/50.21 inference(transitivity,[status(thm)],[11508, 11287])).
% 50.02/50.21 tff(11510,plain,
% 50.02/50.21 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76))),
% 50.02/50.21 inference(monotonicity,[status(thm)],[11509])).
% 50.02/50.21 tff(11511,plain,
% 50.02/50.21 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 50.02/50.21 inference(transitivity,[status(thm)],[11510, 11286])).
% 50.02/50.21 tff(11512,plain,
% 50.02/50.21 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77))),
% 50.02/50.21 inference(monotonicity,[status(thm)],[11511])).
% 50.02/50.21 tff(11513,plain,
% 50.02/50.21 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 50.02/50.22 inference(transitivity,[status(thm)],[11512, 11285])).
% 50.02/50.22 tff(11514,plain,
% 50.02/50.22 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78))),
% 50.02/50.22 inference(monotonicity,[status(thm)],[11513])).
% 50.02/50.22 tff(11515,plain,
% 50.02/50.22 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 50.02/50.22 inference(transitivity,[status(thm)],[11514, 11284])).
% 50.02/50.22 tff(11516,plain,
% 50.02/50.22 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79))),
% 50.02/50.22 inference(monotonicity,[status(thm)],[11515])).
% 50.02/50.22 tff(11517,plain,
% 50.02/50.22 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 50.02/50.23 inference(transitivity,[status(thm)],[11516, 11283])).
% 50.02/50.23 tff(11518,plain,
% 50.02/50.23 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80))),
% 50.02/50.23 inference(monotonicity,[status(thm)],[11517])).
% 50.02/50.23 tff(11519,plain,
% 50.02/50.23 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 50.07/50.23 inference(transitivity,[status(thm)],[11518, 11282])).
% 50.07/50.23 tff(11520,plain,
% 50.07/50.23 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81))),
% 50.07/50.24 inference(monotonicity,[status(thm)],[11519])).
% 50.07/50.24 tff(11521,plain,
% 50.07/50.24 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 50.07/50.24 inference(transitivity,[status(thm)],[11520, 11281])).
% 50.07/50.24 tff(11522,plain,
% 50.07/50.24 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82))),
% 50.07/50.24 inference(monotonicity,[status(thm)],[11521])).
% 50.07/50.24 tff(11523,plain,
% 50.07/50.24 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 50.07/50.24 inference(transitivity,[status(thm)],[11522, 11280])).
% 50.07/50.24 tff(11524,plain,
% 50.07/50.24 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83))),
% 50.08/50.25 inference(monotonicity,[status(thm)],[11523])).
% 50.08/50.25 tff(11525,plain,
% 50.08/50.25 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 50.08/50.25 inference(transitivity,[status(thm)],[11524, 11279])).
% 50.08/50.25 tff(11526,plain,
% 50.08/50.25 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84))),
% 50.08/50.25 inference(monotonicity,[status(thm)],[11525])).
% 50.08/50.25 tff(11527,plain,
% 50.08/50.25 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 50.08/50.25 inference(transitivity,[status(thm)],[11526, 11278])).
% 50.08/50.25 tff(11528,plain,
% 50.08/50.25 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85))),
% 50.08/50.26 inference(monotonicity,[status(thm)],[11527])).
% 50.08/50.26 tff(11529,plain,
% 50.08/50.26 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 50.08/50.26 inference(transitivity,[status(thm)],[11528, 11277])).
% 50.08/50.26 tff(11530,plain,
% 50.08/50.26 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86))),
% 50.08/50.26 inference(monotonicity,[status(thm)],[11529])).
% 50.08/50.26 tff(11531,plain,
% 50.08/50.26 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 50.08/50.26 inference(transitivity,[status(thm)],[11530, 11276])).
% 50.08/50.26 tff(11532,plain,
% 50.08/50.26 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87))),
% 50.08/50.27 inference(monotonicity,[status(thm)],[11531])).
% 50.08/50.27 tff(11533,plain,
% 50.08/50.27 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 50.08/50.27 inference(transitivity,[status(thm)],[11532, 11275])).
% 50.08/50.27 tff(11534,plain,
% 50.08/50.27 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88))),
% 50.08/50.27 inference(monotonicity,[status(thm)],[11533])).
% 50.08/50.27 tff(11535,plain,
% 50.08/50.27 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 50.08/50.28 inference(transitivity,[status(thm)],[11534, 11274])).
% 50.08/50.28 tff(11536,plain,
% 50.08/50.28 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89))),
% 50.08/50.28 inference(monotonicity,[status(thm)],[11535])).
% 50.08/50.28 tff(11537,plain,
% 50.08/50.28 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 50.08/50.28 inference(transitivity,[status(thm)],[11536, 11273])).
% 50.08/50.28 tff(11538,plain,
% 50.08/50.28 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90))),
% 50.08/50.28 inference(monotonicity,[status(thm)],[11537])).
% 50.08/50.28 tff(11539,plain,
% 50.08/50.28 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 50.08/50.29 inference(transitivity,[status(thm)],[11538, 11272])).
% 50.08/50.29 tff(11540,plain,
% 50.08/50.29 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91))),
% 50.08/50.29 inference(monotonicity,[status(thm)],[11539])).
% 50.08/50.29 tff(11541,plain,
% 50.08/50.29 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 50.08/50.29 inference(transitivity,[status(thm)],[11540, 11271])).
% 50.08/50.29 tff(11542,plain,
% 50.08/50.29 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92))),
% 50.08/50.30 inference(monotonicity,[status(thm)],[11541])).
% 50.08/50.30 tff(11543,plain,
% 50.08/50.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 50.08/50.30 inference(transitivity,[status(thm)],[11542, 11270])).
% 50.08/50.30 tff(11544,plain,
% 50.08/50.30 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93))),
% 50.08/50.30 inference(monotonicity,[status(thm)],[11543])).
% 50.08/50.30 tff(11545,plain,
% 50.08/50.30 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 50.08/50.30 inference(transitivity,[status(thm)],[11544, 11269])).
% 50.08/50.30 tff(11546,plain,
% 50.08/50.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94))),
% 50.08/50.30 inference(monotonicity,[status(thm)],[11545])).
% 50.08/50.30 tff(11547,plain,
% 50.08/50.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 50.08/50.31 inference(transitivity,[status(thm)],[11546, 11268])).
% 50.08/50.31 tff(11548,plain,
% 50.08/50.31 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95))),
% 50.14/50.31 inference(monotonicity,[status(thm)],[11547])).
% 50.14/50.31 tff(11549,plain,
% 50.14/50.31 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 50.14/50.31 inference(transitivity,[status(thm)],[11548, 11267])).
% 50.14/50.31 tff(11550,plain,
% 50.14/50.31 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96))),
% 50.14/50.32 inference(monotonicity,[status(thm)],[11549])).
% 50.14/50.32 tff(11551,plain,
% 50.14/50.32 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 50.14/50.32 inference(transitivity,[status(thm)],[11550, 11266])).
% 50.14/50.32 tff(11552,plain,
% 50.14/50.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97))),
% 50.14/50.32 inference(monotonicity,[status(thm)],[11551])).
% 50.14/50.32 tff(11553,plain,
% 50.14/50.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 50.14/50.33 inference(transitivity,[status(thm)],[11552, 11265])).
% 50.14/50.33 tff(11554,plain,
% 50.14/50.33 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98))),
% 50.14/50.33 inference(monotonicity,[status(thm)],[11553])).
% 50.14/50.33 tff(11555,plain,
% 50.14/50.33 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 50.14/50.33 inference(transitivity,[status(thm)],[11554, 11264])).
% 50.14/50.33 tff(11556,plain,
% 50.14/50.33 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99))),
% 50.14/50.34 inference(monotonicity,[status(thm)],[11555])).
% 50.14/50.34 tff(11557,plain,
% 50.14/50.34 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 50.14/50.34 inference(transitivity,[status(thm)],[11556, 11263])).
% 50.14/50.34 tff(11558,axiom,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound102')).
% 50.14/50.34 tff(11559,plain,
% 50.14/50.34 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.34 inference(modus_ponens,[status(thm)],[11558, 11557])).
% 50.14/50.34 tff(11560,plain,
% 50.14/50.34 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.34 inference(modus_ponens,[status(thm)],[11559, 11262])).
% 50.14/50.34 tff(11561,plain,
% 50.14/50.34 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.34 inference(modus_ponens,[status(thm)],[11560, 11262])).
% 50.14/50.34 tff(11562,plain,
% 50.14/50.35 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11561, 11262])).
% 50.14/50.35 tff(11563,plain,
% 50.14/50.35 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11562, 11262])).
% 50.14/50.35 tff(11564,plain,
% 50.14/50.35 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11563, 11261])).
% 50.14/50.35 tff(11565,plain,
% 50.14/50.35 (trans(s99, s1)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11564, 10834, 10823, 10812, 10801, 10790, 10779, 10768, 10757, 10746, 10735, 10724, 10713, 10702, 10691, 10680, 10669, 10658, 10647, 10636, 10625, 10614, 10603, 10592, 10581, 10570, 10559, 10548, 10537, 10526, 10515, 10504, 10493, 10482, 10471, 10460, 10449, 10438, 10427, 10416, 10405, 10394, 10383, 10372, 10361, 10350, 10339, 10328, 10317, 10306, 10295, 10284, 10273, 10262, 10251, 10240, 10229, 10218, 10207, 10196, 10185, 10174, 10163, 10152, 10141, 10119, 10108, 10097, 10086, 10075, 10064, 10053, 10042, 10031, 10020, 10009, 9998, 9987, 9976, 9965, 9954, 9943, 9932, 9921, 9910, 9899, 9888, 9877, 9866, 9855, 9844, 9833, 9822, 9811, 9800, 9789, 9778, 9767, 9756, 9745])).
% 50.14/50.35 tff(11566,plain,
% 50.14/50.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11567,plain,
% 50.14/50.35 (((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1)) <=> (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11568,plain,
% 50.14/50.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1))))),
% 50.14/50.35 inference(monotonicity,[status(thm)],[11567])).
% 50.14/50.35 tff(11569,plain,
% 50.14/50.35 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 50.14/50.35 inference(transitivity,[status(thm)],[11568, 11566])).
% 50.14/50.35 tff(11570,plain,
% 50.14/50.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11571,plain,
% 50.14/50.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1))),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11570, 11569])).
% 50.14/50.35 tff(11572,plain,
% 50.14/50.35 ($false),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11571, 8701, 11565, 9733, 9723, 8691])).
% 50.14/50.35 tff(11573,plain,(always5(s99) | always5(s1)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.35 tff(11574,plain,
% 50.14/50.35 (always5(s1)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11573, 6595])).
% 50.14/50.35 tff(11575,plain,
% 50.14/50.35 (always5(s2)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7484, 11574])).
% 50.14/50.35 tff(11576,plain,
% 50.14/50.35 (always5(s3)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7476, 11575])).
% 50.14/50.35 tff(11577,plain,
% 50.14/50.35 (always5(s4)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7468, 11576])).
% 50.14/50.35 tff(11578,plain,
% 50.14/50.35 (always5(s5)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7460, 11577])).
% 50.14/50.35 tff(11579,plain,
% 50.14/50.35 (always5(s6)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7452, 11578])).
% 50.14/50.35 tff(11580,plain,
% 50.14/50.35 (always5(s7)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7444, 11579])).
% 50.14/50.35 tff(11581,plain,
% 50.14/50.35 (always5(s8)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7436, 11580])).
% 50.14/50.35 tff(11582,plain,
% 50.14/50.35 (always5(s9)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7420, 11581])).
% 50.14/50.35 tff(11583,plain,
% 50.14/50.35 (always5(s10)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7399, 11582])).
% 50.14/50.35 tff(11584,plain,
% 50.14/50.35 (always5(s11)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7378, 11583])).
% 50.14/50.35 tff(11585,plain,
% 50.14/50.35 (always5(s12)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7357, 11584])).
% 50.14/50.35 tff(11586,plain,
% 50.14/50.35 (always5(s13)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7336, 11585])).
% 50.14/50.35 tff(11587,plain,
% 50.14/50.35 (always5(s14)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7315, 11586])).
% 50.14/50.35 tff(11588,plain,
% 50.14/50.35 (always5(s15)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7261, 11587])).
% 50.14/50.35 tff(11589,plain,
% 50.14/50.35 (always5(s16)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7252, 11588])).
% 50.14/50.35 tff(11590,plain,
% 50.14/50.35 (always5(s17)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7244, 11589])).
% 50.14/50.35 tff(11591,plain,
% 50.14/50.35 (always5(s18)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7236, 11590])).
% 50.14/50.35 tff(11592,plain,
% 50.14/50.35 (always5(s19)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7228, 11591])).
% 50.14/50.35 tff(11593,plain,
% 50.14/50.35 (always5(s20)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7220, 11592])).
% 50.14/50.35 tff(11594,plain,
% 50.14/50.35 (always5(s21)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7212, 11593])).
% 50.14/50.35 tff(11595,plain,
% 50.14/50.35 (always5(s22)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7204, 11594])).
% 50.14/50.35 tff(11596,plain,
% 50.14/50.35 (always5(s23)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7196, 11595])).
% 50.14/50.35 tff(11597,plain,
% 50.14/50.35 (always5(s24)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7188, 11596])).
% 50.14/50.35 tff(11598,plain,
% 50.14/50.35 (always5(s25)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7180, 11597])).
% 50.14/50.35 tff(11599,plain,
% 50.14/50.35 (always5(s26)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7172, 11598])).
% 50.14/50.35 tff(11600,plain,
% 50.14/50.35 (always5(s27)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7164, 11599])).
% 50.14/50.35 tff(11601,plain,
% 50.14/50.35 (always5(s28)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7156, 11600])).
% 50.14/50.35 tff(11602,plain,
% 50.14/50.35 (always5(s29)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7148, 11601])).
% 50.14/50.35 tff(11603,plain,
% 50.14/50.35 (always5(s30)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7140, 11602])).
% 50.14/50.35 tff(11604,plain,
% 50.14/50.35 (always5(s31)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7132, 11603])).
% 50.14/50.35 tff(11605,plain,
% 50.14/50.35 (always5(s32)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7124, 11604])).
% 50.14/50.35 tff(11606,plain,
% 50.14/50.35 (always5(s33)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7116, 11605])).
% 50.14/50.35 tff(11607,plain,
% 50.14/50.35 (always5(s34)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7108, 11606])).
% 50.14/50.35 tff(11608,plain,
% 50.14/50.35 (always5(s35)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7100, 11607])).
% 50.14/50.35 tff(11609,plain,
% 50.14/50.35 (always5(s36)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7092, 11608])).
% 50.14/50.35 tff(11610,plain,
% 50.14/50.35 (always5(s37)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7084, 11609])).
% 50.14/50.35 tff(11611,plain,
% 50.14/50.35 (always5(s38)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7076, 11610])).
% 50.14/50.35 tff(11612,plain,
% 50.14/50.35 (always5(s39)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7068, 11611])).
% 50.14/50.35 tff(11613,plain,
% 50.14/50.35 (always5(s40)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7060, 11612])).
% 50.14/50.35 tff(11614,plain,
% 50.14/50.35 (always5(s41)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7052, 11613])).
% 50.14/50.35 tff(11615,plain,
% 50.14/50.35 (always5(s42)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7044, 11614])).
% 50.14/50.35 tff(11616,plain,
% 50.14/50.35 (always5(s43)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7036, 11615])).
% 50.14/50.35 tff(11617,plain,
% 50.14/50.35 (always5(s44)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7028, 11616])).
% 50.14/50.35 tff(11618,plain,
% 50.14/50.35 (always5(s45)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7020, 11617])).
% 50.14/50.35 tff(11619,plain,
% 50.14/50.35 (always5(s46)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7012, 11618])).
% 50.14/50.35 tff(11620,plain,
% 50.14/50.35 (always5(s47)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7004, 11619])).
% 50.14/50.35 tff(11621,plain,
% 50.14/50.35 (always5(s48)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6996, 11620])).
% 50.14/50.35 tff(11622,plain,
% 50.14/50.35 (always5(s49)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6988, 11621])).
% 50.14/50.35 tff(11623,plain,
% 50.14/50.35 ($false),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6980, 11622, 6973])).
% 50.14/50.35 tff(11624,plain,(always5(s99)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.35 tff(11625,plain,
% 50.14/50.35 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11626,plain,
% 50.14/50.35 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11627,plain,
% 50.14/50.35 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99))),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11626, 11625])).
% 50.14/50.35 tff(11628,plain,
% 50.14/50.35 (~m_counter_cell_v_carry_out(c_bit2, s99)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11627, 6200, 11624])).
% 50.14/50.35 tff(11629,plain,
% 50.14/50.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11630,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11631,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99)),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11630, 11629])).
% 50.14/50.35 tff(11632,plain,
% 50.14/50.35 ((~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99))),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11631, 2906, 11628])).
% 50.14/50.35 tff(11633,plain,
% 50.14/50.35 (~m_counter_cell_v_value(c_bit2, s99)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11632, 6594])).
% 50.14/50.35 tff(11634,plain,
% 50.14/50.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11635,plain,
% 50.14/50.35 ((node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99)) <=> (m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11636,plain,
% 50.14/50.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99))))),
% 50.14/50.35 inference(monotonicity,[status(thm)],[11635])).
% 50.14/50.35 tff(11637,plain,
% 50.14/50.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 50.14/50.35 inference(transitivity,[status(thm)],[11636, 11634])).
% 50.14/50.35 tff(11638,plain,
% 50.14/50.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11639,plain,
% 50.14/50.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99))),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11638, 11637])).
% 50.14/50.35 tff(11640,plain,
% 50.14/50.35 (node1(c_bit2, s98)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11639, 84, 11633, 6394])).
% 50.14/50.35 tff(11641,plain,
% 50.14/50.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11642,plain,
% 50.14/50.35 (((~node1(c_bit2, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98))) <=> (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11643,plain,
% 50.14/50.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))))),
% 50.14/50.35 inference(monotonicity,[status(thm)],[11642])).
% 50.14/50.35 tff(11644,plain,
% 50.14/50.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 50.14/50.35 inference(transitivity,[status(thm)],[11643, 11641])).
% 50.14/50.35 tff(11645,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11646,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11645, 11644])).
% 50.14/50.35 tff(11647,plain,
% 50.14/50.35 (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98))),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11646, 3095, 11640])).
% 50.14/50.35 tff(11648,plain,
% 50.14/50.35 (m_counter_cell_v_carry_in(c_bit2, s98)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11647, 6383])).
% 50.14/50.35 tff(11649,plain,
% 50.14/50.35 (always5(s98)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6610, 6348])).
% 50.14/50.35 tff(11650,plain,
% 50.14/50.35 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s98)) | (~m_counter_cell_v_carry_out(c_bit2, s98)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s98)) | (~m_counter_cell_v_carry_out(c_bit2, s98)))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11651,plain,
% 50.14/50.35 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s98)) | (~m_counter_cell_v_carry_out(c_bit2, s98)))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11652,plain,
% 50.14/50.35 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s98)) | (~m_counter_cell_v_carry_out(c_bit2, s98))),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11651, 11650])).
% 50.14/50.35 tff(11653,plain,
% 50.14/50.35 (~m_counter_cell_v_carry_out(c_bit2, s98)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11652, 6200, 11649])).
% 50.14/50.35 tff(11654,plain,
% 50.14/50.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit2, s98))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit2, s98))),
% 50.14/50.35 inference(rewrite,[status(thm)],[])).
% 50.14/50.35 tff(11655,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit2, s98))),
% 50.14/50.35 inference(quant_inst,[status(thm)],[])).
% 50.14/50.35 tff(11656,plain,
% 50.14/50.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit2, s98)),
% 50.14/50.35 inference(modus_ponens,[status(thm)],[11655, 11654])).
% 50.14/50.35 tff(11657,plain,
% 50.14/50.35 ((~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98))),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11656, 2906, 11653])).
% 50.14/50.35 tff(11658,plain,
% 50.14/50.35 ($false),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[11657, 11648, 6383])).
% 50.14/50.35 tff(11659,plain,(~always5(s95)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.35 tff(11660,plain,
% 50.14/50.35 (~always5(s94)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6620, 11659])).
% 50.14/50.35 tff(11661,plain,
% 50.14/50.35 (~always5(s93)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6628, 11660])).
% 50.14/50.35 tff(11662,plain,
% 50.14/50.35 (~always5(s92)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6636, 11661])).
% 50.14/50.35 tff(11663,plain,
% 50.14/50.35 (~always5(s91)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6644, 11662])).
% 50.14/50.35 tff(11664,plain,
% 50.14/50.35 (~always5(s90)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6652, 11663])).
% 50.14/50.35 tff(11665,plain,
% 50.14/50.35 (~always5(s89)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6660, 11664])).
% 50.14/50.35 tff(11666,plain,
% 50.14/50.35 (~always5(s88)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6668, 11665])).
% 50.14/50.35 tff(11667,plain,
% 50.14/50.35 (~always5(s87)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6676, 11666])).
% 50.14/50.35 tff(11668,plain,
% 50.14/50.35 (~always5(s86)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6684, 11667])).
% 50.14/50.35 tff(11669,plain,
% 50.14/50.35 (~always5(s85)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6692, 11668])).
% 50.14/50.35 tff(11670,plain,
% 50.14/50.35 (~always5(s84)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6700, 11669])).
% 50.14/50.35 tff(11671,plain,
% 50.14/50.35 (~always5(s83)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6708, 11670])).
% 50.14/50.35 tff(11672,plain,
% 50.14/50.35 (~always5(s82)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6716, 11671])).
% 50.14/50.35 tff(11673,plain,
% 50.14/50.35 (~always5(s81)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6724, 11672])).
% 50.14/50.35 tff(11674,plain,
% 50.14/50.35 (~always5(s80)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6732, 11673])).
% 50.14/50.35 tff(11675,plain,
% 50.14/50.35 (~always5(s79)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6740, 11674])).
% 50.14/50.35 tff(11676,plain,
% 50.14/50.35 (~always5(s78)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6748, 11675])).
% 50.14/50.35 tff(11677,plain,
% 50.14/50.35 (~always5(s77)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6756, 11676])).
% 50.14/50.35 tff(11678,plain,
% 50.14/50.35 (~always5(s76)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6764, 11677])).
% 50.14/50.35 tff(11679,plain,
% 50.14/50.35 (~always5(s75)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6772, 11678])).
% 50.14/50.35 tff(11680,plain,
% 50.14/50.35 (~always5(s74)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6780, 11679])).
% 50.14/50.35 tff(11681,plain,
% 50.14/50.35 (~always5(s73)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6788, 11680])).
% 50.14/50.35 tff(11682,plain,
% 50.14/50.35 (~always5(s72)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6796, 11681])).
% 50.14/50.35 tff(11683,plain,
% 50.14/50.35 (~always5(s71)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6804, 11682])).
% 50.14/50.35 tff(11684,plain,
% 50.14/50.35 (~always5(s70)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6812, 11683])).
% 50.14/50.35 tff(11685,plain,
% 50.14/50.35 (~always5(s69)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6820, 11684])).
% 50.14/50.35 tff(11686,plain,
% 50.14/50.35 (~always5(s68)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6828, 11685])).
% 50.14/50.35 tff(11687,plain,
% 50.14/50.35 (~always5(s67)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6836, 11686])).
% 50.14/50.35 tff(11688,plain,
% 50.14/50.35 (~always5(s66)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6844, 11687])).
% 50.14/50.35 tff(11689,plain,
% 50.14/50.35 (~always5(s65)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6852, 11688])).
% 50.14/50.35 tff(11690,plain,
% 50.14/50.35 (~always5(s64)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6860, 11689])).
% 50.14/50.35 tff(11691,plain,
% 50.14/50.35 (~always5(s63)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6868, 11690])).
% 50.14/50.35 tff(11692,plain,
% 50.14/50.35 (~always5(s62)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6876, 11691])).
% 50.14/50.35 tff(11693,plain,
% 50.14/50.35 (~always5(s61)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6884, 11692])).
% 50.14/50.35 tff(11694,plain,
% 50.14/50.35 (~always5(s60)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6892, 11693])).
% 50.14/50.35 tff(11695,plain,
% 50.14/50.35 (~always5(s59)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6900, 11694])).
% 50.14/50.35 tff(11696,plain,
% 50.14/50.35 (~always5(s58)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6908, 11695])).
% 50.14/50.35 tff(11697,plain,
% 50.14/50.35 (~always5(s57)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6916, 11696])).
% 50.14/50.35 tff(11698,plain,
% 50.14/50.35 (~always5(s56)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6924, 11697])).
% 50.14/50.35 tff(11699,plain,
% 50.14/50.35 (~always5(s55)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6932, 11698])).
% 50.14/50.35 tff(11700,plain,
% 50.14/50.35 (~always5(s54)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6940, 11699])).
% 50.14/50.35 tff(11701,plain,
% 50.14/50.35 (~always5(s53)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6948, 11700])).
% 50.14/50.35 tff(11702,plain,
% 50.14/50.35 (~always5(s52)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6956, 11701])).
% 50.14/50.35 tff(11703,plain,
% 50.14/50.35 (~always5(s51)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6964, 11702])).
% 50.14/50.35 tff(11704,plain,
% 50.14/50.35 (~always5(s50)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6972, 11703])).
% 50.14/50.35 tff(11705,plain,
% 50.14/50.35 (~always5(s49)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6980, 11704])).
% 50.14/50.35 tff(11706,plain,
% 50.14/50.35 (~always5(s48)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6988, 11705])).
% 50.14/50.35 tff(11707,plain,
% 50.14/50.35 (~always5(s47)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[6996, 11706])).
% 50.14/50.35 tff(11708,plain,
% 50.14/50.35 (~always5(s46)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7004, 11707])).
% 50.14/50.35 tff(11709,plain,
% 50.14/50.35 (~always5(s45)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7012, 11708])).
% 50.14/50.35 tff(11710,plain,
% 50.14/50.35 (~always5(s44)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7020, 11709])).
% 50.14/50.35 tff(11711,plain,
% 50.14/50.35 (~always5(s43)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7028, 11710])).
% 50.14/50.35 tff(11712,plain,
% 50.14/50.35 (~always5(s42)),
% 50.14/50.35 inference(unit_resolution,[status(thm)],[7036, 11711])).
% 50.14/50.35 tff(11713,assumption,(~always5(s42)), introduced(assumption)).
% 50.14/50.36 tff(11714,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s42) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11715,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s42)) | always5(s42)) <=> ((~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11716,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s42) | (~trans(s99, s42))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11715])).
% 50.14/50.36 tff(11717,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11716, 11714])).
% 50.14/50.36 tff(11718,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11719,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11718, 11717])).
% 50.14/50.36 tff(11720,plain,
% 50.14/50.36 ($false),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11719, 9780, 6332, 11624, 11713])).
% 50.14/50.36 tff(11721,plain,((~trans(s99, s42)) | always5(s42)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.36 tff(11722,plain,
% 50.14/50.36 (~trans(s99, s42)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11721, 11712])).
% 50.14/50.36 tff(11723,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s43) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11724,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s43)) | always5(s43)) <=> ((~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11725,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s43) | (~trans(s99, s43))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11724])).
% 50.14/50.36 tff(11726,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11725, 11723])).
% 50.14/50.36 tff(11727,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11728,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11727, 11726])).
% 50.14/50.36 tff(11729,plain,
% 50.14/50.36 (always5(s43) | (~trans(s99, s43))),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11728, 6332, 11624])).
% 50.14/50.36 tff(11730,plain,
% 50.14/50.36 (~trans(s99, s43)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11729, 11711])).
% 50.14/50.36 tff(11731,plain,
% 50.14/50.36 (~always5(s41)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[7044, 11712])).
% 50.14/50.36 tff(11732,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s41) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11733,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s41)) | always5(s41)) <=> ((~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11734,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s41) | (~trans(s99, s41))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11733])).
% 50.14/50.36 tff(11735,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11734, 11732])).
% 50.14/50.36 tff(11736,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11737,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11736, 11735])).
% 50.14/50.36 tff(11738,plain,
% 50.14/50.36 (always5(s41) | (~trans(s99, s41))),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11737, 6332, 11624])).
% 50.14/50.36 tff(11739,plain,
% 50.14/50.36 (~trans(s99, s41)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11738, 11731])).
% 50.14/50.36 tff(11740,plain,
% 50.14/50.36 (~always5(s40)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[7052, 11731])).
% 50.14/50.36 tff(11741,assumption,(~always5(s40)), introduced(assumption)).
% 50.14/50.36 tff(11742,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s40) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11743,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s40)) | always5(s40)) <=> ((~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11744,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s40) | (~trans(s99, s40))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11743])).
% 50.14/50.36 tff(11745,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11744, 11742])).
% 50.14/50.36 tff(11746,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11747,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11746, 11745])).
% 50.14/50.36 tff(11748,plain,
% 50.14/50.36 ($false),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11747, 10594, 6332, 11624, 11741])).
% 50.14/50.36 tff(11749,plain,((~trans(s99, s40)) | always5(s40)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.36 tff(11750,plain,
% 50.14/50.36 (~trans(s99, s40)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11749, 11740])).
% 50.14/50.36 tff(11751,assumption,(~always5(s94)), introduced(assumption)).
% 50.14/50.36 tff(11752,plain,
% 50.14/50.36 (~always5(s93)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6628, 11751])).
% 50.14/50.36 tff(11753,plain,
% 50.14/50.36 (~always5(s92)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6636, 11752])).
% 50.14/50.36 tff(11754,plain,
% 50.14/50.36 (~always5(s91)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6644, 11753])).
% 50.14/50.36 tff(11755,plain,
% 50.14/50.36 (~always5(s90)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6652, 11754])).
% 50.14/50.36 tff(11756,plain,
% 50.14/50.36 (~always5(s89)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6660, 11755])).
% 50.14/50.36 tff(11757,plain,
% 50.14/50.36 (~always5(s88)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6668, 11756])).
% 50.14/50.36 tff(11758,plain,
% 50.14/50.36 (~always5(s87)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6676, 11757])).
% 50.14/50.36 tff(11759,plain,
% 50.14/50.36 (~always5(s86)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6684, 11758])).
% 50.14/50.36 tff(11760,assumption,(~always5(s86)), introduced(assumption)).
% 50.14/50.36 tff(11761,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s86) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11762,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s86)) | always5(s86)) <=> ((~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11763,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s86) | (~trans(s99, s86))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11762])).
% 50.14/50.36 tff(11764,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11763, 11761])).
% 50.14/50.36 tff(11765,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11766,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11765, 11764])).
% 50.14/50.36 tff(11767,plain,
% 50.14/50.36 ($false),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11766, 9747, 6332, 11624, 11760])).
% 50.14/50.36 tff(11768,plain,((~trans(s99, s86)) | always5(s86)), inference(lemma,lemma(discharge,[]))).
% 50.14/50.36 tff(11769,plain,
% 50.14/50.36 (~trans(s99, s86)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11768, 11759])).
% 50.14/50.36 tff(11770,plain,
% 50.14/50.36 (~always5(s85)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6692, 11759])).
% 50.14/50.36 tff(11771,plain,
% 50.14/50.36 (~always5(s84)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6700, 11770])).
% 50.14/50.36 tff(11772,plain,
% 50.14/50.36 (~always5(s83)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6708, 11771])).
% 50.14/50.36 tff(11773,plain,
% 50.14/50.36 (~always5(s82)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6716, 11772])).
% 50.14/50.36 tff(11774,plain,
% 50.14/50.36 (~always5(s81)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6724, 11773])).
% 50.14/50.36 tff(11775,plain,
% 50.14/50.36 (~always5(s80)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6732, 11774])).
% 50.14/50.36 tff(11776,plain,
% 50.14/50.36 (~always5(s79)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6740, 11775])).
% 50.14/50.36 tff(11777,plain,
% 50.14/50.36 (~always5(s78)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6748, 11776])).
% 50.14/50.36 tff(11778,plain,
% 50.14/50.36 (~always5(s77)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6756, 11777])).
% 50.14/50.36 tff(11779,plain,
% 50.14/50.36 (~always5(s76)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6764, 11778])).
% 50.14/50.36 tff(11780,plain,
% 50.14/50.36 (~always5(s75)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6772, 11779])).
% 50.14/50.36 tff(11781,plain,
% 50.14/50.36 (~always5(s74)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6780, 11780])).
% 50.14/50.36 tff(11782,plain,
% 50.14/50.36 (~always5(s73)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[6788, 11781])).
% 50.14/50.36 tff(11783,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s73) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11784,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s73)) | always5(s73)) <=> ((~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11785,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s73) | (~trans(s99, s73))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11784])).
% 50.14/50.36 tff(11786,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11785, 11783])).
% 50.14/50.36 tff(11787,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11788,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11787, 11786])).
% 50.14/50.36 tff(11789,plain,
% 50.14/50.36 (always5(s73) | (~trans(s99, s73))),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11788, 6332, 11624])).
% 50.14/50.36 tff(11790,plain,
% 50.14/50.36 (~trans(s99, s73)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11789, 11782])).
% 50.14/50.36 tff(11791,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s75) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11792,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s75)) | always5(s75)) <=> ((~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11793,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s75) | (~trans(s99, s75))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11792])).
% 50.14/50.36 tff(11794,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 50.14/50.36 inference(transitivity,[status(thm)],[11793, 11791])).
% 50.14/50.36 tff(11795,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))),
% 50.14/50.36 inference(quant_inst,[status(thm)],[])).
% 50.14/50.36 tff(11796,plain,
% 50.14/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75))),
% 50.14/50.36 inference(modus_ponens,[status(thm)],[11795, 11794])).
% 50.14/50.36 tff(11797,plain,
% 50.14/50.36 (always5(s75) | (~trans(s99, s75))),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11796, 6332, 11624])).
% 50.14/50.36 tff(11798,plain,
% 50.14/50.36 (~trans(s99, s75)),
% 50.14/50.36 inference(unit_resolution,[status(thm)],[11797, 11780])).
% 50.14/50.36 tff(11799,assumption,(~always5(s74)), introduced(assumption)).
% 50.14/50.36 tff(11800,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s74) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11801,plain,
% 50.14/50.36 (((~always5(s99)) | (~trans(s99, s74)) | always5(s74)) <=> ((~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 50.14/50.36 inference(rewrite,[status(thm)],[])).
% 50.14/50.36 tff(11802,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s74) | (~trans(s99, s74))))),
% 50.14/50.36 inference(monotonicity,[status(thm)],[11801])).
% 50.14/50.36 tff(11803,plain,
% 50.14/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11802, 11800])).
% 50.20/50.36 tff(11804,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11805,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11804, 11803])).
% 50.20/50.36 tff(11806,plain,
% 50.20/50.36 ($false),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11805, 10275, 6332, 11624, 11799])).
% 50.20/50.36 tff(11807,plain,((~trans(s99, s74)) | always5(s74)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.36 tff(11808,plain,
% 50.20/50.36 (~trans(s99, s74)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11807, 11781])).
% 50.20/50.36 tff(11809,plain,
% 50.20/50.36 (~always5(s72)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6796, 11782])).
% 50.20/50.36 tff(11810,plain,
% 50.20/50.36 (~always5(s71)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6804, 11809])).
% 50.20/50.36 tff(11811,plain,
% 50.20/50.36 (~always5(s70)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6812, 11810])).
% 50.20/50.36 tff(11812,plain,
% 50.20/50.36 (~always5(s69)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6820, 11811])).
% 50.20/50.36 tff(11813,plain,
% 50.20/50.36 (~always5(s68)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6828, 11812])).
% 50.20/50.36 tff(11814,plain,
% 50.20/50.36 (~always5(s67)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6836, 11813])).
% 50.20/50.36 tff(11815,plain,
% 50.20/50.36 (~always5(s66)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6844, 11814])).
% 50.20/50.36 tff(11816,plain,
% 50.20/50.36 (~always5(s65)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6852, 11815])).
% 50.20/50.36 tff(11817,plain,
% 50.20/50.36 (~always5(s64)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6860, 11816])).
% 50.20/50.36 tff(11818,plain,
% 50.20/50.36 (~always5(s63)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6868, 11817])).
% 50.20/50.36 tff(11819,plain,
% 50.20/50.36 (~always5(s62)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6876, 11818])).
% 50.20/50.36 tff(11820,plain,
% 50.20/50.36 (~always5(s61)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6884, 11819])).
% 50.20/50.36 tff(11821,plain,
% 50.20/50.36 (~always5(s60)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6892, 11820])).
% 50.20/50.36 tff(11822,plain,
% 50.20/50.36 (~always5(s59)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6900, 11821])).
% 50.20/50.36 tff(11823,plain,
% 50.20/50.36 (~always5(s58)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6908, 11822])).
% 50.20/50.36 tff(11824,plain,
% 50.20/50.36 (~always5(s57)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6916, 11823])).
% 50.20/50.36 tff(11825,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s57) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11826,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s57)) | always5(s57)) <=> ((~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11827,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s57) | (~trans(s99, s57))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11826])).
% 50.20/50.36 tff(11828,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11827, 11825])).
% 50.20/50.36 tff(11829,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11830,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11829, 11828])).
% 50.20/50.36 tff(11831,plain,
% 50.20/50.36 (always5(s57) | (~trans(s99, s57))),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11830, 6332, 11624])).
% 50.20/50.36 tff(11832,plain,
% 50.20/50.36 (~trans(s99, s57)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11831, 11824])).
% 50.20/50.36 tff(11833,plain,
% 50.20/50.36 (~always5(s56)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6924, 11824])).
% 50.20/50.36 tff(11834,plain,
% 50.20/50.36 (~always5(s55)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6932, 11833])).
% 50.20/50.36 tff(11835,plain,
% 50.20/50.36 (~always5(s54)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6940, 11834])).
% 50.20/50.36 tff(11836,plain,
% 50.20/50.36 (~always5(s53)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6948, 11835])).
% 50.20/50.36 tff(11837,plain,
% 50.20/50.36 (~always5(s52)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6956, 11836])).
% 50.20/50.36 tff(11838,plain,
% 50.20/50.36 (~always5(s51)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6964, 11837])).
% 50.20/50.36 tff(11839,plain,
% 50.20/50.36 (~always5(s50)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6972, 11838])).
% 50.20/50.36 tff(11840,plain,
% 50.20/50.36 (~always5(s49)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[6980, 11839])).
% 50.20/50.36 tff(11841,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s49) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11842,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s49)) | always5(s49)) <=> ((~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11843,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s49) | (~trans(s99, s49))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11842])).
% 50.20/50.36 tff(11844,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11843, 11841])).
% 50.20/50.36 tff(11845,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11846,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11845, 11844])).
% 50.20/50.36 tff(11847,plain,
% 50.20/50.36 (always5(s49) | (~trans(s99, s49))),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11846, 6332, 11624])).
% 50.20/50.36 tff(11848,plain,
% 50.20/50.36 (~trans(s99, s49)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11847, 11840])).
% 50.20/50.36 tff(11849,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s76) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11850,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s76)) | always5(s76)) <=> ((~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11851,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s76) | (~trans(s99, s76))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11850])).
% 50.20/50.36 tff(11852,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11851, 11849])).
% 50.20/50.36 tff(11853,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11854,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11853, 11852])).
% 50.20/50.36 tff(11855,plain,
% 50.20/50.36 (always5(s76) | (~trans(s99, s76))),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11854, 6332, 11624])).
% 50.20/50.36 tff(11856,plain,
% 50.20/50.36 (~trans(s99, s76)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11855, 11779])).
% 50.20/50.36 tff(11857,assumption,(~always5(s77)), introduced(assumption)).
% 50.20/50.36 tff(11858,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s77) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11859,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s77)) | always5(s77)) <=> ((~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11860,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s77) | (~trans(s99, s77))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11859])).
% 50.20/50.36 tff(11861,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11860, 11858])).
% 50.20/50.36 tff(11862,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11863,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11862, 11861])).
% 50.20/50.36 tff(11864,plain,
% 50.20/50.36 ($false),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11863, 10792, 6332, 11624, 11857])).
% 50.20/50.36 tff(11865,plain,((~trans(s99, s77)) | always5(s77)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.36 tff(11866,plain,
% 50.20/50.36 (~trans(s99, s77)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11865, 11778])).
% 50.20/50.36 tff(11867,assumption,(~always5(s78)), introduced(assumption)).
% 50.20/50.36 tff(11868,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s78) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11869,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s78)) | always5(s78)) <=> ((~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11870,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s78) | (~trans(s99, s78))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11869])).
% 50.20/50.36 tff(11871,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11870, 11868])).
% 50.20/50.36 tff(11872,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11873,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11872, 11871])).
% 50.20/50.36 tff(11874,plain,
% 50.20/50.36 ($false),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11873, 10715, 6332, 11624, 11867])).
% 50.20/50.36 tff(11875,plain,((~trans(s99, s78)) | always5(s78)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.36 tff(11876,plain,
% 50.20/50.36 (~trans(s99, s78)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11875, 11777])).
% 50.20/50.36 tff(11877,assumption,(~trans(s99, s43)), introduced(assumption)).
% 50.20/50.36 tff(11878,assumption,(~always5(s80)), introduced(assumption)).
% 50.20/50.36 tff(11879,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s80) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11880,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s80)) | always5(s80)) <=> ((~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11881,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s80) | (~trans(s99, s80))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11880])).
% 50.20/50.36 tff(11882,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11881, 11879])).
% 50.20/50.36 tff(11883,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11884,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11883, 11882])).
% 50.20/50.36 tff(11885,plain,
% 50.20/50.36 ($false),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11884, 10550, 6332, 11624, 11878])).
% 50.20/50.36 tff(11886,plain,((~trans(s99, s80)) | always5(s80)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.36 tff(11887,plain,
% 50.20/50.36 (~trans(s99, s80)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11886, 11775])).
% 50.20/50.36 tff(11888,assumption,(~always5(s79)), introduced(assumption)).
% 50.20/50.36 tff(11889,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s79) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11890,plain,
% 50.20/50.36 (((~always5(s99)) | (~trans(s99, s79)) | always5(s79)) <=> ((~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 50.20/50.36 inference(rewrite,[status(thm)],[])).
% 50.20/50.36 tff(11891,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s79) | (~trans(s99, s79))))),
% 50.20/50.36 inference(monotonicity,[status(thm)],[11890])).
% 50.20/50.36 tff(11892,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 50.20/50.36 inference(transitivity,[status(thm)],[11891, 11889])).
% 50.20/50.36 tff(11893,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))),
% 50.20/50.36 inference(quant_inst,[status(thm)],[])).
% 50.20/50.36 tff(11894,plain,
% 50.20/50.36 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79))),
% 50.20/50.36 inference(modus_ponens,[status(thm)],[11893, 11892])).
% 50.20/50.36 tff(11895,plain,
% 50.20/50.36 ($false),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11894, 10517, 6332, 11624, 11888])).
% 50.20/50.36 tff(11896,plain,((~trans(s99, s79)) | always5(s79)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.36 tff(11897,plain,
% 50.20/50.36 (~trans(s99, s79)),
% 50.20/50.36 inference(unit_resolution,[status(thm)],[11896, 11776])).
% 50.20/50.36 tff(11898,assumption,(~always5(s81)), introduced(assumption)).
% 50.20/50.36 tff(11899,plain,
% 50.20/50.36 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s81) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11900,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s81)) | always5(s81)) <=> ((~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11901,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s81) | (~trans(s99, s81))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11900])).
% 50.20/50.37 tff(11902,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11901, 11899])).
% 50.20/50.37 tff(11903,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11904,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11903, 11902])).
% 50.20/50.37 tff(11905,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11904, 10396, 6332, 11624, 11898])).
% 50.20/50.37 tff(11906,plain,((~trans(s99, s81)) | always5(s81)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(11907,plain,
% 50.20/50.37 (~trans(s99, s81)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11906, 11774])).
% 50.20/50.37 tff(11908,assumption,(~always5(s82)), introduced(assumption)).
% 50.20/50.37 tff(11909,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s82) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11910,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s82)) | always5(s82)) <=> ((~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11911,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s82) | (~trans(s99, s82))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11910])).
% 50.20/50.37 tff(11912,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11911, 11909])).
% 50.20/50.37 tff(11913,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11914,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11913, 11912])).
% 50.20/50.37 tff(11915,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11914, 10429, 6332, 11624, 11908])).
% 50.20/50.37 tff(11916,plain,((~trans(s99, s82)) | always5(s82)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(11917,plain,
% 50.20/50.37 (~trans(s99, s82)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11916, 11773])).
% 50.20/50.37 tff(11918,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s68) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11919,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s68)) | always5(s68)) <=> ((~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11920,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s68) | (~trans(s99, s68))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11919])).
% 50.20/50.37 tff(11921,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11920, 11918])).
% 50.20/50.37 tff(11922,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11923,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11922, 11921])).
% 50.20/50.37 tff(11924,plain,
% 50.20/50.37 (always5(s68) | (~trans(s99, s68))),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11923, 6332, 11624])).
% 50.20/50.37 tff(11925,plain,
% 50.20/50.37 (~trans(s99, s68)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11924, 11813])).
% 50.20/50.37 tff(11926,plain,
% 50.20/50.37 (~always5(s48)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[6988, 11840])).
% 50.20/50.37 tff(11927,plain,
% 50.20/50.37 (~always5(s47)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[6996, 11926])).
% 50.20/50.37 tff(11928,plain,
% 50.20/50.37 (~always5(s46)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[7004, 11927])).
% 50.20/50.37 tff(11929,plain,
% 50.20/50.37 (~always5(s45)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[7012, 11928])).
% 50.20/50.37 tff(11930,plain,
% 50.20/50.37 (~always5(s44)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[7020, 11929])).
% 50.20/50.37 tff(11931,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s44) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11932,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s44)) | always5(s44)) <=> ((~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11933,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s44) | (~trans(s99, s44))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11932])).
% 50.20/50.37 tff(11934,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11933, 11931])).
% 50.20/50.37 tff(11935,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11936,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11935, 11934])).
% 50.20/50.37 tff(11937,plain,
% 50.20/50.37 (always5(s44) | (~trans(s99, s44))),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11936, 6332, 11624])).
% 50.20/50.37 tff(11938,plain,
% 50.20/50.37 (~trans(s99, s44)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11937, 11930])).
% 50.20/50.37 tff(11939,assumption,(~always5(s83)), introduced(assumption)).
% 50.20/50.37 tff(11940,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s83) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11941,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s83)) | always5(s83)) <=> ((~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11942,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s83) | (~trans(s99, s83))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11941])).
% 50.20/50.37 tff(11943,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11942, 11940])).
% 50.20/50.37 tff(11944,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11945,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11944, 11943])).
% 50.20/50.37 tff(11946,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11945, 10737, 6332, 11624, 11939])).
% 50.20/50.37 tff(11947,plain,((~trans(s99, s83)) | always5(s83)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(11948,plain,
% 50.20/50.37 (~trans(s99, s83)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11947, 11772])).
% 50.20/50.37 tff(11949,assumption,(~always5(s84)), introduced(assumption)).
% 50.20/50.37 tff(11950,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s84) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11951,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s84)) | always5(s84)) <=> ((~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11952,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s84) | (~trans(s99, s84))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11951])).
% 50.20/50.37 tff(11953,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11952, 11950])).
% 50.20/50.37 tff(11954,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11955,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11954, 11953])).
% 50.20/50.37 tff(11956,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11955, 10220, 6332, 11624, 11949])).
% 50.20/50.37 tff(11957,plain,((~trans(s99, s84)) | always5(s84)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(11958,plain,
% 50.20/50.37 (~trans(s99, s84)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11957, 11771])).
% 50.20/50.37 tff(11959,assumption,(~trans(s99, s41)), introduced(assumption)).
% 50.20/50.37 tff(11960,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s51) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11961,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s51)) | always5(s51)) <=> ((~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11962,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s51) | (~trans(s99, s51))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11961])).
% 50.20/50.37 tff(11963,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11962, 11960])).
% 50.20/50.37 tff(11964,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11965,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11964, 11963])).
% 50.20/50.37 tff(11966,plain,
% 50.20/50.37 (always5(s51) | (~trans(s99, s51))),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11965, 6332, 11624])).
% 50.20/50.37 tff(11967,plain,
% 50.20/50.37 (~trans(s99, s51)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11966, 11838])).
% 50.20/50.37 tff(11968,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s50) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11969,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s50)) | always5(s50)) <=> ((~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11970,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s50) | (~trans(s99, s50))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11969])).
% 50.20/50.37 tff(11971,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11970, 11968])).
% 50.20/50.37 tff(11972,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11973,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11972, 11971])).
% 50.20/50.37 tff(11974,plain,
% 50.20/50.37 (always5(s50) | (~trans(s99, s50))),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11973, 6332, 11624])).
% 50.20/50.37 tff(11975,plain,
% 50.20/50.37 (~trans(s99, s50)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11974, 11839])).
% 50.20/50.37 tff(11976,assumption,(~always5(s63)), introduced(assumption)).
% 50.20/50.37 tff(11977,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s63) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11978,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s63)) | always5(s63)) <=> ((~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11979,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s63) | (~trans(s99, s63))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11978])).
% 50.20/50.37 tff(11980,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11979, 11977])).
% 50.20/50.37 tff(11981,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11982,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11981, 11980])).
% 50.20/50.37 tff(11983,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11982, 9758, 6332, 11624, 11976])).
% 50.20/50.37 tff(11984,plain,((~trans(s99, s63)) | always5(s63)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(11985,plain,
% 50.20/50.37 (~trans(s99, s63)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11984, 11818])).
% 50.20/50.37 tff(11986,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s70) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11987,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s70)) | always5(s70)) <=> ((~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11988,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s70) | (~trans(s99, s70))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11987])).
% 50.20/50.37 tff(11989,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11988, 11986])).
% 50.20/50.37 tff(11990,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(11991,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[11990, 11989])).
% 50.20/50.37 tff(11992,plain,
% 50.20/50.37 (always5(s70) | (~trans(s99, s70))),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11991, 6332, 11624])).
% 50.20/50.37 tff(11993,plain,
% 50.20/50.37 (~trans(s99, s70)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[11992, 11811])).
% 50.20/50.37 tff(11994,assumption,(~trans(s99, s42)), introduced(assumption)).
% 50.20/50.37 tff(11995,assumption,(~always5(s47)), introduced(assumption)).
% 50.20/50.37 tff(11996,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s47) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11997,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s47)) | always5(s47)) <=> ((~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(11998,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s47) | (~trans(s99, s47))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[11997])).
% 50.20/50.37 tff(11999,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[11998, 11996])).
% 50.20/50.37 tff(12000,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(12001,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[12000, 11999])).
% 50.20/50.37 tff(12002,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12001, 9879, 6332, 11624, 11995])).
% 50.20/50.37 tff(12003,plain,((~trans(s99, s47)) | always5(s47)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(12004,plain,
% 50.20/50.37 (~trans(s99, s47)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12003, 11927])).
% 50.20/50.37 tff(12005,assumption,(~always5(s52)), introduced(assumption)).
% 50.20/50.37 tff(12006,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s52) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12007,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s52)) | always5(s52)) <=> ((~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12008,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s52) | (~trans(s99, s52))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[12007])).
% 50.20/50.37 tff(12009,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[12008, 12006])).
% 50.20/50.37 tff(12010,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(12011,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[12010, 12009])).
% 50.20/50.37 tff(12012,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12011, 9945, 6332, 11624, 12005])).
% 50.20/50.37 tff(12013,plain,((~trans(s99, s52)) | always5(s52)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(12014,plain,
% 50.20/50.37 (~trans(s99, s52)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12013, 11837])).
% 50.20/50.37 tff(12015,assumption,(~always5(s72)), introduced(assumption)).
% 50.20/50.37 tff(12016,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s72) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12017,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s72)) | always5(s72)) <=> ((~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12018,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s72) | (~trans(s99, s72))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[12017])).
% 50.20/50.37 tff(12019,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[12018, 12016])).
% 50.20/50.37 tff(12020,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(12021,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[12020, 12019])).
% 50.20/50.37 tff(12022,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12021, 10198, 6332, 11624, 12015])).
% 50.20/50.37 tff(12023,plain,((~trans(s99, s72)) | always5(s72)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(12024,plain,
% 50.20/50.37 (~trans(s99, s72)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12023, 11809])).
% 50.20/50.37 tff(12025,assumption,(~always5(s55)), introduced(assumption)).
% 50.20/50.37 tff(12026,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s55) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12027,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s55)) | always5(s55)) <=> ((~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12028,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s55) | (~trans(s99, s55))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[12027])).
% 50.20/50.37 tff(12029,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[12028, 12026])).
% 50.20/50.37 tff(12030,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(12031,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[12030, 12029])).
% 50.20/50.37 tff(12032,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12031, 9989, 6332, 11624, 12025])).
% 50.20/50.37 tff(12033,plain,((~trans(s99, s55)) | always5(s55)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(12034,plain,
% 50.20/50.37 (~trans(s99, s55)),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12033, 11834])).
% 50.20/50.37 tff(12035,assumption,(~always5(s66)), introduced(assumption)).
% 50.20/50.37 tff(12036,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s66) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12037,plain,
% 50.20/50.37 (((~always5(s99)) | (~trans(s99, s66)) | always5(s66)) <=> ((~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 50.20/50.37 inference(rewrite,[status(thm)],[])).
% 50.20/50.37 tff(12038,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s66) | (~trans(s99, s66))))),
% 50.20/50.37 inference(monotonicity,[status(thm)],[12037])).
% 50.20/50.37 tff(12039,plain,
% 50.20/50.37 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 50.20/50.37 inference(transitivity,[status(thm)],[12038, 12036])).
% 50.20/50.37 tff(12040,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))),
% 50.20/50.37 inference(quant_inst,[status(thm)],[])).
% 50.20/50.37 tff(12041,plain,
% 50.20/50.37 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66))),
% 50.20/50.37 inference(modus_ponens,[status(thm)],[12040, 12039])).
% 50.20/50.37 tff(12042,plain,
% 50.20/50.37 ($false),
% 50.20/50.37 inference(unit_resolution,[status(thm)],[12041, 10231, 6332, 11624, 12035])).
% 50.20/50.37 tff(12043,plain,((~trans(s99, s66)) | always5(s66)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.37 tff(12044,plain,
% 50.20/50.37 (~trans(s99, s66)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12043, 11815])).
% 50.20/50.38 tff(12045,assumption,(~trans(s99, s40)), introduced(assumption)).
% 50.20/50.38 tff(12046,assumption,(~always5(s46)), introduced(assumption)).
% 50.20/50.38 tff(12047,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s46) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12048,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s46)) | always5(s46)) <=> ((~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12049,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s46) | (~trans(s99, s46))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12048])).
% 50.20/50.38 tff(12050,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12049, 12047])).
% 50.20/50.38 tff(12051,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12052,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12051, 12050])).
% 50.20/50.38 tff(12053,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12052, 10000, 6332, 11624, 12046])).
% 50.20/50.38 tff(12054,plain,((~trans(s99, s46)) | always5(s46)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12055,plain,
% 50.20/50.38 (~trans(s99, s46)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12054, 11928])).
% 50.20/50.38 tff(12056,assumption,(~always5(s71)), introduced(assumption)).
% 50.20/50.38 tff(12057,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s71) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12058,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s71)) | always5(s71)) <=> ((~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12059,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s71) | (~trans(s99, s71))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12058])).
% 50.20/50.38 tff(12060,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12059, 12057])).
% 50.20/50.38 tff(12061,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12062,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12061, 12060])).
% 50.20/50.38 tff(12063,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12062, 10330, 6332, 11624, 12056])).
% 50.20/50.38 tff(12064,plain,((~trans(s99, s71)) | always5(s71)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12065,plain,
% 50.20/50.38 (~trans(s99, s71)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12064, 11810])).
% 50.20/50.38 tff(12066,assumption,(~always5(s48)), introduced(assumption)).
% 50.20/50.38 tff(12067,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s48) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12068,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s48)) | always5(s48)) <=> ((~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12069,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s48) | (~trans(s99, s48))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12068])).
% 50.20/50.38 tff(12070,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12069, 12067])).
% 50.20/50.38 tff(12071,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12072,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12071, 12070])).
% 50.20/50.38 tff(12073,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12072, 10077, 6332, 11624, 12066])).
% 50.20/50.38 tff(12074,plain,((~trans(s99, s48)) | always5(s48)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12075,plain,
% 50.20/50.38 (~trans(s99, s48)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12074, 11926])).
% 50.20/50.38 tff(12076,assumption,(~always5(s53)), introduced(assumption)).
% 50.20/50.38 tff(12077,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s53) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12078,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s53)) | always5(s53)) <=> ((~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12079,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s53) | (~trans(s99, s53))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12078])).
% 50.20/50.38 tff(12080,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12079, 12077])).
% 50.20/50.38 tff(12081,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12082,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12081, 12080])).
% 50.20/50.38 tff(12083,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12082, 10583, 6332, 11624, 12076])).
% 50.20/50.38 tff(12084,plain,((~trans(s99, s53)) | always5(s53)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12085,plain,
% 50.20/50.38 (~trans(s99, s53)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12084, 11836])).
% 50.20/50.38 tff(12086,assumption,(~always5(s56)), introduced(assumption)).
% 50.20/50.38 tff(12087,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s56) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12088,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s56)) | always5(s56)) <=> ((~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12089,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s56) | (~trans(s99, s56))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12088])).
% 50.20/50.38 tff(12090,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12089, 12087])).
% 50.20/50.38 tff(12091,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12092,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12091, 12090])).
% 50.20/50.38 tff(12093,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12092, 10572, 6332, 11624, 12086])).
% 50.20/50.38 tff(12094,plain,((~trans(s99, s56)) | always5(s56)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12095,plain,
% 50.20/50.38 (~trans(s99, s56)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12094, 11833])).
% 50.20/50.38 tff(12096,assumption,(~always5(s67)), introduced(assumption)).
% 50.20/50.38 tff(12097,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s67) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12098,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s67)) | always5(s67)) <=> ((~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12099,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s67) | (~trans(s99, s67))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12098])).
% 50.20/50.38 tff(12100,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12099, 12097])).
% 50.20/50.38 tff(12101,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12102,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12101, 12100])).
% 50.20/50.38 tff(12103,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12102, 10539, 6332, 11624, 12096])).
% 50.20/50.38 tff(12104,plain,((~trans(s99, s67)) | always5(s67)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12105,plain,
% 50.20/50.38 (~trans(s99, s67)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12104, 11814])).
% 50.20/50.38 tff(12106,assumption,(~always5(s69)), introduced(assumption)).
% 50.20/50.38 tff(12107,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s69) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12108,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s69)) | always5(s69)) <=> ((~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12109,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s69) | (~trans(s99, s69))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12108])).
% 50.20/50.38 tff(12110,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12109, 12107])).
% 50.20/50.38 tff(12111,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12112,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12111, 12110])).
% 50.20/50.38 tff(12113,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12112, 10616, 6332, 11624, 12106])).
% 50.20/50.38 tff(12114,plain,((~trans(s99, s69)) | always5(s69)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12115,plain,
% 50.20/50.38 (~trans(s99, s69)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12114, 11812])).
% 50.20/50.38 tff(12116,assumption,(~always5(s54)), introduced(assumption)).
% 50.20/50.38 tff(12117,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s54) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12118,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s54)) | always5(s54)) <=> ((~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12119,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s54) | (~trans(s99, s54))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12118])).
% 50.20/50.38 tff(12120,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12119, 12117])).
% 50.20/50.38 tff(12121,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12122,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12121, 12120])).
% 50.20/50.38 tff(12123,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12122, 10176, 6332, 11624, 12116])).
% 50.20/50.38 tff(12124,plain,((~trans(s99, s54)) | always5(s54)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12125,plain,
% 50.20/50.38 (~trans(s99, s54)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12124, 11835])).
% 50.20/50.38 tff(12126,assumption,(~always5(s59)), introduced(assumption)).
% 50.20/50.38 tff(12127,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s59) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12128,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s59)) | always5(s59)) <=> ((~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12129,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s59) | (~trans(s99, s59))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12128])).
% 50.20/50.38 tff(12130,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12129, 12127])).
% 50.20/50.38 tff(12131,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12132,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 50.20/50.38 tff(12133,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12132, 10649, 6332, 11624, 12126])).
% 50.20/50.38 tff(12134,plain,((~trans(s99, s59)) | always5(s59)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12135,plain,
% 50.20/50.38 (~trans(s99, s59)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12134, 11822])).
% 50.20/50.38 tff(12136,assumption,(~always5(s65)), introduced(assumption)).
% 50.20/50.38 tff(12137,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s65) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12138,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s65)) | always5(s65)) <=> ((~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12139,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s65) | (~trans(s99, s65))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12138])).
% 50.20/50.38 tff(12140,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12139, 12137])).
% 50.20/50.38 tff(12141,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12142,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12141, 12140])).
% 50.20/50.38 tff(12143,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12142, 10462, 6332, 11624, 12136])).
% 50.20/50.38 tff(12144,plain,((~trans(s99, s65)) | always5(s65)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12145,plain,
% 50.20/50.38 (~trans(s99, s65)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12144, 11816])).
% 50.20/50.38 tff(12146,assumption,(~always5(s58)), introduced(assumption)).
% 50.20/50.38 tff(12147,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s58) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12148,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s58)) | always5(s58)) <=> ((~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12149,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s58) | (~trans(s99, s58))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12148])).
% 50.20/50.38 tff(12150,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12149, 12147])).
% 50.20/50.38 tff(12151,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12152,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12151, 12150])).
% 50.20/50.38 tff(12153,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12152, 10473, 6332, 11624, 12146])).
% 50.20/50.38 tff(12154,plain,((~trans(s99, s58)) | always5(s58)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12155,plain,
% 50.20/50.38 (~trans(s99, s58)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12154, 11823])).
% 50.20/50.38 tff(12156,assumption,(~always5(s64)), introduced(assumption)).
% 50.20/50.38 tff(12157,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s64) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12158,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s64)) | always5(s64)) <=> ((~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12159,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s64) | (~trans(s99, s64))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12158])).
% 50.20/50.38 tff(12160,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12159, 12157])).
% 50.20/50.38 tff(12161,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12162,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12161, 12160])).
% 50.20/50.38 tff(12163,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12162, 10484, 6332, 11624, 12156])).
% 50.20/50.38 tff(12164,plain,((~trans(s99, s64)) | always5(s64)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12165,plain,
% 50.20/50.38 (~trans(s99, s64)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12164, 11817])).
% 50.20/50.38 tff(12166,assumption,(~always5(s60)), introduced(assumption)).
% 50.20/50.38 tff(12167,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s60) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12168,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s60)) | always5(s60)) <=> ((~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12169,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s60) | (~trans(s99, s60))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12168])).
% 50.20/50.38 tff(12170,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12169, 12167])).
% 50.20/50.38 tff(12171,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12172,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12171, 12170])).
% 50.20/50.38 tff(12173,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12172, 10418, 6332, 11624, 12166])).
% 50.20/50.38 tff(12174,plain,((~trans(s99, s60)) | always5(s60)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12175,plain,
% 50.20/50.38 (~trans(s99, s60)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12174, 11821])).
% 50.20/50.38 tff(12176,assumption,(~always5(s62)), introduced(assumption)).
% 50.20/50.38 tff(12177,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s62) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12178,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s62)) | always5(s62)) <=> ((~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12179,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s62) | (~trans(s99, s62))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12178])).
% 50.20/50.38 tff(12180,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12179, 12177])).
% 50.20/50.38 tff(12181,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12182,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62))),
% 50.20/50.38 inference(modus_ponens,[status(thm)],[12181, 12180])).
% 50.20/50.38 tff(12183,plain,
% 50.20/50.38 ($false),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12182, 10407, 6332, 11624, 12176])).
% 50.20/50.38 tff(12184,plain,((~trans(s99, s62)) | always5(s62)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.38 tff(12185,plain,
% 50.20/50.38 (~trans(s99, s62)),
% 50.20/50.38 inference(unit_resolution,[status(thm)],[12184, 11819])).
% 50.20/50.38 tff(12186,assumption,(~always5(s61)), introduced(assumption)).
% 50.20/50.38 tff(12187,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s61) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12188,plain,
% 50.20/50.38 (((~always5(s99)) | (~trans(s99, s61)) | always5(s61)) <=> ((~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 50.20/50.38 inference(rewrite,[status(thm)],[])).
% 50.20/50.38 tff(12189,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s61) | (~trans(s99, s61))))),
% 50.20/50.38 inference(monotonicity,[status(thm)],[12188])).
% 50.20/50.38 tff(12190,plain,
% 50.20/50.38 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 50.20/50.38 inference(transitivity,[status(thm)],[12189, 12187])).
% 50.20/50.38 tff(12191,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))),
% 50.20/50.38 inference(quant_inst,[status(thm)],[])).
% 50.20/50.38 tff(12192,plain,
% 50.20/50.38 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12191, 12190])).
% 50.20/50.39 tff(12193,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12192, 10704, 6332, 11624, 12186])).
% 50.20/50.39 tff(12194,plain,((~trans(s99, s61)) | always5(s61)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12195,plain,
% 50.20/50.39 (~trans(s99, s61)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12194, 11820])).
% 50.20/50.39 tff(12196,assumption,(~always5(s45)), introduced(assumption)).
% 50.20/50.39 tff(12197,plain,
% 50.20/50.39 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s45) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12198,plain,
% 50.20/50.39 (((~always5(s99)) | (~trans(s99, s45)) | always5(s45)) <=> ((~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12199,plain,
% 50.20/50.39 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s45) | (~trans(s99, s45))))),
% 50.20/50.39 inference(monotonicity,[status(thm)],[12198])).
% 50.20/50.39 tff(12200,plain,
% 50.20/50.39 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 50.20/50.39 inference(transitivity,[status(thm)],[12199, 12197])).
% 50.20/50.39 tff(12201,plain,
% 50.20/50.39 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12202,plain,
% 50.20/50.39 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12201, 12200])).
% 50.20/50.39 tff(12203,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12202, 10385, 6332, 11624, 12196])).
% 50.20/50.39 tff(12204,plain,((~trans(s99, s45)) | always5(s45)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12205,plain,
% 50.20/50.39 (~trans(s99, s45)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12204, 11929])).
% 50.20/50.39 tff(12206,assumption,(node3(c_bit1, s99, s98)), introduced(assumption)).
% 50.20/50.39 tff(12207,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12208,plain,
% 50.20/50.39 ((node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98))) <=> ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12209,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98))))),
% 50.20/50.39 inference(monotonicity,[status(thm)],[12208])).
% 50.20/50.39 tff(12210,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 50.20/50.39 inference(transitivity,[status(thm)],[12209, 12207])).
% 50.20/50.39 tff(12211,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12212,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12211, 12210])).
% 50.20/50.39 tff(12213,plain,
% 50.20/50.39 ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12212, 130, 12206])).
% 50.20/50.39 tff(12214,plain,
% 50.20/50.39 (node2(c_bit1, s99)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12213, 6522])).
% 50.20/50.39 tff(12215,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12216,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12217,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12216, 12215])).
% 50.20/50.39 tff(12218,plain,
% 50.20/50.39 ((~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99))),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12217, 104, 6581])).
% 50.20/50.39 tff(12219,plain,
% 50.20/50.39 (~m_counter_cell_v_value(c_bit1, s99)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12218, 12214])).
% 50.20/50.39 tff(12220,plain,
% 50.20/50.39 (node1(c_bit1, s98)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[6543, 12219])).
% 50.20/50.39 tff(12221,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[6529, 3095, 12220, 6522, 6521])).
% 50.20/50.39 tff(12222,plain,((~m_counter_cell_v_value(c_bit1, s98)) | (~node3(c_bit1, s99, s98))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12223,plain,
% 50.20/50.39 (~node3(c_bit1, s99, s98)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12222, 6490])).
% 50.20/50.39 tff(12224,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit1, s99, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit1, s99, s98))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12225,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit1, s99, s98))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12226,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit1, s99, s98)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12225, 12224])).
% 50.20/50.39 tff(12227,plain,
% 50.20/50.39 ((~trans(s99, s98)) | node3(c_bit1, s99, s98)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12226, 21])).
% 50.20/50.39 tff(12228,plain,
% 50.20/50.39 (~trans(s99, s98)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12227, 12223])).
% 50.20/50.39 tff(12229,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12230,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12231,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12230, 12229])).
% 50.20/50.39 tff(12232,plain,
% 50.20/50.39 ((~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12231, 2906, 4428])).
% 50.20/50.39 tff(12233,plain,
% 50.20/50.39 (m_counter_cell_v_carry_out(c_bit1, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12232, 4419])).
% 50.20/50.39 tff(12234,plain,
% 50.20/50.39 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12235,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12236,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s43)) | m_counter_cell_v_carry_in(c_bit2, s43)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12235, 12234])).
% 50.20/50.39 tff(12237,plain,
% 50.20/50.39 (m_counter_cell_v_carry_in(c_bit2, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12236, 6183, 12233])).
% 50.20/50.39 tff(12238,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12239,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12240,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12239, 12238])).
% 50.20/50.39 tff(12241,plain,
% 50.20/50.39 (~node4(c_bit1, s41)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12240, 2823, 4350])).
% 50.20/50.39 tff(12242,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12243,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12244,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12243, 12242])).
% 50.20/50.39 tff(12245,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_out(c_bit1, s41)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12244, 2836, 12241])).
% 50.20/50.39 tff(12246,assumption,(m_counter_cell_v_carry_in(c_bit2, s41)), introduced(assumption)).
% 50.20/50.39 tff(12247,assumption,(~m_counter_cell_v_carry_out(c_bit1, s41)), introduced(assumption)).
% 50.20/50.39 tff(12248,plain,
% 50.20/50.39 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12249,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12250,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s41)) | m_counter_cell_v_carry_out(c_bit1, s41)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12249, 12248])).
% 50.20/50.39 tff(12251,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12250, 6291, 12247, 12246])).
% 50.20/50.39 tff(12252,plain,((~m_counter_cell_v_carry_in(c_bit2, s41)) | m_counter_cell_v_carry_out(c_bit1, s41)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12253,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_in(c_bit2, s41)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12252, 12245])).
% 50.20/50.39 tff(12254,assumption,(~m_counter_cell_v_carry_out(c_bit1, s39)), introduced(assumption)).
% 50.20/50.39 tff(12255,assumption,(m_counter_cell_v_value(c_bit1, s39)), introduced(assumption)).
% 50.20/50.39 tff(12256,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12257,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12258,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12257, 12256])).
% 50.20/50.39 tff(12259,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12258, 2906, 12255, 2925, 12254])).
% 50.20/50.39 tff(12260,plain,(m_counter_cell_v_carry_out(c_bit1, s39) | (~m_counter_cell_v_value(c_bit1, s39))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12261,plain,
% 50.20/50.39 (m_counter_cell_v_carry_out(c_bit1, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12260, 4295])).
% 50.20/50.39 tff(12262,assumption,(~m_counter_cell_v_carry_in(c_bit2, s39)), introduced(assumption)).
% 50.20/50.39 tff(12263,assumption,(m_counter_cell_v_carry_out(c_bit1, s39)), introduced(assumption)).
% 50.20/50.39 tff(12264,plain,
% 50.20/50.39 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12265,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12266,plain,
% 50.20/50.39 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s39)) | m_counter_cell_v_carry_in(c_bit2, s39)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12265, 12264])).
% 50.20/50.39 tff(12267,plain,
% 50.20/50.39 ($false),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12266, 6183, 12263, 12262])).
% 50.20/50.39 tff(12268,plain,(m_counter_cell_v_carry_in(c_bit2, s39) | (~m_counter_cell_v_carry_out(c_bit1, s39))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.39 tff(12269,plain,
% 50.20/50.39 (m_counter_cell_v_carry_in(c_bit2, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12268, 12261])).
% 50.20/50.39 tff(12270,assumption,(m_counter_cell_v_carry_in(c_bit2, s39)), introduced(assumption)).
% 50.20/50.39 tff(12271,assumption,(always5(s39)), introduced(assumption)).
% 50.20/50.39 tff(12272,plain,
% 50.20/50.39 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12273,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12274,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12273, 12272])).
% 50.20/50.39 tff(12275,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_out(c_bit2, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12274, 6200, 12271])).
% 50.20/50.39 tff(12276,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12277,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12278,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12277, 12276])).
% 50.20/50.39 tff(12279,plain,
% 50.20/50.39 (~m_counter_cell_v_value(c_bit2, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12278, 2906, 12270, 12275])).
% 50.20/50.39 tff(12280,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12281,plain,
% 50.20/50.39 (((~node1(c_bit2, s39)) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12282,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s39)) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39))))),
% 50.20/50.39 inference(monotonicity,[status(thm)],[12281])).
% 50.20/50.39 tff(12283,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s39)) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39)))),
% 50.20/50.39 inference(transitivity,[status(thm)],[12282, 12280])).
% 50.20/50.39 tff(12284,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s39)) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12285,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_value(c_bit2, s39) | (~node1(c_bit2, s39))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12284, 12283])).
% 50.20/50.39 tff(12286,plain,
% 50.20/50.39 (~node1(c_bit2, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12285, 55, 12279, 12270])).
% 50.20/50.39 tff(12287,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit2, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit2, s39, s40))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12288,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit2, s39, s40))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12289,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit2, s39, s40)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12288, 12287])).
% 50.20/50.39 tff(12290,plain,
% 50.20/50.39 (node3(c_bit2, s39, s40)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12289, 21, 1217])).
% 50.20/50.39 tff(12291,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12292,plain,
% 50.20/50.39 ((node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | m_counter_cell_v_value(c_bit2, s40)) <=> (m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12293,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | m_counter_cell_v_value(c_bit2, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40))))),
% 50.20/50.39 inference(monotonicity,[status(thm)],[12292])).
% 50.20/50.39 tff(12294,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | m_counter_cell_v_value(c_bit2, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 50.20/50.39 inference(transitivity,[status(thm)],[12293, 12291])).
% 50.20/50.39 tff(12295,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | m_counter_cell_v_value(c_bit2, s40))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12296,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39) | (~node3(c_bit2, s39, s40))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12295, 12294])).
% 50.20/50.39 tff(12297,plain,
% 50.20/50.39 (m_counter_cell_v_value(c_bit2, s40) | node1(c_bit2, s39)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12296, 84, 12290])).
% 50.20/50.39 tff(12298,plain,
% 50.20/50.39 (m_counter_cell_v_value(c_bit2, s40)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12297, 12286])).
% 50.20/50.39 tff(12299,plain,
% 50.20/50.39 (always5(s40)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[7060, 12271])).
% 50.20/50.39 tff(12300,plain,
% 50.20/50.39 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s40)) | (~m_counter_cell_v_carry_out(c_bit2, s40)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s40)) | (~m_counter_cell_v_carry_out(c_bit2, s40)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12301,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s40)) | (~m_counter_cell_v_carry_out(c_bit2, s40)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12302,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s40)) | (~m_counter_cell_v_carry_out(c_bit2, s40))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12301, 12300])).
% 50.20/50.39 tff(12303,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_out(c_bit2, s40)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12302, 6200, 12299])).
% 50.20/50.39 tff(12304,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s40)) | (~m_counter_cell_v_value(c_bit2, s40)) | m_counter_cell_v_carry_out(c_bit2, s40))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s40)) | (~m_counter_cell_v_value(c_bit2, s40)) | m_counter_cell_v_carry_out(c_bit2, s40))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12305,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s40)) | (~m_counter_cell_v_value(c_bit2, s40)) | m_counter_cell_v_carry_out(c_bit2, s40))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12306,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s40)) | (~m_counter_cell_v_value(c_bit2, s40)) | m_counter_cell_v_carry_out(c_bit2, s40)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12305, 12304])).
% 50.20/50.39 tff(12307,plain,
% 50.20/50.39 ((~m_counter_cell_v_carry_in(c_bit2, s40)) | (~m_counter_cell_v_value(c_bit2, s40))),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12306, 2906, 12303])).
% 50.20/50.39 tff(12308,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_in(c_bit2, s40)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12307, 12298])).
% 50.20/50.39 tff(12309,plain,
% 50.20/50.39 (always5(s41)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[7052, 12299])).
% 50.20/50.39 tff(12310,plain,
% 50.20/50.39 (always5(s42)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[7044, 12309])).
% 50.20/50.39 tff(12311,plain,
% 50.20/50.39 (always5(s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[7036, 12310])).
% 50.20/50.39 tff(12312,plain,
% 50.20/50.39 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s43)) | (~m_counter_cell_v_carry_out(c_bit2, s43)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s43)) | (~m_counter_cell_v_carry_out(c_bit2, s43)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12313,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s43)) | (~m_counter_cell_v_carry_out(c_bit2, s43)))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12314,plain,
% 50.20/50.39 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s43)) | (~m_counter_cell_v_carry_out(c_bit2, s43))),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12313, 12312])).
% 50.20/50.39 tff(12315,plain,
% 50.20/50.39 (~m_counter_cell_v_carry_out(c_bit2, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12314, 6200, 12311])).
% 50.20/50.39 tff(12316,assumption,(m_counter_cell_v_carry_in(c_bit2, s43)), introduced(assumption)).
% 50.20/50.39 tff(12317,plain,
% 50.20/50.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s43)) | (~m_counter_cell_v_value(c_bit2, s43)) | m_counter_cell_v_carry_out(c_bit2, s43))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | (~m_counter_cell_v_value(c_bit2, s43)) | m_counter_cell_v_carry_out(c_bit2, s43))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12318,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s43)) | (~m_counter_cell_v_value(c_bit2, s43)) | m_counter_cell_v_carry_out(c_bit2, s43))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12319,plain,
% 50.20/50.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | (~m_counter_cell_v_value(c_bit2, s43)) | m_counter_cell_v_carry_out(c_bit2, s43)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12318, 12317])).
% 50.20/50.39 tff(12320,plain,
% 50.20/50.39 ((~m_counter_cell_v_value(c_bit2, s43)) | m_counter_cell_v_carry_out(c_bit2, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12319, 2906, 12316])).
% 50.20/50.39 tff(12321,plain,
% 50.20/50.39 (~m_counter_cell_v_value(c_bit2, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12320, 12315])).
% 50.20/50.39 tff(12322,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit2, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit2, s42, s43))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12323,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit2, s42, s43))),
% 50.20/50.39 inference(quant_inst,[status(thm)],[])).
% 50.20/50.39 tff(12324,plain,
% 50.20/50.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit2, s42, s43)),
% 50.20/50.39 inference(modus_ponens,[status(thm)],[12323, 12322])).
% 50.20/50.39 tff(12325,plain,
% 50.20/50.39 (node3(c_bit2, s42, s43)),
% 50.20/50.39 inference(unit_resolution,[status(thm)],[12324, 21, 1307])).
% 50.20/50.39 tff(12326,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12327,plain,
% 50.20/50.39 ((node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | m_counter_cell_v_value(c_bit2, s43)) <=> (m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 50.20/50.39 inference(rewrite,[status(thm)],[])).
% 50.20/50.39 tff(12328,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | m_counter_cell_v_value(c_bit2, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43))))),
% 50.20/50.39 inference(monotonicity,[status(thm)],[12327])).
% 50.20/50.39 tff(12329,plain,
% 50.20/50.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | m_counter_cell_v_value(c_bit2, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12328, 12326])).
% 50.20/50.40 tff(12330,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | m_counter_cell_v_value(c_bit2, s43))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12331,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42) | (~node3(c_bit2, s42, s43))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12330, 12329])).
% 50.20/50.40 tff(12332,plain,
% 50.20/50.40 (m_counter_cell_v_value(c_bit2, s43) | node1(c_bit2, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12331, 84, 12325])).
% 50.20/50.40 tff(12333,plain,
% 50.20/50.40 (node1(c_bit2, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12332, 12321])).
% 50.20/50.40 tff(12334,assumption,(node4(c_bit1, s42)), introduced(assumption)).
% 50.20/50.40 tff(12335,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12336,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12337,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12336, 12335])).
% 50.20/50.40 tff(12338,plain,
% 50.20/50.40 ($false),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12337, 6276, 4396, 12334])).
% 50.20/50.40 tff(12339,plain,(~node4(c_bit1, s42)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.40 tff(12340,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12341,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12342,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42)),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12341, 12340])).
% 50.20/50.40 tff(12343,plain,
% 50.20/50.40 (~m_counter_cell_v_carry_out(c_bit1, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12342, 2836, 12339])).
% 50.20/50.40 tff(12344,plain,
% 50.20/50.40 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12345,plain,
% 50.20/50.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12346,plain,
% 50.20/50.40 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s42)) | m_counter_cell_v_carry_out(c_bit1, s42)),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12345, 12344])).
% 50.20/50.40 tff(12347,plain,
% 50.20/50.40 (~m_counter_cell_v_carry_in(c_bit2, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12346, 6291, 12343])).
% 50.20/50.40 tff(12348,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12349,plain,
% 50.20/50.40 (((~node1(c_bit2, s42)) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42))) <=> (m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12350,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s42)) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12349])).
% 50.20/50.40 tff(12351,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s42)) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12350, 12348])).
% 50.20/50.40 tff(12352,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s42)) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12353,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s42) | (~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12352, 12351])).
% 50.20/50.40 tff(12354,plain,
% 50.20/50.40 ((~m_counter_cell_v_value(c_bit2, s42)) | (~node1(c_bit2, s42))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12353, 3095, 12347])).
% 50.20/50.40 tff(12355,plain,
% 50.20/50.40 (~m_counter_cell_v_value(c_bit2, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12354, 12333])).
% 50.20/50.40 tff(12356,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit2, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit2, s41, s42))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12357,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit2, s41, s42))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12358,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit2, s41, s42)),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12357, 12356])).
% 50.20/50.40 tff(12359,plain,
% 50.20/50.40 (node3(c_bit2, s41, s42)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12358, 21, 1276])).
% 50.20/50.40 tff(12360,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12361,plain,
% 50.20/50.40 ((node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | m_counter_cell_v_value(c_bit2, s42)) <=> (m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12362,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | m_counter_cell_v_value(c_bit2, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12361])).
% 50.20/50.40 tff(12363,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | m_counter_cell_v_value(c_bit2, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12362, 12360])).
% 50.20/50.40 tff(12364,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | m_counter_cell_v_value(c_bit2, s42))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12365,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41) | (~node3(c_bit2, s41, s42))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12364, 12363])).
% 50.20/50.40 tff(12366,plain,
% 50.20/50.40 (m_counter_cell_v_value(c_bit2, s42) | node1(c_bit2, s41)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12365, 84, 12359])).
% 50.20/50.40 tff(12367,plain,
% 50.20/50.40 (node1(c_bit2, s41)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12366, 12355])).
% 50.20/50.40 tff(12368,assumption,(~m_counter_cell_v_carry_in(c_bit2, s41)), introduced(assumption)).
% 50.20/50.40 tff(12369,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12370,plain,
% 50.20/50.40 (((~node1(c_bit2, s41)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41))) <=> (m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12371,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s41)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12370])).
% 50.20/50.40 tff(12372,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s41)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12371, 12369])).
% 50.20/50.40 tff(12373,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s41)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12374,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_value(c_bit2, s41)) | (~node1(c_bit2, s41))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12373, 12372])).
% 50.20/50.40 tff(12375,plain,
% 50.20/50.40 (~m_counter_cell_v_value(c_bit2, s41)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12374, 3095, 12368, 12367])).
% 50.20/50.40 tff(12376,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit2, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit2, s40, s41))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12377,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit2, s40, s41))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12378,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit2, s40, s41)),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12377, 12376])).
% 50.20/50.40 tff(12379,plain,
% 50.20/50.40 (node3(c_bit2, s40, s41)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12378, 21, 1248])).
% 50.20/50.40 tff(12380,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12381,plain,
% 50.20/50.40 ((node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | m_counter_cell_v_value(c_bit2, s41)) <=> (m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12382,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | m_counter_cell_v_value(c_bit2, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12381])).
% 50.20/50.40 tff(12383,plain,
% 50.20/50.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | m_counter_cell_v_value(c_bit2, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12382, 12380])).
% 50.20/50.40 tff(12384,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | m_counter_cell_v_value(c_bit2, s41))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12385,plain,
% 50.20/50.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40) | (~node3(c_bit2, s40, s41))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12384, 12383])).
% 50.20/50.40 tff(12386,plain,
% 50.20/50.40 (m_counter_cell_v_value(c_bit2, s41) | node1(c_bit2, s40)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12385, 84, 12379])).
% 50.20/50.40 tff(12387,plain,
% 50.20/50.40 (node1(c_bit2, s40)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12386, 12375])).
% 50.20/50.40 tff(12388,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12389,plain,
% 50.20/50.40 (((~node1(c_bit2, s40)) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40))) <=> (m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12390,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s40)) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12389])).
% 50.20/50.40 tff(12391,plain,
% 50.20/50.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s40)) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12390, 12388])).
% 50.20/50.40 tff(12392,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s40)) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12393,plain,
% 50.20/50.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40)) | (~node1(c_bit2, s40))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12392, 12391])).
% 50.20/50.40 tff(12394,plain,
% 50.20/50.40 (m_counter_cell_v_carry_in(c_bit2, s40) | (~m_counter_cell_v_value(c_bit2, s40))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12393, 3095, 12387])).
% 50.20/50.40 tff(12395,plain,
% 50.20/50.40 ($false),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12394, 12308, 12298])).
% 50.20/50.40 tff(12396,plain,((~always5(s39)) | (~m_counter_cell_v_carry_in(c_bit2, s39)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_carry_in(c_bit2, s43))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.40 tff(12397,plain,
% 50.20/50.40 ((~always5(s39)) | m_counter_cell_v_carry_in(c_bit2, s41) | (~m_counter_cell_v_carry_in(c_bit2, s43))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12396, 12269])).
% 50.20/50.40 tff(12398,plain,
% 50.20/50.40 (~always5(s39)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12397, 12253, 12237])).
% 50.20/50.40 tff(12399,plain,
% 50.20/50.40 (~always5(s38)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7068, 12398])).
% 50.20/50.40 tff(12400,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s38) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12401,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s38)) | always5(s38)) <=> ((~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12402,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s38) | (~trans(s99, s38))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12401])).
% 50.20/50.40 tff(12403,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12402, 12400])).
% 50.20/50.40 tff(12404,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12405,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12404, 12403])).
% 50.20/50.40 tff(12406,plain,
% 50.20/50.40 (always5(s38) | (~trans(s99, s38))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12405, 6332, 11624])).
% 50.20/50.40 tff(12407,plain,
% 50.20/50.40 (~trans(s99, s38)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12406, 12399])).
% 50.20/50.40 tff(12408,plain,
% 50.20/50.40 (~always5(s37)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7076, 12399])).
% 50.20/50.40 tff(12409,plain,
% 50.20/50.40 (~always5(s36)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7084, 12408])).
% 50.20/50.40 tff(12410,plain,
% 50.20/50.40 (~always5(s35)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7092, 12409])).
% 50.20/50.40 tff(12411,plain,
% 50.20/50.40 (~always5(s34)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7100, 12410])).
% 50.20/50.40 tff(12412,plain,
% 50.20/50.40 (~always5(s33)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7108, 12411])).
% 50.20/50.40 tff(12413,plain,
% 50.20/50.40 (~always5(s32)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7116, 12412])).
% 50.20/50.40 tff(12414,plain,
% 50.20/50.40 (~always5(s31)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7124, 12413])).
% 50.20/50.40 tff(12415,plain,
% 50.20/50.40 (~always5(s30)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7132, 12414])).
% 50.20/50.40 tff(12416,plain,
% 50.20/50.40 (~always5(s29)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7140, 12415])).
% 50.20/50.40 tff(12417,plain,
% 50.20/50.40 (~always5(s28)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7148, 12416])).
% 50.20/50.40 tff(12418,plain,
% 50.20/50.40 (~always5(s27)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7156, 12417])).
% 50.20/50.40 tff(12419,plain,
% 50.20/50.40 (~always5(s26)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7164, 12418])).
% 50.20/50.40 tff(12420,plain,
% 50.20/50.40 (~always5(s25)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7172, 12419])).
% 50.20/50.40 tff(12421,plain,
% 50.20/50.40 (~always5(s24)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7180, 12420])).
% 50.20/50.40 tff(12422,plain,
% 50.20/50.40 (~always5(s23)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7188, 12421])).
% 50.20/50.40 tff(12423,plain,
% 50.20/50.40 (~always5(s22)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7196, 12422])).
% 50.20/50.40 tff(12424,plain,
% 50.20/50.40 (~always5(s21)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7204, 12423])).
% 50.20/50.40 tff(12425,plain,
% 50.20/50.40 (~always5(s20)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7212, 12424])).
% 50.20/50.40 tff(12426,plain,
% 50.20/50.40 (~always5(s19)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7220, 12425])).
% 50.20/50.40 tff(12427,plain,
% 50.20/50.40 (~always5(s18)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7228, 12426])).
% 50.20/50.40 tff(12428,plain,
% 50.20/50.40 (~always5(s17)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7236, 12427])).
% 50.20/50.40 tff(12429,plain,
% 50.20/50.40 (~always5(s16)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7244, 12428])).
% 50.20/50.40 tff(12430,plain,
% 50.20/50.40 (~always5(s15)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7252, 12429])).
% 50.20/50.40 tff(12431,plain,
% 50.20/50.40 (~always5(s14)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7261, 12430])).
% 50.20/50.40 tff(12432,plain,
% 50.20/50.40 (~always5(s13)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7315, 12431])).
% 50.20/50.40 tff(12433,plain,
% 50.20/50.40 (~always5(s12)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7336, 12432])).
% 50.20/50.40 tff(12434,plain,
% 50.20/50.40 (~always5(s11)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7357, 12433])).
% 50.20/50.40 tff(12435,plain,
% 50.20/50.40 (~always5(s10)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7378, 12434])).
% 50.20/50.40 tff(12436,plain,
% 50.20/50.40 (~always5(s9)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7399, 12435])).
% 50.20/50.40 tff(12437,plain,
% 50.20/50.40 (~always5(s8)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7420, 12436])).
% 50.20/50.40 tff(12438,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s8) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12439,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s8)) | always5(s8)) <=> ((~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12440,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s8) | (~trans(s99, s8))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12439])).
% 50.20/50.40 tff(12441,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12440, 12438])).
% 50.20/50.40 tff(12442,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12443,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12442, 12441])).
% 50.20/50.40 tff(12444,plain,
% 50.20/50.40 (always5(s8) | (~trans(s99, s8))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12443, 6332, 11624])).
% 50.20/50.40 tff(12445,plain,
% 50.20/50.40 (~trans(s99, s8)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12444, 12437])).
% 50.20/50.40 tff(12446,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s9) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12447,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s9)) | always5(s9)) <=> ((~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12448,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s9) | (~trans(s99, s9))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12447])).
% 50.20/50.40 tff(12449,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12448, 12446])).
% 50.20/50.40 tff(12450,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12451,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12450, 12449])).
% 50.20/50.40 tff(12452,plain,
% 50.20/50.40 (always5(s9) | (~trans(s99, s9))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12451, 6332, 11624])).
% 50.20/50.40 tff(12453,plain,
% 50.20/50.40 (~trans(s99, s9)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12452, 12436])).
% 50.20/50.40 tff(12454,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s17) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12455,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s17)) | always5(s17)) <=> ((~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12456,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s17) | (~trans(s99, s17))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12455])).
% 50.20/50.40 tff(12457,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12456, 12454])).
% 50.20/50.40 tff(12458,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12459,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12458, 12457])).
% 50.20/50.40 tff(12460,plain,
% 50.20/50.40 (always5(s17) | (~trans(s99, s17))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12459, 6332, 11624])).
% 50.20/50.40 tff(12461,plain,
% 50.20/50.40 (~trans(s99, s17)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12460, 12428])).
% 50.20/50.40 tff(12462,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s27) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12463,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s27)) | always5(s27)) <=> ((~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12464,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s27) | (~trans(s99, s27))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12463])).
% 50.20/50.40 tff(12465,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12464, 12462])).
% 50.20/50.40 tff(12466,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12467,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12466, 12465])).
% 50.20/50.40 tff(12468,plain,
% 50.20/50.40 (always5(s27) | (~trans(s99, s27))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12467, 6332, 11624])).
% 50.20/50.40 tff(12469,plain,
% 50.20/50.40 (~trans(s99, s27)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12468, 12418])).
% 50.20/50.40 tff(12470,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s39) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12471,plain,
% 50.20/50.40 (((~always5(s99)) | (~trans(s99, s39)) | always5(s39)) <=> ((~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 50.20/50.40 inference(rewrite,[status(thm)],[])).
% 50.20/50.40 tff(12472,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s39) | (~trans(s99, s39))))),
% 50.20/50.40 inference(monotonicity,[status(thm)],[12471])).
% 50.20/50.40 tff(12473,plain,
% 50.20/50.40 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 50.20/50.40 inference(transitivity,[status(thm)],[12472, 12470])).
% 50.20/50.40 tff(12474,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))),
% 50.20/50.40 inference(quant_inst,[status(thm)],[])).
% 50.20/50.40 tff(12475,plain,
% 50.20/50.40 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39))),
% 50.20/50.40 inference(modus_ponens,[status(thm)],[12474, 12473])).
% 50.20/50.40 tff(12476,plain,
% 50.20/50.40 (always5(s39) | (~trans(s99, s39))),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12475, 6332, 11624])).
% 50.20/50.40 tff(12477,plain,
% 50.20/50.40 (~trans(s99, s39)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[12476, 12398])).
% 50.20/50.40 tff(12478,plain,
% 50.20/50.40 (~always5(s7)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7436, 12437])).
% 50.20/50.40 tff(12479,plain,
% 50.20/50.40 (~always5(s6)),
% 50.20/50.40 inference(unit_resolution,[status(thm)],[7444, 12478])).
% 50.20/50.41 tff(12480,plain,
% 50.20/50.41 (~always5(s5)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[7452, 12479])).
% 50.20/50.41 tff(12481,plain,
% 50.20/50.41 (~always5(s4)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[7460, 12480])).
% 50.20/50.41 tff(12482,plain,
% 50.20/50.41 (~always5(s3)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[7468, 12481])).
% 50.20/50.41 tff(12483,plain,
% 50.20/50.41 (~always5(s2)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[7476, 12482])).
% 50.20/50.41 tff(12484,plain,
% 50.20/50.41 (~always5(s1)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[7484, 12483])).
% 50.20/50.41 tff(12485,assumption,(always5(s99)), introduced(assumption)).
% 50.20/50.41 tff(12486,assumption,(trans(s99, s1)), introduced(assumption)).
% 50.20/50.41 tff(12487,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s1) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12488,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s1)) | always5(s1)) <=> ((~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12489,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s1) | (~trans(s99, s1))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12488])).
% 50.20/50.41 tff(12490,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12489, 12487])).
% 50.20/50.41 tff(12491,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12492,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12491, 12490])).
% 50.20/50.41 tff(12493,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12492, 12486, 6332, 12485, 9718])).
% 50.20/50.41 tff(12494,plain,((~trans(s99, s1)) | (~always5(s99)) | always5(s1)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12495,plain,
% 50.20/50.41 ((~trans(s99, s1)) | always5(s1)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12494, 11624])).
% 50.20/50.41 tff(12496,plain,
% 50.20/50.41 (~trans(s99, s1)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12495, 12484])).
% 50.20/50.41 tff(12497,assumption,(~always5(s2)), introduced(assumption)).
% 50.20/50.41 tff(12498,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s2) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12499,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s2)) | always5(s2)) <=> ((~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12500,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s2) | (~trans(s99, s2))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12499])).
% 50.20/50.41 tff(12501,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12500, 12498])).
% 50.20/50.41 tff(12502,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12503,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12502, 12501])).
% 50.20/50.41 tff(12504,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12503, 10671, 6332, 11624, 12497])).
% 50.20/50.41 tff(12505,plain,((~trans(s99, s2)) | always5(s2)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12506,plain,
% 50.20/50.41 (~trans(s99, s2)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12505, 12483])).
% 50.20/50.41 tff(12507,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s28) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12508,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s28)) | always5(s28)) <=> ((~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12509,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s28) | (~trans(s99, s28))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12508])).
% 50.20/50.41 tff(12510,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12509, 12507])).
% 50.20/50.41 tff(12511,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12512,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12511, 12510])).
% 50.20/50.41 tff(12513,plain,
% 50.20/50.41 (always5(s28) | (~trans(s99, s28))),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12512, 6332, 11624])).
% 50.20/50.41 tff(12514,plain,
% 50.20/50.41 (~trans(s99, s28)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12513, 12417])).
% 50.20/50.41 tff(12515,assumption,(~always5(s36)), introduced(assumption)).
% 50.20/50.41 tff(12516,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s36) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12517,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s36)) | always5(s36)) <=> ((~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12518,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s36) | (~trans(s99, s36))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12517])).
% 50.20/50.41 tff(12519,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12518, 12516])).
% 50.20/50.41 tff(12520,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12521,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12520, 12519])).
% 50.20/50.41 tff(12522,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12521, 9769, 6332, 11624, 12515])).
% 50.20/50.41 tff(12523,plain,((~trans(s99, s36)) | always5(s36)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12524,plain,
% 50.20/50.41 (~trans(s99, s36)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12523, 12409])).
% 50.20/50.41 tff(12525,assumption,(~always5(s10)), introduced(assumption)).
% 50.20/50.41 tff(12526,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s10) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12527,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s10)) | always5(s10)) <=> ((~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12528,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s10) | (~trans(s99, s10))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12527])).
% 50.20/50.41 tff(12529,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12528, 12526])).
% 50.20/50.41 tff(12530,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12531,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12530, 12529])).
% 50.20/50.41 tff(12532,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12531, 9835, 6332, 11624, 12525])).
% 50.20/50.41 tff(12533,plain,((~trans(s99, s10)) | always5(s10)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12534,plain,
% 50.20/50.41 (~trans(s99, s10)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12533, 12435])).
% 50.20/50.41 tff(12535,assumption,(~always5(s5)), introduced(assumption)).
% 50.20/50.41 tff(12536,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s5) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12537,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s5)) | always5(s5)) <=> ((~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12538,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s5) | (~trans(s99, s5))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12537])).
% 50.20/50.41 tff(12539,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12538, 12536])).
% 50.20/50.41 tff(12540,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12541,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12540, 12539])).
% 50.20/50.41 tff(12542,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12541, 9846, 6332, 11624, 12535])).
% 50.20/50.41 tff(12543,plain,((~trans(s99, s5)) | always5(s5)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12544,plain,
% 50.20/50.41 (~trans(s99, s5)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12543, 12480])).
% 50.20/50.41 tff(12545,assumption,(~always5(s4)), introduced(assumption)).
% 50.20/50.41 tff(12546,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s4) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12547,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s4)) | always5(s4)) <=> ((~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12548,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s4) | (~trans(s99, s4))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12547])).
% 50.20/50.41 tff(12549,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12548, 12546])).
% 50.20/50.41 tff(12550,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12551,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12550, 12549])).
% 50.20/50.41 tff(12552,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12551, 10297, 6332, 11624, 12545])).
% 50.20/50.41 tff(12553,plain,((~trans(s99, s4)) | always5(s4)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12554,plain,
% 50.20/50.41 (~trans(s99, s4)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12553, 12481])).
% 50.20/50.41 tff(12555,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s15) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12556,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s15)) | always5(s15)) <=> ((~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12557,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s15) | (~trans(s99, s15))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12556])).
% 50.20/50.41 tff(12558,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12557, 12555])).
% 50.20/50.41 tff(12559,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12560,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12559, 12558])).
% 50.20/50.41 tff(12561,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12560, 9857, 6332, 11624, 7254])).
% 50.20/50.41 tff(12562,plain,((~trans(s99, s15)) | always5(s15)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12563,plain,
% 50.20/50.41 (~trans(s99, s15)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12562, 12430])).
% 50.20/50.41 tff(12564,assumption,(~always5(s32)), introduced(assumption)).
% 50.20/50.41 tff(12565,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s32) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12566,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s32)) | always5(s32)) <=> ((~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12567,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s32) | (~trans(s99, s32))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12566])).
% 50.20/50.41 tff(12568,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12567, 12565])).
% 50.20/50.41 tff(12569,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12570,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12569, 12568])).
% 50.20/50.41 tff(12571,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12570, 10286, 6332, 11624, 12564])).
% 50.20/50.41 tff(12572,plain,((~trans(s99, s32)) | always5(s32)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12573,plain,
% 50.20/50.41 (~trans(s99, s32)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12572, 12413])).
% 50.20/50.41 tff(12574,assumption,(~always5(s33)), introduced(assumption)).
% 50.20/50.41 tff(12575,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s33) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12576,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s33)) | always5(s33)) <=> ((~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12577,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s33) | (~trans(s99, s33))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12576])).
% 50.20/50.41 tff(12578,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12577, 12575])).
% 50.20/50.41 tff(12579,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12580,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12579, 12578])).
% 50.20/50.41 tff(12581,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12580, 10781, 6332, 11624, 12574])).
% 50.20/50.41 tff(12582,plain,((~trans(s99, s33)) | always5(s33)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12583,plain,
% 50.20/50.41 (~trans(s99, s33)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12582, 12412])).
% 50.20/50.41 tff(12584,assumption,(~always5(s13)), introduced(assumption)).
% 50.20/50.41 tff(12585,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s13) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12586,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s13)) | always5(s13)) <=> ((~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12587,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s13) | (~trans(s99, s13))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12586])).
% 50.20/50.41 tff(12588,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12587, 12585])).
% 50.20/50.41 tff(12589,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12590,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12589, 12588])).
% 50.20/50.41 tff(12591,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12590, 9956, 6332, 11624, 12584])).
% 50.20/50.41 tff(12592,plain,((~trans(s99, s13)) | always5(s13)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12593,plain,
% 50.20/50.41 (~trans(s99, s13)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12592, 12432])).
% 50.20/50.41 tff(12594,assumption,(~always5(s37)), introduced(assumption)).
% 50.20/50.41 tff(12595,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s37) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12596,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s37)) | always5(s37)) <=> ((~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12597,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s37) | (~trans(s99, s37))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12596])).
% 50.20/50.41 tff(12598,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12597, 12595])).
% 50.20/50.41 tff(12599,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12600,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12599, 12598])).
% 50.20/50.41 tff(12601,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12600, 10242, 6332, 11624, 12594])).
% 50.20/50.41 tff(12602,plain,((~trans(s99, s37)) | always5(s37)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12603,plain,
% 50.20/50.41 (~trans(s99, s37)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12602, 12408])).
% 50.20/50.41 tff(12604,assumption,(~always5(s35)), introduced(assumption)).
% 50.20/50.41 tff(12605,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s35) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12606,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s35)) | always5(s35)) <=> ((~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12607,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s35) | (~trans(s99, s35))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12606])).
% 50.20/50.41 tff(12608,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12607, 12605])).
% 50.20/50.41 tff(12609,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12610,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12609, 12608])).
% 50.20/50.41 tff(12611,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12610, 10803, 6332, 11624, 12604])).
% 50.20/50.41 tff(12612,plain,((~trans(s99, s35)) | always5(s35)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12613,plain,
% 50.20/50.41 (~trans(s99, s35)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12612, 12410])).
% 50.20/50.41 tff(12614,assumption,(~always5(s34)), introduced(assumption)).
% 50.20/50.41 tff(12615,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s34) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12616,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s34)) | always5(s34)) <=> ((~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12617,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s34) | (~trans(s99, s34))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12616])).
% 50.20/50.41 tff(12618,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12617, 12615])).
% 50.20/50.41 tff(12619,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))),
% 50.20/50.41 inference(quant_inst,[status(thm)],[])).
% 50.20/50.41 tff(12620,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34))),
% 50.20/50.41 inference(modus_ponens,[status(thm)],[12619, 12618])).
% 50.20/50.41 tff(12621,plain,
% 50.20/50.41 ($false),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12620, 10319, 6332, 11624, 12614])).
% 50.20/50.41 tff(12622,plain,((~trans(s99, s34)) | always5(s34)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.41 tff(12623,plain,
% 50.20/50.41 (~trans(s99, s34)),
% 50.20/50.41 inference(unit_resolution,[status(thm)],[12622, 12411])).
% 50.20/50.41 tff(12624,assumption,(~always5(s18)), introduced(assumption)).
% 50.20/50.41 tff(12625,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s18) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12626,plain,
% 50.20/50.41 (((~always5(s99)) | (~trans(s99, s18)) | always5(s18)) <=> ((~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 50.20/50.41 inference(rewrite,[status(thm)],[])).
% 50.20/50.41 tff(12627,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s18) | (~trans(s99, s18))))),
% 50.20/50.41 inference(monotonicity,[status(thm)],[12626])).
% 50.20/50.41 tff(12628,plain,
% 50.20/50.41 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 50.20/50.41 inference(transitivity,[status(thm)],[12627, 12625])).
% 50.20/50.41 tff(12629,plain,
% 50.20/50.41 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12630,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12629, 12628])).
% 50.20/50.42 tff(12631,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12630, 10011, 6332, 11624, 12624])).
% 50.20/50.42 tff(12632,plain,((~trans(s99, s18)) | always5(s18)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12633,plain,
% 50.20/50.42 (~trans(s99, s18)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12632, 12427])).
% 50.20/50.42 tff(12634,assumption,(~always5(s3)), introduced(assumption)).
% 50.20/50.42 tff(12635,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s3) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12636,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s3)) | always5(s3)) <=> ((~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12637,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s3) | (~trans(s99, s3))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12636])).
% 50.20/50.42 tff(12638,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12637, 12635])).
% 50.20/50.42 tff(12639,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12640,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12639, 12638])).
% 50.20/50.42 tff(12641,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12640, 10044, 6332, 11624, 12634])).
% 50.20/50.42 tff(12642,plain,((~trans(s99, s3)) | always5(s3)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12643,plain,
% 50.20/50.42 (~trans(s99, s3)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12642, 12482])).
% 50.20/50.42 tff(12644,assumption,(~always5(s30)), introduced(assumption)).
% 50.20/50.42 tff(12645,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s30) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12646,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s30)) | always5(s30)) <=> ((~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12647,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s30) | (~trans(s99, s30))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12646])).
% 50.20/50.42 tff(12648,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12647, 12645])).
% 50.20/50.42 tff(12649,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12650,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12649, 12648])).
% 50.20/50.42 tff(12651,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12650, 10099, 6332, 11624, 12644])).
% 50.20/50.42 tff(12652,plain,((~trans(s99, s30)) | always5(s30)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12653,plain,
% 50.20/50.42 (~trans(s99, s30)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12652, 12415])).
% 50.20/50.42 tff(12654,assumption,(~always5(s7)), introduced(assumption)).
% 50.20/50.42 tff(12655,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s7) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12656,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s7)) | always5(s7)) <=> ((~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12657,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s7) | (~trans(s99, s7))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12656])).
% 50.20/50.42 tff(12658,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12657, 12655])).
% 50.20/50.42 tff(12659,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12660,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12659, 12658])).
% 50.20/50.42 tff(12661,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12660, 10451, 6332, 11624, 12654])).
% 50.20/50.42 tff(12662,plain,((~trans(s99, s7)) | always5(s7)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12663,plain,
% 50.20/50.42 (~trans(s99, s7)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12662, 12478])).
% 50.20/50.42 tff(12664,assumption,(~always5(s24)), introduced(assumption)).
% 50.20/50.42 tff(12665,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s24) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12666,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s24)) | always5(s24)) <=> ((~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12667,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s24) | (~trans(s99, s24))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12666])).
% 50.20/50.42 tff(12668,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12667, 12665])).
% 50.20/50.42 tff(12669,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12670,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12669, 12668])).
% 50.20/50.42 tff(12671,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12670, 10209, 6332, 11624, 12664])).
% 50.20/50.42 tff(12672,plain,((~trans(s99, s24)) | always5(s24)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12673,plain,
% 50.20/50.42 (~trans(s99, s24)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12672, 12421])).
% 50.20/50.42 tff(12674,assumption,(~always5(s11)), introduced(assumption)).
% 50.20/50.42 tff(12675,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s11) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12676,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s11)) | always5(s11)) <=> ((~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12677,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s11) | (~trans(s99, s11))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12676])).
% 50.20/50.42 tff(12678,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12677, 12675])).
% 50.20/50.42 tff(12679,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12680,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12679, 12678])).
% 50.20/50.42 tff(12681,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12680, 10253, 6332, 11624, 12674])).
% 50.20/50.42 tff(12682,plain,((~trans(s99, s11)) | always5(s11)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12683,plain,
% 50.20/50.42 (~trans(s99, s11)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12682, 12434])).
% 50.20/50.42 tff(12684,assumption,(~always5(s6)), introduced(assumption)).
% 50.20/50.42 tff(12685,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s6) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12686,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s6)) | always5(s6)) <=> ((~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12687,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s6) | (~trans(s99, s6))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12686])).
% 50.20/50.42 tff(12688,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12687, 12685])).
% 50.20/50.42 tff(12689,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12690,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12689, 12688])).
% 50.20/50.42 tff(12691,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12690, 10528, 6332, 11624, 12684])).
% 50.20/50.42 tff(12692,plain,((~trans(s99, s6)) | always5(s6)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12693,plain,
% 50.20/50.42 (~trans(s99, s6)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12692, 12479])).
% 50.20/50.42 tff(12694,assumption,(~always5(s19)), introduced(assumption)).
% 50.20/50.42 tff(12695,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s19) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12696,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s19)) | always5(s19)) <=> ((~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12697,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s19) | (~trans(s99, s19))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12696])).
% 50.20/50.42 tff(12698,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12697, 12695])).
% 50.20/50.42 tff(12699,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12700,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12699, 12698])).
% 50.20/50.42 tff(12701,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12700, 10341, 6332, 11624, 12694])).
% 50.20/50.42 tff(12702,plain,((~trans(s99, s19)) | always5(s19)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12703,plain,
% 50.20/50.42 (~trans(s99, s19)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12702, 12426])).
% 50.20/50.42 tff(12704,assumption,(~always5(s26)), introduced(assumption)).
% 50.20/50.42 tff(12705,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s26) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12706,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s26)) | always5(s26)) <=> ((~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12707,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s26) | (~trans(s99, s26))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12706])).
% 50.20/50.42 tff(12708,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12707, 12705])).
% 50.20/50.42 tff(12709,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12710,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12709, 12708])).
% 50.20/50.42 tff(12711,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12710, 10352, 6332, 11624, 12704])).
% 50.20/50.42 tff(12712,plain,((~trans(s99, s26)) | always5(s26)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12713,plain,
% 50.20/50.42 (~trans(s99, s26)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12712, 12419])).
% 50.20/50.42 tff(12714,assumption,(~always5(s12)), introduced(assumption)).
% 50.20/50.42 tff(12715,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s12) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12716,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s12)) | always5(s12)) <=> ((~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12717,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s12) | (~trans(s99, s12))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12716])).
% 50.20/50.42 tff(12718,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12717, 12715])).
% 50.20/50.42 tff(12719,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12720,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12719, 12718])).
% 50.20/50.42 tff(12721,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12720, 10363, 6332, 11624, 12714])).
% 50.20/50.42 tff(12722,plain,((~trans(s99, s12)) | always5(s12)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12723,plain,
% 50.20/50.42 (~trans(s99, s12)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12722, 12433])).
% 50.20/50.42 tff(12724,assumption,(~always5(s25)), introduced(assumption)).
% 50.20/50.42 tff(12725,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s25) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12726,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s25)) | always5(s25)) <=> ((~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12727,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s25) | (~trans(s99, s25))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12726])).
% 50.20/50.42 tff(12728,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12727, 12725])).
% 50.20/50.42 tff(12729,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12730,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12729, 12728])).
% 50.20/50.42 tff(12731,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12730, 10440, 6332, 11624, 12724])).
% 50.20/50.42 tff(12732,plain,((~trans(s99, s25)) | always5(s25)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12733,plain,
% 50.20/50.42 (~trans(s99, s25)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12732, 12420])).
% 50.20/50.42 tff(12734,assumption,(~always5(s14)), introduced(assumption)).
% 50.20/50.42 tff(12735,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s14) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12736,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s14)) | always5(s14)) <=> ((~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12737,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s14) | (~trans(s99, s14))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12736])).
% 50.20/50.42 tff(12738,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12737, 12735])).
% 50.20/50.42 tff(12739,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12740,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12739, 12738])).
% 50.20/50.42 tff(12741,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12740, 10495, 6332, 11624, 12734])).
% 50.20/50.42 tff(12742,plain,((~trans(s99, s14)) | always5(s14)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12743,plain,
% 50.20/50.42 (~trans(s99, s14)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12742, 12431])).
% 50.20/50.42 tff(12744,assumption,(~always5(s16)), introduced(assumption)).
% 50.20/50.42 tff(12745,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s16) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12746,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s16)) | always5(s16)) <=> ((~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12747,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s16) | (~trans(s99, s16))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12746])).
% 50.20/50.42 tff(12748,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12747, 12745])).
% 50.20/50.42 tff(12749,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12750,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12749, 12748])).
% 50.20/50.42 tff(12751,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12750, 10561, 6332, 11624, 12744])).
% 50.20/50.42 tff(12752,plain,((~trans(s99, s16)) | always5(s16)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12753,plain,
% 50.20/50.42 (~trans(s99, s16)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12752, 12429])).
% 50.20/50.42 tff(12754,assumption,(~always5(s29)), introduced(assumption)).
% 50.20/50.42 tff(12755,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s29) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12756,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s29)) | always5(s29)) <=> ((~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12757,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s29) | (~trans(s99, s29))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12756])).
% 50.20/50.42 tff(12758,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12757, 12755])).
% 50.20/50.42 tff(12759,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12760,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12759, 12758])).
% 50.20/50.42 tff(12761,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12760, 10506, 6332, 11624, 12754])).
% 50.20/50.42 tff(12762,plain,((~trans(s99, s29)) | always5(s29)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12763,plain,
% 50.20/50.42 (~trans(s99, s29)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12762, 12416])).
% 50.20/50.42 tff(12764,assumption,(~always5(s20)), introduced(assumption)).
% 50.20/50.42 tff(12765,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s20) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12766,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s20)) | always5(s20)) <=> ((~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12767,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s20) | (~trans(s99, s20))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12766])).
% 50.20/50.42 tff(12768,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12767, 12765])).
% 50.20/50.42 tff(12769,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12770,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12769, 12768])).
% 50.20/50.42 tff(12771,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12770, 10605, 6332, 11624, 12764])).
% 50.20/50.42 tff(12772,plain,((~trans(s99, s20)) | always5(s20)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12773,plain,
% 50.20/50.42 (~trans(s99, s20)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12772, 12425])).
% 50.20/50.42 tff(12774,assumption,(~always5(s23)), introduced(assumption)).
% 50.20/50.42 tff(12775,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s23) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12776,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s23)) | always5(s23)) <=> ((~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12777,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s23) | (~trans(s99, s23))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12776])).
% 50.20/50.42 tff(12778,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12777, 12775])).
% 50.20/50.42 tff(12779,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12780,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12779, 12778])).
% 50.20/50.42 tff(12781,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12780, 10638, 6332, 11624, 12774])).
% 50.20/50.42 tff(12782,plain,((~trans(s99, s23)) | always5(s23)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12783,plain,
% 50.20/50.42 (~trans(s99, s23)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12782, 12422])).
% 50.20/50.42 tff(12784,assumption,(~always5(s22)), introduced(assumption)).
% 50.20/50.42 tff(12785,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s22) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12786,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s22)) | always5(s22)) <=> ((~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12787,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s22) | (~trans(s99, s22))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12786])).
% 50.20/50.42 tff(12788,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12787, 12785])).
% 50.20/50.42 tff(12789,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))),
% 50.20/50.42 inference(quant_inst,[status(thm)],[])).
% 50.20/50.42 tff(12790,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22))),
% 50.20/50.42 inference(modus_ponens,[status(thm)],[12789, 12788])).
% 50.20/50.42 tff(12791,plain,
% 50.20/50.42 ($false),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12790, 10627, 6332, 11624, 12784])).
% 50.20/50.42 tff(12792,plain,((~trans(s99, s22)) | always5(s22)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.42 tff(12793,plain,
% 50.20/50.42 (~trans(s99, s22)),
% 50.20/50.42 inference(unit_resolution,[status(thm)],[12792, 12423])).
% 50.20/50.42 tff(12794,assumption,(~always5(s31)), introduced(assumption)).
% 50.20/50.42 tff(12795,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s31) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12796,plain,
% 50.20/50.42 (((~always5(s99)) | (~trans(s99, s31)) | always5(s31)) <=> ((~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 50.20/50.42 inference(rewrite,[status(thm)],[])).
% 50.20/50.42 tff(12797,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s31) | (~trans(s99, s31))))),
% 50.20/50.42 inference(monotonicity,[status(thm)],[12796])).
% 50.20/50.42 tff(12798,plain,
% 50.20/50.42 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 50.20/50.42 inference(transitivity,[status(thm)],[12797, 12795])).
% 50.20/50.42 tff(12799,plain,
% 50.20/50.42 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12800,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12799, 12798])).
% 50.20/50.43 tff(12801,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12800, 10814, 6332, 12485, 12794])).
% 50.20/50.43 tff(12802,plain,((~trans(s99, s31)) | (~always5(s99)) | always5(s31)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12803,plain,
% 50.20/50.43 ((~trans(s99, s31)) | always5(s31)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12802, 11624])).
% 50.20/50.43 tff(12804,plain,
% 50.20/50.43 (~trans(s99, s31)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12803, 12414])).
% 50.20/50.43 tff(12805,plain,
% 50.20/50.43 (~always5(s0)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[7492, 12484])).
% 50.20/50.43 tff(12806,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12807,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s0)) | always5(s0)) <=> ((~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12808,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s0) | (~trans(s99, s0))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12807])).
% 50.20/50.43 tff(12809,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12808, 12806])).
% 50.20/50.43 tff(12810,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12811,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12810, 12809])).
% 50.20/50.43 tff(12812,plain,
% 50.20/50.43 (always5(s0) | (~trans(s99, s0))),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12811, 6332, 11624])).
% 50.20/50.43 tff(12813,plain,
% 50.20/50.43 (~trans(s99, s0)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12812, 12805])).
% 50.20/50.43 tff(12814,plain,
% 50.20/50.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12815,plain,
% 50.20/50.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12816,plain,
% 50.20/50.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12815, 12814])).
% 50.20/50.43 tff(12817,plain,
% 50.20/50.43 ((~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99))),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12816, 104, 6572])).
% 50.20/50.43 tff(12818,plain,
% 50.20/50.43 (~node2(c_bit0, s99)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12817, 6568])).
% 50.20/50.43 tff(12819,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12820,plain,
% 50.20/50.43 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)) | (~m_counter_cell_v_value(c_bit0, s85))) <=> ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12821,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12820])).
% 50.20/50.43 tff(12822,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12821, 12819])).
% 50.20/50.43 tff(12823,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12824,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12823, 12822])).
% 50.20/50.43 tff(12825,plain,
% 50.20/50.43 ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s85))),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12824, 130])).
% 50.20/50.43 tff(12826,plain,
% 50.20/50.43 (~node3(c_bit0, s99, s85)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12825, 12818, 2556])).
% 50.20/50.43 tff(12827,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s85)) | node3(c_bit0, s99, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s85)) | node3(c_bit0, s99, s85))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12828,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s85)) | node3(c_bit0, s99, s85))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12829,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s85)) | node3(c_bit0, s99, s85)),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12828, 12827])).
% 50.20/50.43 tff(12830,plain,
% 50.20/50.43 (~trans(s99, s85)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12829, 21, 12826])).
% 50.20/50.43 tff(12831,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12832,plain,
% 50.20/50.43 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)) | (~m_counter_cell_v_value(c_bit0, s21))) <=> ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12833,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12832])).
% 50.20/50.43 tff(12834,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12833, 12831])).
% 50.20/50.43 tff(12835,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s21)) | (~m_counter_cell_v_value(c_bit0, s21)))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12836,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12835, 12834])).
% 50.20/50.43 tff(12837,plain,
% 50.20/50.43 ((~m_counter_cell_v_value(c_bit0, s21)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s21))),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12836, 130])).
% 50.20/50.43 tff(12838,plain,
% 50.20/50.43 (~node3(c_bit0, s99, s21)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12837, 12818, 674])).
% 50.20/50.43 tff(12839,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s21)) | node3(c_bit0, s99, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s21)) | node3(c_bit0, s99, s21))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12840,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s21)) | node3(c_bit0, s99, s21))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12841,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s21)) | node3(c_bit0, s99, s21)),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12840, 12839])).
% 50.20/50.43 tff(12842,plain,
% 50.20/50.43 (~trans(s99, s21)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12841, 21, 12838])).
% 50.20/50.43 tff(12843,assumption,(node3(c_bit0, s99, s97)), introduced(assumption)).
% 50.20/50.43 tff(12844,assumption,(m_counter_cell_v_value(c_bit0, s97)), introduced(assumption)).
% 50.20/50.43 tff(12845,plain,
% 50.20/50.43 (~node2(c_bit0, s97)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6494, 12844])).
% 50.20/50.43 tff(12846,plain,
% 50.20/50.43 (~m_counter_cell_v_value(c_bit0, s98)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6506, 12845])).
% 50.20/50.43 tff(12847,plain,
% 50.20/50.43 (~node1(c_bit0, s98)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6555, 12846])).
% 50.20/50.43 tff(12848,plain,
% 50.20/50.43 (m_counter_cell_v_value(c_bit0, s99)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6567, 12847])).
% 50.20/50.43 tff(12849,plain,
% 50.20/50.43 (~node2(c_bit0, s99)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12817, 12848])).
% 50.20/50.43 tff(12850,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12851,plain,
% 50.20/50.43 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97))) <=> ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12852,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12851])).
% 50.20/50.43 tff(12853,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12852, 12850])).
% 50.20/50.43 tff(12854,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12855,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12854, 12853])).
% 50.20/50.43 tff(12856,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12855, 130, 12844, 12849, 12843])).
% 50.20/50.43 tff(12857,plain,((~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12858,plain,
% 50.20/50.43 (~node3(c_bit0, s99, s97)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12857, 6455])).
% 50.20/50.43 tff(12859,plain,
% 50.20/50.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s97)) | node3(c_bit0, s99, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s97)) | node3(c_bit0, s99, s97))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12860,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s97)) | node3(c_bit0, s99, s97))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12861,plain,
% 50.20/50.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s97)) | node3(c_bit0, s99, s97)),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12860, 12859])).
% 50.20/50.43 tff(12862,plain,
% 50.20/50.43 ((~trans(s99, s97)) | node3(c_bit0, s99, s97)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12861, 21])).
% 50.20/50.43 tff(12863,plain,
% 50.20/50.43 (~trans(s99, s97)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12862, 12858])).
% 50.20/50.43 tff(12864,assumption,(~trans(s99, s38)), introduced(assumption)).
% 50.20/50.43 tff(12865,assumption,(~trans(s99, s86)), introduced(assumption)).
% 50.20/50.43 tff(12866,assumption,(~trans(s99, s73)), introduced(assumption)).
% 50.20/50.43 tff(12867,assumption,(~trans(s99, s75)), introduced(assumption)).
% 50.20/50.43 tff(12868,assumption,(~trans(s99, s74)), introduced(assumption)).
% 50.20/50.43 tff(12869,assumption,(~trans(s99, s57)), introduced(assumption)).
% 50.20/50.43 tff(12870,assumption,(~trans(s99, s49)), introduced(assumption)).
% 50.20/50.43 tff(12871,assumption,(~trans(s99, s8)), introduced(assumption)).
% 50.20/50.43 tff(12872,assumption,(~trans(s99, s9)), introduced(assumption)).
% 50.20/50.43 tff(12873,assumption,(~trans(s99, s76)), introduced(assumption)).
% 50.20/50.43 tff(12874,assumption,(~trans(s99, s77)), introduced(assumption)).
% 50.20/50.43 tff(12875,assumption,(~trans(s99, s78)), introduced(assumption)).
% 50.20/50.43 tff(12876,assumption,(~trans(s99, s80)), introduced(assumption)).
% 50.20/50.43 tff(12877,assumption,(~trans(s99, s17)), introduced(assumption)).
% 50.20/50.43 tff(12878,assumption,(~trans(s99, s27)), introduced(assumption)).
% 50.20/50.43 tff(12879,assumption,(~trans(s99, s79)), introduced(assumption)).
% 50.20/50.43 tff(12880,assumption,(~trans(s99, s39)), introduced(assumption)).
% 50.20/50.43 tff(12881,assumption,(~always5(s96)), introduced(assumption)).
% 50.20/50.43 tff(12882,plain,
% 50.20/50.43 (~always5(s95)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6339, 12881])).
% 50.20/50.43 tff(12883,plain,
% 50.20/50.43 (~always5(s94)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6620, 12882])).
% 50.20/50.43 tff(12884,plain,
% 50.20/50.43 (~always5(s93)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6628, 12883])).
% 50.20/50.43 tff(12885,plain,
% 50.20/50.43 (~always5(s92)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6636, 12884])).
% 50.20/50.43 tff(12886,plain,
% 50.20/50.43 (~always5(s91)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6644, 12885])).
% 50.20/50.43 tff(12887,plain,
% 50.20/50.43 (~always5(s90)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6652, 12886])).
% 50.20/50.43 tff(12888,plain,
% 50.20/50.43 (~always5(s89)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[6660, 12887])).
% 50.20/50.43 tff(12889,assumption,(~always5(s89)), introduced(assumption)).
% 50.20/50.43 tff(12890,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s89) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12891,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s89)) | always5(s89)) <=> ((~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12892,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s89) | (~trans(s99, s89))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12891])).
% 50.20/50.43 tff(12893,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12892, 12890])).
% 50.20/50.43 tff(12894,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12895,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12894, 12893])).
% 50.20/50.43 tff(12896,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12895, 10726, 6332, 11624, 12889])).
% 50.20/50.43 tff(12897,plain,((~trans(s99, s89)) | always5(s89)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12898,plain,
% 50.20/50.43 (~trans(s99, s89)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12897, 12888])).
% 50.20/50.43 tff(12899,assumption,(~trans(s99, s81)), introduced(assumption)).
% 50.20/50.43 tff(12900,assumption,(~trans(s99, s82)), introduced(assumption)).
% 50.20/50.43 tff(12901,assumption,(~trans(s99, s68)), introduced(assumption)).
% 50.20/50.43 tff(12902,assumption,(~trans(s99, s44)), introduced(assumption)).
% 50.20/50.43 tff(12903,assumption,(~trans(s99, s83)), introduced(assumption)).
% 50.20/50.43 tff(12904,assumption,(~trans(s99, s84)), introduced(assumption)).
% 50.20/50.43 tff(12905,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s91) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12906,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s91)) | always5(s91)) <=> ((~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12907,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s91) | (~trans(s99, s91))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12906])).
% 50.20/50.43 tff(12908,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12907, 12905])).
% 50.20/50.43 tff(12909,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12910,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12909, 12908])).
% 50.20/50.43 tff(12911,plain,
% 50.20/50.43 (always5(s91) | (~trans(s99, s91))),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12910, 6332, 11624])).
% 50.20/50.43 tff(12912,plain,
% 50.20/50.43 (~trans(s99, s91)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12911, 12886])).
% 50.20/50.43 tff(12913,assumption,(~always5(s90)), introduced(assumption)).
% 50.20/50.43 tff(12914,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s90) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12915,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s90)) | always5(s90)) <=> ((~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12916,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s90) | (~trans(s99, s90))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12915])).
% 50.20/50.43 tff(12917,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12916, 12914])).
% 50.20/50.43 tff(12918,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12919,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12918, 12917])).
% 50.20/50.43 tff(12920,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12919, 10748, 6332, 11624, 12913])).
% 50.20/50.43 tff(12921,plain,((~trans(s99, s90)) | always5(s90)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12922,plain,
% 50.20/50.43 (~trans(s99, s90)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12921, 12887])).
% 50.20/50.43 tff(12923,assumption,(~always5(s93)), introduced(assumption)).
% 50.20/50.43 tff(12924,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s93) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12925,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s93)) | always5(s93)) <=> ((~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12926,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s93) | (~trans(s99, s93))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12925])).
% 50.20/50.43 tff(12927,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12926, 12924])).
% 50.20/50.43 tff(12928,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12929,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12928, 12927])).
% 50.20/50.43 tff(12930,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12929, 10660, 6332, 11624, 12923])).
% 50.20/50.43 tff(12931,plain,((~trans(s99, s93)) | always5(s93)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12932,plain,
% 50.20/50.43 (~trans(s99, s93)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12931, 12884])).
% 50.20/50.43 tff(12933,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s96) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12934,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s96)) | always5(s96)) <=> ((~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12935,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s96) | (~trans(s99, s96))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12934])).
% 50.20/50.43 tff(12936,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12935, 12933])).
% 50.20/50.43 tff(12937,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12938,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12937, 12936])).
% 50.20/50.43 tff(12939,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12938, 10055, 6332, 11624, 12881])).
% 50.20/50.43 tff(12940,plain,((~trans(s99, s96)) | always5(s96)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12941,plain,
% 50.20/50.43 (~trans(s99, s96)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12940, 12881])).
% 50.20/50.43 tff(12942,assumption,(~always5(s92)), introduced(assumption)).
% 50.20/50.43 tff(12943,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s92) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12944,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s92)) | always5(s92)) <=> ((~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12945,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s92) | (~trans(s99, s92))))),
% 50.20/50.43 inference(monotonicity,[status(thm)],[12944])).
% 50.20/50.43 tff(12946,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 50.20/50.43 inference(transitivity,[status(thm)],[12945, 12943])).
% 50.20/50.43 tff(12947,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))),
% 50.20/50.43 inference(quant_inst,[status(thm)],[])).
% 50.20/50.43 tff(12948,plain,
% 50.20/50.43 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92))),
% 50.20/50.43 inference(modus_ponens,[status(thm)],[12947, 12946])).
% 50.20/50.43 tff(12949,plain,
% 50.20/50.43 ($false),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12948, 10682, 6332, 11624, 12942])).
% 50.20/50.43 tff(12950,plain,((~trans(s99, s92)) | always5(s92)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.43 tff(12951,plain,
% 50.20/50.43 (~trans(s99, s92)),
% 50.20/50.43 inference(unit_resolution,[status(thm)],[12950, 12885])).
% 50.20/50.43 tff(12952,plain,
% 50.20/50.43 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s94) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 50.20/50.43 inference(rewrite,[status(thm)],[])).
% 50.20/50.43 tff(12953,plain,
% 50.20/50.43 (((~always5(s99)) | (~trans(s99, s94)) | always5(s94)) <=> ((~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(12954,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s94) | (~trans(s99, s94))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[12953])).
% 50.20/50.44 tff(12955,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[12954, 12952])).
% 50.20/50.44 tff(12956,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(12957,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[12956, 12955])).
% 50.20/50.44 tff(12958,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[12957, 10770, 6332, 11624, 11751])).
% 50.20/50.44 tff(12959,plain,((~trans(s99, s94)) | always5(s94)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.44 tff(12960,plain,
% 50.20/50.44 (~trans(s99, s94)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[12959, 12883])).
% 50.20/50.44 tff(12961,assumption,(~always5(s95)), introduced(assumption)).
% 50.20/50.44 tff(12962,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s95) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(12963,plain,
% 50.20/50.44 (((~always5(s99)) | (~trans(s99, s95)) | always5(s95)) <=> ((~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(12964,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s95) | (~trans(s99, s95))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[12963])).
% 50.20/50.44 tff(12965,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[12964, 12962])).
% 50.20/50.44 tff(12966,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(12967,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[12966, 12965])).
% 50.20/50.44 tff(12968,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[12967, 10693, 6332, 11624, 12961])).
% 50.20/50.44 tff(12969,plain,((~trans(s99, s95)) | always5(s95)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.44 tff(12970,plain,
% 50.20/50.44 (~trans(s99, s95)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[12969, 12882])).
% 50.20/50.44 tff(12971,assumption,(~trans(s99, s1)), introduced(assumption)).
% 50.20/50.44 tff(12972,assumption,(~trans(s99, s51)), introduced(assumption)).
% 50.20/50.44 tff(12973,assumption,(~trans(s99, s0)), introduced(assumption)).
% 50.20/50.44 tff(12974,assumption,(~trans(s99, s28)), introduced(assumption)).
% 50.20/50.44 tff(12975,assumption,(~trans(s99, s50)), introduced(assumption)).
% 50.20/50.44 tff(12976,assumption,(~trans(s99, s63)), introduced(assumption)).
% 50.20/50.44 tff(12977,assumption,(~trans(s99, s70)), introduced(assumption)).
% 50.20/50.44 tff(12978,assumption,(~trans(s99, s36)), introduced(assumption)).
% 50.20/50.44 tff(12979,assumption,(~trans(s99, s10)), introduced(assumption)).
% 50.20/50.44 tff(12980,assumption,(~trans(s99, s5)), introduced(assumption)).
% 50.20/50.44 tff(12981,assumption,(~trans(s99, s2)), introduced(assumption)).
% 50.20/50.44 tff(12982,assumption,(~trans(s99, s15)), introduced(assumption)).
% 50.20/50.44 tff(12983,assumption,(~trans(s99, s47)), introduced(assumption)).
% 50.20/50.44 tff(12984,assumption,(~trans(s99, s52)), introduced(assumption)).
% 50.20/50.44 tff(12985,assumption,(~trans(s99, s32)), introduced(assumption)).
% 50.20/50.44 tff(12986,assumption,(~trans(s99, s33)), introduced(assumption)).
% 50.20/50.44 tff(12987,assumption,(~trans(s99, s13)), introduced(assumption)).
% 50.20/50.44 tff(12988,assumption,(~trans(s99, s85)), introduced(assumption)).
% 50.20/50.44 tff(12989,assumption,(~trans(s99, s72)), introduced(assumption)).
% 50.20/50.44 tff(12990,assumption,(~trans(s99, s55)), introduced(assumption)).
% 50.20/50.44 tff(12991,assumption,(~trans(s99, s66)), introduced(assumption)).
% 50.20/50.44 tff(12992,assumption,(~trans(s99, s37)), introduced(assumption)).
% 50.20/50.44 tff(12993,assumption,(~trans(s99, s35)), introduced(assumption)).
% 50.20/50.44 tff(12994,assumption,(~trans(s99, s34)), introduced(assumption)).
% 50.20/50.44 tff(12995,assumption,(~trans(s99, s46)), introduced(assumption)).
% 50.20/50.44 tff(12996,assumption,(~trans(s99, s71)), introduced(assumption)).
% 50.20/50.44 tff(12997,assumption,(~trans(s99, s45)), introduced(assumption)).
% 50.20/50.44 tff(12998,assumption,(~trans(s99, s53)), introduced(assumption)).
% 50.20/50.44 tff(12999,assumption,(~trans(s99, s18)), introduced(assumption)).
% 50.20/50.44 tff(13000,assumption,(~trans(s99, s56)), introduced(assumption)).
% 50.20/50.44 tff(13001,assumption,(~trans(s99, s67)), introduced(assumption)).
% 50.20/50.44 tff(13002,assumption,(~trans(s99, s3)), introduced(assumption)).
% 50.20/50.44 tff(13003,assumption,(~trans(s99, s69)), introduced(assumption)).
% 50.20/50.44 tff(13004,assumption,(~trans(s99, s48)), introduced(assumption)).
% 50.20/50.44 tff(13005,assumption,(~trans(s99, s30)), introduced(assumption)).
% 50.20/50.44 tff(13006,assumption,(~trans(s99, s54)), introduced(assumption)).
% 50.20/50.44 tff(13007,assumption,(~trans(s99, s4)), introduced(assumption)).
% 50.20/50.44 tff(13008,assumption,(~trans(s99, s65)), introduced(assumption)).
% 50.20/50.44 tff(13009,assumption,(~trans(s99, s58)), introduced(assumption)).
% 50.20/50.44 tff(13010,assumption,(~trans(s99, s64)), introduced(assumption)).
% 50.20/50.44 tff(13011,assumption,(~trans(s99, s60)), introduced(assumption)).
% 50.20/50.44 tff(13012,assumption,(~trans(s99, s62)), introduced(assumption)).
% 50.20/50.44 tff(13013,assumption,(~trans(s99, s59)), introduced(assumption)).
% 50.20/50.44 tff(13014,assumption,(~trans(s99, s61)), introduced(assumption)).
% 50.20/50.44 tff(13015,assumption,(~trans(s99, s24)), introduced(assumption)).
% 50.20/50.44 tff(13016,assumption,(~trans(s99, s11)), introduced(assumption)).
% 50.20/50.44 tff(13017,assumption,(~trans(s99, s6)), introduced(assumption)).
% 50.20/50.44 tff(13018,assumption,(~trans(s99, s19)), introduced(assumption)).
% 50.20/50.44 tff(13019,assumption,(~trans(s99, s26)), introduced(assumption)).
% 50.20/50.44 tff(13020,assumption,(~trans(s99, s12)), introduced(assumption)).
% 50.20/50.44 tff(13021,assumption,(~trans(s99, s25)), introduced(assumption)).
% 50.20/50.44 tff(13022,assumption,(~trans(s99, s7)), introduced(assumption)).
% 50.20/50.44 tff(13023,assumption,(~trans(s99, s14)), introduced(assumption)).
% 50.20/50.44 tff(13024,assumption,(~trans(s99, s29)), introduced(assumption)).
% 50.20/50.44 tff(13025,assumption,(~trans(s99, s16)), introduced(assumption)).
% 50.20/50.44 tff(13026,assumption,(~trans(s99, s21)), introduced(assumption)).
% 50.20/50.44 tff(13027,assumption,(~trans(s99, s20)), introduced(assumption)).
% 50.20/50.44 tff(13028,assumption,(~trans(s99, s22)), introduced(assumption)).
% 50.20/50.44 tff(13029,assumption,(~trans(s99, s23)), introduced(assumption)).
% 50.20/50.44 tff(13030,assumption,(~trans(s99, s31)), introduced(assumption)).
% 50.20/50.44 tff(13031,assumption,(~trans(s99, s98)), introduced(assumption)).
% 50.20/50.44 tff(13032,assumption,(~trans(s99, s97)), introduced(assumption)).
% 50.20/50.44 tff(13033,plain,
% 50.20/50.44 (~always5(s88)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[6668, 12888])).
% 50.20/50.44 tff(13034,assumption,(~always5(s88)), introduced(assumption)).
% 50.20/50.44 tff(13035,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s88) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13036,plain,
% 50.20/50.44 (((~always5(s99)) | (~trans(s99, s88)) | always5(s88)) <=> ((~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13037,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s88) | (~trans(s99, s88))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[13036])).
% 50.20/50.44 tff(13038,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[13037, 13035])).
% 50.20/50.44 tff(13039,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13040,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13039, 13038])).
% 50.20/50.44 tff(13041,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13040, 10264, 6332, 11624, 13034])).
% 50.20/50.44 tff(13042,plain,((~trans(s99, s88)) | always5(s88)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.44 tff(13043,plain,
% 50.20/50.44 (~trans(s99, s88)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13042, 13033])).
% 50.20/50.44 tff(13044,plain,
% 50.20/50.44 (~always5(s87)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[6676, 13033])).
% 50.20/50.44 tff(13045,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s87) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13046,plain,
% 50.20/50.44 (((~always5(s99)) | (~trans(s99, s87)) | always5(s87)) <=> ((~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13047,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s87) | (~trans(s99, s87))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[13046])).
% 50.20/50.44 tff(13048,plain,
% 50.20/50.44 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[13047, 13045])).
% 50.20/50.44 tff(13049,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13050,plain,
% 50.20/50.44 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13049, 13048])).
% 50.20/50.44 tff(13051,plain,
% 50.20/50.44 (always5(s87) | (~trans(s99, s87))),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13050, 6332, 11624])).
% 50.20/50.44 tff(13052,plain,
% 50.20/50.44 (~trans(s99, s87)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13051, 13044])).
% 50.20/50.44 tff(13053,assumption,(node3(c_bit0, s99, s99)), introduced(assumption)).
% 50.20/50.44 tff(13054,assumption,(m_counter_cell_v_value(c_bit0, s99)), introduced(assumption)).
% 50.20/50.44 tff(13055,plain,
% 50.20/50.44 (~node2(c_bit0, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[12817, 13054])).
% 50.20/50.44 tff(13056,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13057,plain,
% 50.20/50.44 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99))) <=> ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13058,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[13057])).
% 50.20/50.44 tff(13059,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[13058, 13056])).
% 50.20/50.44 tff(13060,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13061,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13060, 13059])).
% 50.20/50.44 tff(13062,plain,
% 50.20/50.44 ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13061, 130, 13053])).
% 50.20/50.44 tff(13063,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13062, 13055, 13054])).
% 50.20/50.44 tff(13064,plain,((~m_counter_cell_v_value(c_bit0, s99)) | (~node3(c_bit0, s99, s99))), inference(lemma,lemma(discharge,[]))).
% 50.20/50.44 tff(13065,plain,
% 50.20/50.44 (~m_counter_cell_v_value(c_bit0, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13064, 13053])).
% 50.20/50.44 tff(13066,plain,
% 50.20/50.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13067,plain,
% 50.20/50.44 (((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13068,plain,
% 50.20/50.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[13067])).
% 50.20/50.44 tff(13069,plain,
% 50.20/50.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[13068, 13066])).
% 50.20/50.44 tff(13070,plain,
% 50.20/50.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13071,plain,
% 50.20/50.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13070, 13069])).
% 50.20/50.44 tff(13072,plain,
% 50.20/50.44 (m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13071, 55, 6572])).
% 50.20/50.44 tff(13073,plain,
% 50.20/50.44 (~node1(c_bit0, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13072, 13065])).
% 50.20/50.44 tff(13074,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13075,plain,
% 50.20/50.44 ((node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13076,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99))))),
% 50.20/50.44 inference(monotonicity,[status(thm)],[13075])).
% 50.20/50.44 tff(13077,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 50.20/50.44 inference(transitivity,[status(thm)],[13076, 13074])).
% 50.20/50.44 tff(13078,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13079,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99))),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13078, 13077])).
% 50.20/50.44 tff(13080,plain,
% 50.20/50.44 (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13079, 84, 13053])).
% 50.20/50.44 tff(13081,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13080, 13073, 13065])).
% 50.20/50.44 tff(13082,plain,(~node3(c_bit0, s99, s99)), inference(lemma,lemma(discharge,[]))).
% 50.20/50.44 tff(13083,plain,
% 50.20/50.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s99)) | node3(c_bit0, s99, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s99)) | node3(c_bit0, s99, s99))),
% 50.20/50.44 inference(rewrite,[status(thm)],[])).
% 50.20/50.44 tff(13084,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s99)) | node3(c_bit0, s99, s99))),
% 50.20/50.44 inference(quant_inst,[status(thm)],[])).
% 50.20/50.44 tff(13085,plain,
% 50.20/50.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s99)) | node3(c_bit0, s99, s99)),
% 50.20/50.44 inference(modus_ponens,[status(thm)],[13084, 13083])).
% 50.20/50.44 tff(13086,plain,
% 50.20/50.44 ((~trans(s99, s99)) | node3(c_bit0, s99, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13085, 21])).
% 50.20/50.44 tff(13087,plain,
% 50.20/50.44 (~trans(s99, s99)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13086, 13082])).
% 50.20/50.44 tff(13088,plain,
% 50.20/50.44 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[11564, 13087])).
% 50.20/50.44 tff(13089,plain,
% 50.20/50.44 ($false),
% 50.20/50.44 inference(unit_resolution,[status(thm)],[13088, 13052, 13043, 13032, 13031, 13030, 13029, 13028, 13027, 13026, 13025, 13024, 13023, 13022, 13021, 13020, 13019, 13018, 13017, 13016, 13015, 13014, 13013, 13012, 13011, 13010, 13009, 13008, 13007, 13006, 13005, 13004, 13003, 13002, 13001, 13000, 12999, 12998, 12997, 12996, 12995, 12045, 12994, 12993, 12992, 12991, 12990, 12989, 12988, 12987, 12986, 12985, 12984, 12983, 12982, 12981, 12980, 12979, 11994, 12978, 12977, 12976, 12975, 12974, 12973, 12972, 12971, 12970, 12960, 11959, 12951, 12941, 12932, 12922, 12912, 12904, 12903, 12902, 12901, 12900, 12899, 12898, 12880, 12879, 12878, 12877, 12876, 11877, 12875, 12874, 12873, 12872, 12871, 12870, 12869, 12868, 12867, 12866, 12865, 12864])).
% 50.20/50.44 tff(13090,plain,(always5(s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s31) | trans(s99, s23) | trans(s99, s22) | trans(s99, s20) | trans(s99, s21) | trans(s99, s16) | trans(s99, s29) | trans(s99, s14) | trans(s99, s7) | trans(s99, s25) | trans(s99, s12) | trans(s99, s26) | trans(s99, s19) | trans(s99, s6) | trans(s99, s11) | trans(s99, s24) | trans(s99, s61) | trans(s99, s59) | trans(s99, s62) | trans(s99, s60) | trans(s99, s64) | trans(s99, s58) | trans(s99, s65) | trans(s99, s4) | trans(s99, s54) | trans(s99, s30) | trans(s99, s48) | trans(s99, s69) | trans(s99, s3) | trans(s99, s67) | trans(s99, s56) | trans(s99, s18) | trans(s99, s53) | trans(s99, s45) | trans(s99, s71) | trans(s99, s46) | trans(s99, s40) | trans(s99, s34) | trans(s99, s35) | trans(s99, s37) | trans(s99, s66) | trans(s99, s55) | trans(s99, s72) | trans(s99, s85) | trans(s99, s13) | trans(s99, s33) | trans(s99, s32) | trans(s99, s52) | trans(s99, s47) | trans(s99, s15) | trans(s99, s2) | trans(s99, s5) | trans(s99, s10) | trans(s99, s42) | trans(s99, s36) | trans(s99, s70) | trans(s99, s63) | trans(s99, s50) | trans(s99, s28) | trans(s99, s0) | trans(s99, s51) | trans(s99, s1) | trans(s99, s41) | trans(s99, s84) | trans(s99, s83) | trans(s99, s44) | trans(s99, s68) | trans(s99, s82) | trans(s99, s81) | trans(s99, s39) | trans(s99, s79) | trans(s99, s27) | trans(s99, s17) | trans(s99, s80) | trans(s99, s43) | trans(s99, s78) | trans(s99, s77) | trans(s99, s76) | trans(s99, s9) | trans(s99, s8) | trans(s99, s49) | trans(s99, s57) | trans(s99, s74) | trans(s99, s75) | trans(s99, s73) | trans(s99, s86) | trans(s99, s38)), inference(lemma,lemma(discharge,[]))).
% 50.28/50.45 tff(13091,plain,
% 50.28/50.45 (always5(s96) | trans(s99, s98) | trans(s99, s31) | trans(s99, s23) | trans(s99, s22) | trans(s99, s20) | trans(s99, s16) | trans(s99, s29) | trans(s99, s14) | trans(s99, s7) | trans(s99, s25) | trans(s99, s12) | trans(s99, s26) | trans(s99, s19) | trans(s99, s6) | trans(s99, s11) | trans(s99, s24) | trans(s99, s61) | trans(s99, s59) | trans(s99, s62) | trans(s99, s60) | trans(s99, s64) | trans(s99, s58) | trans(s99, s65) | trans(s99, s4) | trans(s99, s54) | trans(s99, s30) | trans(s99, s48) | trans(s99, s69) | trans(s99, s3) | trans(s99, s67) | trans(s99, s56) | trans(s99, s18) | trans(s99, s53) | trans(s99, s45) | trans(s99, s71) | trans(s99, s46) | trans(s99, s40) | trans(s99, s34) | trans(s99, s35) | trans(s99, s37) | trans(s99, s66) | trans(s99, s55) | trans(s99, s72) | trans(s99, s13) | trans(s99, s33) | trans(s99, s32) | trans(s99, s52) | trans(s99, s47) | trans(s99, s15) | trans(s99, s2) | trans(s99, s5) | trans(s99, s10) | trans(s99, s42) | trans(s99, s36) | trans(s99, s70) | trans(s99, s63) | trans(s99, s50) | trans(s99, s28) | trans(s99, s0) | trans(s99, s51) | trans(s99, s1) | trans(s99, s41) | trans(s99, s84) | trans(s99, s83) | trans(s99, s44) | trans(s99, s68) | trans(s99, s82) | trans(s99, s81) | trans(s99, s39) | trans(s99, s79) | trans(s99, s27) | trans(s99, s17) | trans(s99, s80) | trans(s99, s43) | trans(s99, s78) | trans(s99, s77) | trans(s99, s76) | trans(s99, s9) | trans(s99, s8) | trans(s99, s49) | trans(s99, s57) | trans(s99, s74) | trans(s99, s75) | trans(s99, s73) | trans(s99, s86) | trans(s99, s38)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13090, 12863, 12842, 12830])).
% 50.28/50.45 tff(13092,plain,
% 50.28/50.45 (always5(s96) | trans(s99, s98) | trans(s99, s61) | trans(s99, s59) | trans(s99, s62) | trans(s99, s60) | trans(s99, s64) | trans(s99, s58) | trans(s99, s65) | trans(s99, s54) | trans(s99, s48) | trans(s99, s69) | trans(s99, s67) | trans(s99, s56) | trans(s99, s53) | trans(s99, s45) | trans(s99, s71) | trans(s99, s46) | trans(s99, s40) | trans(s99, s66) | trans(s99, s55) | trans(s99, s72) | trans(s99, s52) | trans(s99, s47) | trans(s99, s42) | trans(s99, s70) | trans(s99, s63) | trans(s99, s50) | trans(s99, s51) | trans(s99, s41) | trans(s99, s84) | trans(s99, s83) | trans(s99, s44) | trans(s99, s68) | trans(s99, s82) | trans(s99, s81) | trans(s99, s79) | trans(s99, s80) | trans(s99, s43) | trans(s99, s78) | trans(s99, s77) | trans(s99, s76) | trans(s99, s49) | trans(s99, s57) | trans(s99, s74) | trans(s99, s75) | trans(s99, s73) | trans(s99, s86)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13091, 12813, 12804, 12793, 12783, 12773, 12763, 12753, 12743, 12733, 12723, 12713, 12703, 12693, 12683, 12673, 12663, 12653, 12643, 12633, 12623, 12613, 12603, 12593, 12583, 12573, 12563, 12554, 12544, 12534, 12524, 12514, 12506, 12496, 12477, 12469, 12461, 12453, 12445, 12407])).
% 50.28/50.45 tff(13093,plain,
% 50.28/50.45 (always5(s96) | trans(s99, s61) | trans(s99, s59) | trans(s99, s62) | trans(s99, s60) | trans(s99, s64) | trans(s99, s58) | trans(s99, s65) | trans(s99, s54) | trans(s99, s48) | trans(s99, s69) | trans(s99, s67) | trans(s99, s56) | trans(s99, s53) | trans(s99, s45) | trans(s99, s71) | trans(s99, s46) | trans(s99, s40) | trans(s99, s66) | trans(s99, s55) | trans(s99, s72) | trans(s99, s52) | trans(s99, s47) | trans(s99, s42) | trans(s99, s70) | trans(s99, s63) | trans(s99, s50) | trans(s99, s51) | trans(s99, s41) | trans(s99, s84) | trans(s99, s83) | trans(s99, s44) | trans(s99, s68) | trans(s99, s82) | trans(s99, s81) | trans(s99, s79) | trans(s99, s80) | trans(s99, s43) | trans(s99, s78) | trans(s99, s77) | trans(s99, s76) | trans(s99, s49) | trans(s99, s57) | trans(s99, s74) | trans(s99, s75) | trans(s99, s73) | trans(s99, s86)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13092, 12228])).
% 50.28/50.45 tff(13094,plain,
% 50.28/50.45 (always5(s96)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13093, 12205, 12195, 12185, 12175, 12165, 12155, 12145, 12135, 12125, 12115, 12105, 12095, 12085, 12075, 12065, 12055, 12045, 12044, 12034, 12024, 12014, 12004, 11994, 11993, 11985, 11975, 11967, 11959, 11958, 11948, 11938, 11925, 11917, 11907, 11897, 11887, 11877, 11876, 11866, 11856, 11848, 11832, 11808, 11798, 11790, 11769])).
% 50.28/50.45 tff(13095,plain,
% 50.28/50.45 (always5(s97)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[6347, 13094])).
% 50.28/50.45 tff(13096,plain,
% 50.28/50.45 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[6351, 6200, 13095])).
% 50.28/50.45 tff(13097,plain,
% 50.28/50.45 (~trans(s99, s91)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12911, 11754])).
% 50.28/50.45 tff(13098,plain,
% 50.28/50.45 (~trans(s99, s89)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12897, 11756])).
% 50.28/50.45 tff(13099,plain,
% 50.28/50.45 (~trans(s99, s90)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12921, 11755])).
% 50.28/50.45 tff(13100,plain,
% 50.28/50.45 (~trans(s99, s92)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12950, 11753])).
% 50.28/50.45 tff(13101,plain,
% 50.28/50.45 (~trans(s99, s93)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12931, 11752])).
% 50.28/50.45 tff(13102,plain,
% 50.28/50.45 (~trans(s99, s88)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13042, 11757])).
% 50.28/50.45 tff(13103,plain,
% 50.28/50.45 (~trans(s99, s87)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13051, 11758])).
% 50.28/50.45 tff(13104,plain,
% 50.28/50.45 (~trans(s99, s94)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[12959, 11751])).
% 50.28/50.45 tff(13105,assumption,(node3(c_bit0, s99, s95)), introduced(assumption)).
% 50.28/50.45 tff(13106,plain,
% 50.28/50.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)))),
% 50.28/50.45 inference(rewrite,[status(thm)],[])).
% 50.28/50.45 tff(13107,plain,
% 50.28/50.45 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)) | (~m_counter_cell_v_value(c_bit0, s95))) <=> ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)))),
% 50.28/50.45 inference(rewrite,[status(thm)],[])).
% 50.28/50.45 tff(13108,plain,
% 50.28/50.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95))))),
% 50.28/50.45 inference(monotonicity,[status(thm)],[13107])).
% 50.28/50.45 tff(13109,plain,
% 50.28/50.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)))),
% 50.28/50.45 inference(transitivity,[status(thm)],[13108, 13106])).
% 50.28/50.45 tff(13110,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))),
% 50.28/50.45 inference(quant_inst,[status(thm)],[])).
% 50.28/50.45 tff(13111,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s95))),
% 50.28/50.45 inference(modus_ponens,[status(thm)],[13110, 13109])).
% 50.28/50.45 tff(13112,plain,
% 50.28/50.45 ($false),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13111, 130, 12818, 6151, 13105])).
% 50.28/50.45 tff(13113,plain,(~node3(c_bit0, s99, s95)), inference(lemma,lemma(discharge,[]))).
% 50.28/50.45 tff(13114,plain,
% 50.28/50.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s95)) | node3(c_bit0, s99, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s95)) | node3(c_bit0, s99, s95))),
% 50.28/50.45 inference(rewrite,[status(thm)],[])).
% 50.28/50.45 tff(13115,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s95)) | node3(c_bit0, s99, s95))),
% 50.28/50.45 inference(quant_inst,[status(thm)],[])).
% 50.28/50.45 tff(13116,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s95)) | node3(c_bit0, s99, s95)),
% 50.28/50.45 inference(modus_ponens,[status(thm)],[13115, 13114])).
% 50.28/50.45 tff(13117,plain,
% 50.28/50.45 ((~trans(s99, s95)) | node3(c_bit0, s99, s95)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13116, 21])).
% 50.28/50.45 tff(13118,plain,
% 50.28/50.45 (~trans(s99, s95)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13117, 13113])).
% 50.28/50.45 tff(13119,plain,
% 50.28/50.45 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s98)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13088, 12863, 12842, 12830])).
% 50.28/50.45 tff(13120,plain,
% 50.28/50.45 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s96) | trans(s99, s98)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13119, 13118])).
% 50.28/50.45 tff(13121,plain,
% 50.28/50.45 (trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s96) | trans(s99, s98)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13120, 12496, 12804, 12793, 12763, 12783, 12753, 12733, 12743, 12713, 12703, 12723, 12683, 12673, 12663, 12653, 12693, 12633, 12623, 12613, 12603, 12593, 12583, 12573, 12563, 12773, 12544, 12534, 12524, 12514, 12554, 12643, 12506, 12813, 12477, 12469, 12461, 12453, 12445, 12407])).
% 50.28/50.45 tff(13122,plain,
% 50.28/50.45 (trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s96)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13121, 12228])).
% 50.28/50.45 tff(13123,plain,
% 50.28/50.45 (trans(s99, s96)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13122, 12205, 13104, 13103, 11790, 12185, 12175, 12165, 12155, 12145, 12135, 12125, 12115, 12105, 12095, 12085, 12075, 12065, 12055, 12045, 12044, 12034, 12024, 12014, 12004, 11994, 12195, 11985, 11975, 11967, 13102, 11993, 11959, 13101, 13100, 13099, 11958, 11948, 11938, 11925, 11917, 11907, 13098, 11897, 11887, 11877, 11876, 11866, 11856, 11848, 11832, 11808, 11798, 13097, 11769])).
% 50.28/50.45 tff(13124,plain,
% 50.28/50.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit2, s99, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit2, s99, s96))),
% 50.28/50.45 inference(rewrite,[status(thm)],[])).
% 50.28/50.45 tff(13125,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit2, s99, s96))),
% 50.28/50.45 inference(quant_inst,[status(thm)],[])).
% 50.28/50.45 tff(13126,plain,
% 50.28/50.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit2, s99, s96)),
% 50.28/50.45 inference(modus_ponens,[status(thm)],[13125, 13124])).
% 50.28/50.45 tff(13127,plain,
% 50.28/50.45 ((~trans(s99, s96)) | node3(c_bit2, s99, s96)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13126, 21])).
% 50.28/50.45 tff(13128,plain,
% 50.28/50.45 (node3(c_bit2, s99, s96)),
% 50.28/50.45 inference(unit_resolution,[status(thm)],[13127, 13123])).
% 50.28/50.45 tff(13129,plain,
% 50.28/50.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 50.28/50.46 inference(rewrite,[status(thm)],[])).
% 50.28/50.46 tff(13130,plain,
% 50.28/50.46 (((~node1(c_bit2, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 50.28/50.46 inference(rewrite,[status(thm)],[])).
% 50.28/50.46 tff(13131,plain,
% 50.28/50.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99))))),
% 50.28/50.46 inference(monotonicity,[status(thm)],[13130])).
% 50.28/50.46 tff(13132,plain,
% 50.28/50.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 50.28/50.46 inference(transitivity,[status(thm)],[13131, 13129])).
% 50.28/50.46 tff(13133,plain,
% 50.28/50.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))),
% 50.28/50.46 inference(quant_inst,[status(thm)],[])).
% 50.28/50.46 tff(13134,plain,
% 50.28/50.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99))),
% 50.28/50.46 inference(modus_ponens,[status(thm)],[13133, 13132])).
% 50.28/50.46 tff(13135,plain,
% 50.28/50.46 (~node1(c_bit2, s99)),
% 50.28/50.46 inference(unit_resolution,[status(thm)],[13134, 55, 6594, 11633])).
% 50.28/50.46 tff(13136,plain,
% 50.28/50.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 50.28/50.46 inference(rewrite,[status(thm)],[])).
% 50.28/50.46 tff(13137,plain,
% 50.28/50.46 ((node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96)) <=> (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 50.28/50.46 inference(rewrite,[status(thm)],[])).
% 50.28/50.46 tff(13138,plain,
% 50.28/50.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96))))),
% 50.28/50.46 inference(monotonicity,[status(thm)],[13137])).
% 50.28/50.46 tff(13139,plain,
% 50.28/50.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 50.28/50.46 inference(transitivity,[status(thm)],[13138, 13136])).
% 50.28/50.46 tff(13140,plain,
% 50.28/50.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))),
% 50.28/50.47 inference(quant_inst,[status(thm)],[])).
% 50.28/50.47 tff(13141,plain,
% 50.28/50.47 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96))),
% 50.28/50.47 inference(modus_ponens,[status(thm)],[13140, 13139])).
% 50.28/50.47 tff(13142,plain,
% 50.28/50.47 (m_counter_cell_v_value(c_bit2, s96)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[13141, 84, 13135, 13128])).
% 50.28/50.47 tff(13143,plain,
% 50.28/50.47 (~node1(c_bit2, s96)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6302, 13142])).
% 50.28/50.47 tff(13144,plain,
% 50.28/50.47 (m_counter_cell_v_value(c_bit2, s97)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6321, 13143])).
% 50.28/50.47 tff(13145,plain,
% 50.28/50.47 (~m_counter_cell_v_carry_in(c_bit2, s97)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6355, 2906, 13144, 13096])).
% 50.28/50.47 tff(13146,plain,
% 50.28/50.47 (~node1(c_bit2, s97)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6363, 3095, 13144, 13145])).
% 50.28/50.47 tff(13147,plain,
% 50.28/50.47 (m_counter_cell_v_value(c_bit2, s98)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6382, 13146])).
% 50.28/50.47 tff(13148,plain,
% 50.28/50.47 (m_counter_cell_v_carry_in(c_bit2, s98)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[11647, 13147])).
% 50.28/50.47 tff(13149,plain,
% 50.28/50.47 (always5(s98)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[6610, 13095])).
% 50.28/50.47 tff(13150,plain,
% 50.28/50.47 (~m_counter_cell_v_carry_out(c_bit2, s98)),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[11652, 6200, 13149])).
% 50.28/50.47 tff(13151,plain,
% 50.28/50.47 ((~m_counter_cell_v_carry_in(c_bit2, s98)) | (~m_counter_cell_v_value(c_bit2, s98))),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[11656, 2906, 13150])).
% 50.28/50.47 tff(13152,plain,
% 50.28/50.47 ($false),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[13151, 13148, 13147])).
% 50.28/50.47 tff(13153,plain,(always5(s94) | trans(s99, s40) | trans(s99, s42) | trans(s99, s41) | trans(s99, s43)), inference(lemma,lemma(discharge,[]))).
% 50.28/50.47 tff(13154,plain,
% 50.28/50.47 ($false),
% 50.28/50.47 inference(unit_resolution,[status(thm)],[13153, 11750, 11739, 11660, 11730, 11722])).
% 50.28/50.47 % SZS output end Proof
% 50.28/50.48 % E exiting
%------------------------------------------------------------------------------