%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN938+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:41:02 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN938+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:01:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(p1_type, type, (
% 0.20/0.47 p1: $i > $o)).
% 0.20/0.47 tff(tptp_fun_X_20_type, type, (
% 0.20/0.47 tptp_fun_X_20: $i)).
% 0.20/0.47 tff(q1_type, type, (
% 0.20/0.47 q1: $i > $o)).
% 0.20/0.47 tff(r1_type, type, (
% 0.20/0.47 r1: $i > $o)).
% 0.20/0.47 tff(tptp_fun_C_3_type, type, (
% 0.20/0.47 tptp_fun_C_3: $i)).
% 0.20/0.47 tff(tptp_fun_B_4_type, type, (
% 0.20/0.47 tptp_fun_B_4: $i)).
% 0.20/0.47 tff(f_type, type, (
% 0.20/0.47 f: $i > $i)).
% 0.20/0.47 tff(elem_71_type, type, (
% 0.20/0.47 elem_71: $i)).
% 0.20/0.47 tff(tptp_fun_Y_15_type, type, (
% 0.20/0.47 tptp_fun_Y_15: $i > $i)).
% 0.20/0.47 tff(tptp_fun_Y_14_type, type, (
% 0.20/0.47 tptp_fun_Y_14: $i)).
% 0.20/0.47 tff(tptp_fun_Y_34_type, type, (
% 0.20/0.47 tptp_fun_Y_34: $i)).
% 0.20/0.47 tff(tptp_fun_X_35_type, type, (
% 0.20/0.47 tptp_fun_X_35: $i)).
% 0.20/0.47 tff(tptp_fun_Y_52_type, type, (
% 0.20/0.47 tptp_fun_Y_52: $i)).
% 0.20/0.47 tff(tptp_fun_C_2_type, type, (
% 0.20/0.47 tptp_fun_C_2: $i)).
% 0.20/0.47 tff(tptp_fun_B_1_type, type, (
% 0.20/0.47 tptp_fun_B_1: $i)).
% 0.20/0.47 tff(tptp_fun_B_31_type, type, (
% 0.20/0.47 tptp_fun_B_31: $i)).
% 0.20/0.47 tff(tptp_fun_A_32_type, type, (
% 0.20/0.47 tptp_fun_A_32: $i)).
% 0.20/0.47 tff(tptp_fun_C_5_type, type, (
% 0.20/0.47 tptp_fun_C_5: $i)).
% 0.20/0.47 tff(tptp_fun_B_6_type, type, (
% 0.20/0.47 tptp_fun_B_6: $i)).
% 0.20/0.47 tff(tptp_fun_B_42_type, type, (
% 0.20/0.47 tptp_fun_B_42: $i)).
% 0.20/0.47 tff(p_type, type, (
% 0.20/0.47 p: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_X_37_type, type, (
% 0.20/0.47 tptp_fun_X_37: $i > $i)).
% 0.20/0.47 tff(elem_87_type, type, (
% 0.20/0.47 elem_87: $i)).
% 0.20/0.47 tff(b_type, type, (
% 0.20/0.47 b: $i > $o)).
% 0.20/0.47 tff(a1_type, type, (
% 0.20/0.47 a1: $i > $o)).
% 0.20/0.47 tff(tptp_fun_X_23_type, type, (
% 0.20/0.47 tptp_fun_X_23: $i)).
% 0.20/0.47 tff(s1_type, type, (
% 0.20/0.47 s1: $i > $o)).
% 0.20/0.47 tff(tptp_fun_A_50_type, type, (
% 0.20/0.47 tptp_fun_A_50: $i)).
% 0.20/0.47 tff(tptp_fun_B_49_type, type, (
% 0.20/0.47 tptp_fun_B_49: $i)).
% 0.20/0.47 tff(s_type, type, (
% 0.20/0.47 s: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_A_8_type, type, (
% 0.20/0.47 tptp_fun_A_8: $i)).
% 0.20/0.47 tff(e_type, type, (
% 0.20/0.47 e: $i > $o)).
% 0.20/0.47 tff(g_type, type, (
% 0.20/0.47 g: $i > $o)).
% 0.20/0.47 tff(c_type, type, (
% 0.20/0.47 c: $i > $o)).
% 0.20/0.47 tff(tptp_fun_A_44_type, type, (
% 0.20/0.47 tptp_fun_A_44: $i)).
% 0.20/0.47 tff(tptp_fun_B_43_type, type, (
% 0.20/0.47 tptp_fun_B_43: $i)).
% 0.20/0.47 tff(tptp_fun_B_12_type, type, (
% 0.20/0.47 tptp_fun_B_12: $i)).
% 0.20/0.47 tff(tptp_fun_A_13_type, type, (
% 0.20/0.47 tptp_fun_A_13: $i)).
% 0.20/0.47 tff(tptp_fun_X_33_type, type, (
% 0.20/0.47 tptp_fun_X_33: $i)).
% 0.20/0.47 tff(tptp_fun_Y_41_type, type, (
% 0.20/0.47 tptp_fun_Y_41: $i > $i)).
% 0.20/0.47 tff(elem_131_type, type, (
% 0.20/0.47 elem_131: $i)).
% 0.20/0.47 tff(tptp_fun_Y_46_type, type, (
% 0.20/0.47 tptp_fun_Y_46: $i)).
% 0.20/0.47 tff(tptp_fun_X_45_type, type, (
% 0.20/0.47 tptp_fun_X_45: $i)).
% 0.20/0.47 tff(a_type, type, (
% 0.20/0.47 a: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_Y_25_type, type, (
% 0.20/0.47 tptp_fun_Y_25: $i)).
% 0.20/0.47 tff(tptp_fun_Y_16_type, type, (
% 0.20/0.47 tptp_fun_Y_16: $i > $i)).
% 0.20/0.47 tff(tptp_fun_Y_17_type, type, (
% 0.20/0.47 tptp_fun_Y_17: $i > $i)).
% 0.20/0.47 tff(elem_57_type, type, (
% 0.20/0.47 elem_57: $i)).
% 0.20/0.47 tff(q_type, type, (
% 0.20/0.47 q: ( $i * $i ) > $o)).
% 0.20/0.47 tff(r_type, type, (
% 0.20/0.47 r: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_C_9_type, type, (
% 0.20/0.47 tptp_fun_C_9: $i)).
% 0.20/0.47 tff(tptp_fun_B_10_type, type, (
% 0.20/0.47 tptp_fun_B_10: $i)).
% 0.20/0.47 tff(tptp_fun_A_11_type, type, (
% 0.20/0.47 tptp_fun_A_11: $i)).
% 0.20/0.47 tff(tptp_fun_X_7_type, type, (
% 0.20/0.47 tptp_fun_X_7: $i)).
% 0.20/0.47 tff(tptp_fun_X_47_type, type, (
% 0.20/0.47 tptp_fun_X_47: $i)).
% 0.20/0.47 tff(tptp_fun_B_21_type, type, (
% 0.20/0.47 tptp_fun_B_21: $i)).
% 0.20/0.47 tff(tptp_fun_A_22_type, type, (
% 0.20/0.47 tptp_fun_A_22: $i)).
% 0.20/0.47 tff(tptp_fun_B_51_type, type, (
% 0.20/0.47 tptp_fun_B_51: $i)).
% 0.20/0.47 tff(tptp_fun_X_26_type, type, (
% 0.20/0.47 tptp_fun_X_26: $i)).
% 0.20/0.48 tff(tptp_fun_X_24_type, type, (
% 0.20/0.48 tptp_fun_X_24: $i)).
% 0.20/0.48 tff(k!0_type, type, (
% 0.20/0.48 k!0: $o)).
% 0.20/0.48 tff(tptp_fun_A_48_type, type, (
% 0.20/0.48 tptp_fun_A_48: $i)).
% 0.20/0.48 tff(a_member_of_type, type, (
% 0.20/0.48 a_member_of: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_Z_38_type, type, (
% 0.20/0.48 tptp_fun_Z_38: ( $i * $i ) > $i)).
% 0.20/0.48 tff(eq_type, type, (
% 0.20/0.48 eq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_A_40_type, type, (
% 0.20/0.48 tptp_fun_A_40: $i)).
% 0.20/0.48 tff(tptp_fun_B_39_type, type, (
% 0.20/0.48 tptp_fun_B_39: $i)).
% 0.20/0.48 tff(tptp_fun_Y_30_type, type, (
% 0.20/0.48 tptp_fun_Y_30: $i)).
% 0.20/0.48 tff(tptp_fun_X_29_type, type, (
% 0.20/0.48 tptp_fun_X_29: $i)).
% 0.20/0.48 tff(tptp_fun_Y_27_type, type, (
% 0.20/0.48 tptp_fun_Y_27: $i)).
% 0.20/0.48 tff(tptp_fun_X_28_type, type, (
% 0.20/0.48 tptp_fun_X_28: $i)).
% 0.20/0.48 tff(tptp_fun_Y_36_type, type, (
% 0.20/0.48 tptp_fun_Y_36: $i)).
% 0.20/0.48 tff(tptp_fun_B_18_type, type, (
% 0.20/0.48 tptp_fun_B_18: $i)).
% 0.20/0.48 tff(tptp_fun_A_19_type, type, (
% 0.20/0.48 tptp_fun_A_19: $i)).
% 0.20/0.48 tff(a0_type, type, (
% 0.20/0.48 a0: $o)).
% 0.20/0.48 tff(b0_type, type, (
% 0.20/0.48 b0: $o)).
% 0.20/0.48 tff(g0_type, type, (
% 0.20/0.48 g0: $o)).
% 0.20/0.48 tff(f0_type, type, (
% 0.20/0.48 f0: $o)).
% 0.20/0.48 tff(z_type, type, (
% 0.20/0.48 z: $i)).
% 0.20/0.48 tff(q0_type, type, (
% 0.20/0.48 q0: $o)).
% 0.20/0.48 tff(1,assumption,(~![Z: $i] : q1(f(Z))), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))) | ![Z: $i] : q1(f(Z))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 ((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.48 tff(4,assumption,(~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))), introduced(assumption)).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))) | p1(X!35)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (p1(X!35)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))) | ![Y: $i] : (~p1(Y))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![Y: $i] : (~p1(Y))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[7, 4])).
% 0.20/0.48 tff(9,assumption,(p1(X!35)), introduced(assumption)).
% 0.20/0.48 tff(10,assumption,(![Y: $i] : (~p1(Y))), introduced(assumption)).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 ((~![Y: $i] : (~p1(Y))) | (~p1(X!35))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[11, 10, 9])).
% 0.20/0.48 tff(13,plain,((~![Y: $i] : (~p1(Y))) | (~p1(X!35))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[13, 8, 6])).
% 0.20/0.48 tff(15,plain,((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(16,assumption,(~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))), introduced(assumption)).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | ![Z: $i] : (~(r1(Z) | (~p1(Z))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![Z: $i] : (~(r1(Z) | (~p1(Z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.48 tff(19,assumption,(r1(Y!52) | (~p1(Y!52))), introduced(assumption)).
% 0.20/0.48 tff(20,assumption,(![Z: $i] : (~(r1(Z) | (~p1(Z))))), introduced(assumption)).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 ((~![Z: $i] : (~(r1(Z) | (~p1(Z))))) | (~(r1(Y!52) | (~p1(Y!52))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[21, 20, 19])).
% 0.20/0.48 tff(23,plain,((~(r1(Y!52) | (~p1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (~(r1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[23, 18])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((r1(Y!52) | (~p1(Y!52))) | p1(Y!52)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (p1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | (r1(Y!52) | (~q1(Y!52)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (r1(Y!52) | (~q1(Y!52))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[27, 16])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((r1(Y!52) | (~p1(Y!52))) | (~r1(Y!52))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (~r1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 ((~(r1(Y!52) | (~q1(Y!52)))) | r1(Y!52) | (~q1(Y!52))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (~q1(Y!52)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[31, 30, 28])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))) | ![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[33, 16])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(Y!52) | (~p1(Y!52)))) <=> ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(Y!52) | (~p1(Y!52)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(Y!52) | (~p1(Y!52))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 34, 32, 26])).
% 0.20/0.48 tff(39,plain,((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | $false) <=> (~![Y: $i] : (~(p1(Y) | (~p1(X!35)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~$true) <=> $false),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((p1(X!35) | (~p1(X!35))) <=> $true),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((~(p1(X!35) | (~p1(X!35)))) <=> (~$true)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((~(p1(X!35) | (~p1(X!35)))) <=> $false),
% 0.20/0.48 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | (~(p1(X!35) | (~p1(X!35))))) <=> ((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | $false)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~![Y: $i] : (~(p1(Y) | (~p1(X!35))))) | (~(p1(X!35) | (~p1(X!35))))) <=> (~![Y: $i] : (~(p1(Y) | (~p1(X!35)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[45, 40])).
% 0.20/0.48 tff(47,plain,
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% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (~![Y: $i] : (~(p1(Y) | (~p1(X!35))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.48 tff(49,assumption,(![Y: $i] : (~(p1(Y) | (~p1(X!35))))), introduced(assumption)).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.48 tff(51,plain,(~![Y: $i] : (~(p1(Y) | (~p1(X!35))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(52,assumption,((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))), introduced(assumption)).
% 0.20/0.48 tff(53,assumption,(~![Y: $i] : (~(p1(Y) | (~p1(X!35))))), introduced(assumption)).
% 0.20/0.48 tff(54,assumption,((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))), introduced(assumption)).
% 0.20/0.48 tff(55,assumption,(~![X: $i] : p1(X)), introduced(assumption)).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 ((q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) | ![X: $i] : p1(X)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.48 tff(58,assumption,(~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))), introduced(assumption)).
% 0.20/0.48 tff(59,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![Z: $i] : (~p1(Z))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))) | p1(X!35)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (p1(X!35)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 ((~![Z: $i] : (~p1(Z))) | (~p1(X!35))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 62, 60])).
% 0.20/0.48 tff(65,plain,((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(66,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 ((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.20/0.48 tff(68,assumption,((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))), introduced(assumption)).
% 0.20/0.48 tff(69,assumption,((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))), introduced(assumption)).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[70, 55])).
% 0.20/0.48 tff(72,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(73,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[72, 55])).
% 0.20/0.48 tff(74,assumption,(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))), introduced(assumption)).
% 0.20/0.48 tff(75,assumption,(~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))), introduced(assumption)).
% 0.20/0.48 tff(76,assumption,((~r1(B!42)) | (~((~r1(B!6)) | (~r1(C!5))))), introduced(assumption)).
% 0.20/0.48 tff(77,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (q1(f(B!6))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[77, 75])).
% 0.20/0.48 tff(79,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(80,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.20/0.48 tff(81,plain,
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% 0.20/0.48 inference(rewrite,[status(thm)],[])).
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% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(83,plain,
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% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[83, 80, 78])).
% 0.20/0.48 tff(85,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 ((~p1(f(B!6))) | (~((~r1(B!42)) | (~((~r1(B!6)) | (~r1(C!5))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.48 tff(87,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (~p1(f(B!6))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[87, 86, 76])).
% 0.20/0.48 tff(89,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.48 tff(91,plain,
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% 0.20/0.48 inference(rewrite,[status(thm)],[])).
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% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
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% 0.20/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.48 tff(94,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[93, 78, 80, 90])).
% 0.20/0.48 tff(95,plain,(((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))) | (~((~r1(B!42)) | (~((~r1(B!6)) | (~r1(C!5))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(96,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[95, 75])).
% 0.20/0.48 tff(97,plain,
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(98,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[97, 96])).
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% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.48 inference(modus_ponens,[status(thm)],[100, 99])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[101, 80, 78])).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[103, 102])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[93, 78, 80])).
% 0.20/0.48 tff(106,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[89, 105])).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[107, 106, 104])).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (r1(C!5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[109, 108])).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[111, 105])).
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% 0.20/0.48 inference(tautology,[status(thm)],[])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[113, 106, 112])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (((~r1(B!6)) | (~((~r1(B!6)) | (~r1(C!5))))) | r1(B!6)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (r1(B!6)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 ((~((~r1(B!6)) | (~r1(C!5)))) | (~r1(B!6)) | (~r1(C!5))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[117, 116, 110, 98])).
% 0.20/0.48 tff(119,plain,((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(120,assumption,((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))), introduced(assumption)).
% 0.20/0.48 tff(121,assumption,(![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), introduced(assumption)).
% 0.20/0.48 tff(122,assumption,((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87))), introduced(assumption)).
% 0.20/0.48 tff(123,assumption,(~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))), introduced(assumption)).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))) | ![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 ((~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))) | (~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[128, 127, 125])).
% 0.20/0.48 tff(130,plain,((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (((~((~p(tptp_fun_X_37(elem!87), elem!87)) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(elem!87, tptp_fun_X_37(elem!87))))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))))) <=> ((~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!87), elem!87)) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(elem!87, tptp_fun_X_37(elem!87))))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!87), elem!87)) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(elem!87, tptp_fun_X_37(elem!87))))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_37(elem!87), elem!87)) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(elem!87, tptp_fun_X_37(elem!87))))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, tptp_fun_X_37(elem!87))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[136, 121, 130, 122])).
% 0.20/0.48 tff(138,plain,((~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[138, 121])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (((~p(elem!87, tptp_fun_X_37(elem!87))) | p(tptp_fun_X_37(elem!87), tptp_fun_X_37(elem!87)) | (~p(tptp_fun_X_37(elem!87), elem!87))) | p(tptp_fun_X_37(elem!87), elem!87)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (p(tptp_fun_X_37(elem!87), elem!87)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.48 tff(142,assumption,(~![W: $i] : (~p(W, elem!87))), introduced(assumption)).
% 0.20/0.48 tff(143,plain,
% 0.20/0.49 (((~p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87)))) | (~![W: $i] : (~p(W, elem!87)))) | ![W: $i] : (~p(W, elem!87))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 ((~p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87)))) | (~![W: $i] : (~p(W, elem!87)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87)))) | ![W: $i] : (~p(W, elem!87))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~((~p(elem!87, elem!87)) | p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87)))))) <=> ((~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, elem!87)) | p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, elem!87)) | p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[149, 147])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, elem!87)) | p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | (~![W: $i] : (~p(W, elem!87)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (~(p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[152, 146, 121])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 ((p(elem!87, tptp_fun_X_37(elem!87)) | (~p(elem!87, elem!87))) | (~p(elem!87, tptp_fun_X_37(elem!87)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (~p(elem!87, tptp_fun_X_37(elem!87))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (((~p(elem!87, tptp_fun_X_37(elem!87))) | p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87))) | p(elem!87, tptp_fun_X_37(elem!87))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 ((~p(elem!87, tptp_fun_X_37(elem!87))) | p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87)))) | (~![W: $i] : (~p(W, elem!87))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87)))) | (~![W: $i] : (~p(W, elem!87))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(159,plain,
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% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!87, tptp_fun_X_37(elem!87))) | p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87)))) | (~((~p(elem!87, tptp_fun_X_37(tptp_fun_X_37(elem!87)))) | (~![W: $i] : (~p(W, elem!87)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[160, 121, 157, 144])).
% 0.20/0.49 tff(162,plain,(![W: $i] : (~p(W, elem!87)) | (~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (![W: $i] : (~p(W, elem!87))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[162, 121])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 ((~![W: $i] : (~p(W, elem!87))) | (~p(tptp_fun_X_37(elem!87), elem!87))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[164, 163, 141])).
% 0.20/0.49 tff(166,plain,(~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(167,assumption,(~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))), introduced(assumption)).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | ![X: $i] : (b(X) | (~a1(X)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 (![X: $i] : (b(X) | (~a1(X)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | a1(X!23)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (a1(X!23)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[170, 167])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (((~![X: $i] : (b(X) | (~a1(X)))) | (b(X!23) | (~a1(X!23)))) <=> ((~![X: $i] : (b(X) | (~a1(X)))) | b(X!23) | (~a1(X!23)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 ((~![X: $i] : (b(X) | (~a1(X)))) | (b(X!23) | (~a1(X!23)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 ((~![X: $i] : (b(X) | (~a1(X)))) | b(X!23) | (~a1(X!23))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (b(X!23)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[174, 171, 169])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 (((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))) | ![X: $i] : (~b(X))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (![X: $i] : (~b(X))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 167])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 ((~![X: $i] : (~b(X))) | (~b(X!23))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[178, 177, 175])).
% 0.20/0.49 tff(180,plain,((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(181,assumption,(![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))), introduced(assumption)).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 ((~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71)))))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 181])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))) | (~p(A!50, B!49))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (~p(A!50, B!49)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(f(elem!71))) | p(f(elem!71), A!50))) | (~((~r1(f(elem!71))) | p(B!49, f(elem!71)))) | (~((~s1(A!50)) | p(f(elem!71), f(elem!71))))) | s1(A!50)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (s1(A!50)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~((~s1(A!50)) | p(A!50, B!49))) | (~s1(A!50)) | p(A!50, B!49)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (~((~s1(A!50)) | p(A!50, B!49))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[193, 192, 190])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49)))) | ((~s1(A!50)) | p(A!50, B!49))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 ((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 ((~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49))))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))) <=> ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[199, 197])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(A!50)) | p(A!50, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(B!49)) | p(B!49, B!49))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 ((~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))) | (~((~s1(A!50)) | p(A!50, B!49) | (~q1(A!50)) | (~q1(B!49)) | (~r1(A!50)) | (~r1(B!49)) | (~((~q1(A!50)) | p(A!50, A!50))) | (~((~r1(B!49)) | p(B!49, B!49))) | (~((~s1(A!50)) | p(A!50, B!49)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[202, 181, 196])).
% 0.20/0.50 tff(204,plain,(~![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(205,assumption,(![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))), introduced(assumption)).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
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% 0.20/0.50 ((~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(B!6)) | (~g(B!6)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))) <=> (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(B!6)) | (~g(B!6)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(B!6)) | (~g(B!6)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[208, 206])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(f(A!8))) | (~c(f(A!8))))) | (~((~p1(B!6)) | (~g(B!6)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(B!6, f(B!6)) | g(B!6) | (~e(B!6)))) | (~(c(f(B!6)) | g(B!6) | (~e(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (~((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (((~p1(A!8)) | (~e(A!8)) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~((~c(f(A!8))) | (~p1(f(A!8))))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))) | ((~c(f(A!8))) | (~p1(f(A!8))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(214,plain,
% 0.20/0.50 ((~c(f(A!8))) | (~p1(f(A!8)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(216,plain,
% 0.20/0.50 ((~((~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(A!8)) | g(A!8) | (~e(A!8)))) | (~(p1(B!6) | (~s(A!8, B!6)))))) <=> (~((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(217,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(A!8)) | g(A!8) | (~e(A!8)))) | (~(p1(B!6) | (~s(A!8, B!6))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[216])).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(A!8)) | g(A!8) | (~e(A!8)))) | (~(p1(B!6) | (~s(A!8, B!6))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[217, 215])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(A!8, f(A!8)) | g(A!8) | (~e(A!8)))) | (~(c(f(A!8)) | g(A!8) | (~e(A!8)))) | (~(p1(B!6) | (~s(A!8, B!6))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(220,plain,
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% 0.20/0.50 inference(modus_ponens,[status(thm)],[219, 218])).
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[220, 205])).
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% 0.20/0.50 inference(tautology,[status(thm)],[])).
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% 0.20/0.50 ((~e(A!8)) | c(f(A!8)) | g(A!8)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[222, 221])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
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% 0.20/0.50 inference(monotonicity,[status(thm)],[225])).
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% 0.20/0.51 inference(transitivity,[status(thm)],[226, 224])).
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[228, 227])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[229, 205])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[231, 230])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[233, 230])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[237, 236, 234])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
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% 0.20/0.51 (c(f(A!8))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[239, 238, 232, 223])).
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
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% 0.20/0.51 inference(monotonicity,[status(thm)],[242])).
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% 0.20/0.51 inference(transitivity,[status(thm)],[243, 241])).
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))) | (~((~p1(A!8)) | (~e(A!8)) | (~((~c(B!6)) | (~p1(B!6)))) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (~((~p1(A!8)) | (~e(A!8)) | (~((~c(B!6)) | (~p1(B!6)))) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[246, 205])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~p1(A!8)) | (~e(A!8)) | (~((~c(B!6)) | (~p1(B!6)))) | (~(g(B!6) | s(B!6, f(B!6)) | (~e(B!6)))) | (~(g(B!6) | (~e(B!6)) | c(f(B!6)))) | (~((~p1(B!6)) | (~g(B!6)))) | (~(p1(f(A!8)) | (~s(A!8, f(A!8)))))) | (p1(f(A!8)) | (~s(A!8, f(A!8))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (p1(f(A!8)) | (~s(A!8, f(A!8)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (((~p1(A!8)) | (~e(A!8)) | (~(p1(B!6) | (~s(A!8, B!6)))) | (~((~e(A!8)) | c(f(A!8)) | g(A!8))) | (~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~((~p1(A!8)) | (~c(A!8)))) | (~((~p1(A!8)) | (~g(A!8))))) | ((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 ((~e(A!8)) | s(A!8, f(A!8)) | g(A!8)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[250, 221])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((~((~e(A!8)) | s(A!8, f(A!8)) | g(A!8))) | (~e(A!8)) | s(A!8, f(A!8)) | g(A!8)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (s(A!8, f(A!8))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 238, 232, 251])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 ((~(p1(f(A!8)) | (~s(A!8, f(A!8))))) | p1(f(A!8)) | (~s(A!8, f(A!8)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (p1(f(A!8))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 253, 249])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 ((~((~c(f(A!8))) | (~p1(f(A!8))))) | (~c(f(A!8))) | (~p1(f(A!8)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[256, 255, 240, 214])).
% 0.20/0.51 tff(258,plain,(~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(259,assumption,(![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))), introduced(assumption)).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))) | (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(B!42))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(B!42)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(B!42))))) | p1(A!44)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (p1(A!44)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!42) | (~p1(B!42))))) | (~r1(B!43))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 (~r1(B!43)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[264, 261])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 ((~(r1(B!43) | (~p1(A!44)))) | r1(B!43) | (~p1(A!44))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(267,plain,
% 0.20/0.51 (~(r1(B!43) | (~p1(A!44)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[266, 265, 263])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 ((r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))) | (r1(B!43) | (~p1(A!44)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(269,plain,
% 0.20/0.51 (r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))) | (~(r1(B!43) | (~p1(A!44)) | (~(r1(B!43) | (~p1(A!44))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[270, 259, 269])).
% 0.20/0.51 tff(272,plain,(~![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(273,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(274,plain,
% 0.20/0.51 ((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[273, 55])).
% 0.20/0.51 tff(275,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(276,plain,
% 0.20/0.51 ((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[275, 55])).
% 0.20/0.51 tff(277,assumption,(![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))), introduced(assumption)).
% 0.20/0.51 tff(278,plain,
% 0.20/0.51 ((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | (~((~p1(elem!131)) | p1(tptp_fun_Y_41(elem!131))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(279,plain,
% 0.20/0.51 (~((~p1(elem!131)) | p1(tptp_fun_Y_41(elem!131)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.20/0.51 tff(280,plain,
% 0.20/0.51 (((~p1(elem!131)) | p1(tptp_fun_Y_41(elem!131))) | (~p1(tptp_fun_Y_41(elem!131)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(281,plain,
% 0.20/0.51 (~p1(tptp_fun_Y_41(elem!131))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.20/0.51 tff(282,plain,
% 0.20/0.51 (((~p1(tptp_fun_Y_41(elem!131))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!131)))) | p1(tptp_fun_Y_41(elem!131))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(283,plain,
% 0.20/0.51 ((~p1(tptp_fun_Y_41(elem!131))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!131)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 ((~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))) | (~((~p1(tptp_fun_Y_41(elem!131))) | p1(tptp_fun_Y_41(tptp_fun_Y_41(elem!131)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(285,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[284, 277, 283])).
% 0.20/0.51 tff(286,plain,(~![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(287,assumption,(~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))), introduced(assumption)).
% 0.20/0.51 tff(288,plain,
% 0.20/0.51 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) | ![X: $i] : (~p(X, Y!46))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(289,plain,
% 0.20/0.51 (![X: $i] : (~p(X, Y!46))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 ((~![X: $i] : (~p(X, Y!46))) | (~p(X!45, Y!46))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 (~p(X!45, Y!46)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) | ![Y: $i] : p(X!45, Y)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 (![Y: $i] : p(X!45, Y)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[292, 287])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 ((~![Y: $i] : p(X!45, Y)) | p(X!45, Y!46)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[294, 293, 291])).
% 0.20/0.51 tff(296,plain,((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))) | $false) <=> (~![X: $i] : (~(a(X, X) <=> a(X, Y!25))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 ((a(Y!25, Y!25) <=> a(Y!25, Y!25)) <=> $true),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(299,plain,
% 0.20/0.51 ((~(a(Y!25, Y!25) <=> a(Y!25, Y!25))) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[298])).
% 0.20/0.51 tff(300,plain,
% 0.20/0.51 ((~(a(Y!25, Y!25) <=> a(Y!25, Y!25))) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[299, 41])).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))) | (~(a(Y!25, Y!25) <=> a(Y!25, Y!25)))) <=> ((~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))) | $false)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.51 tff(302,plain,
% 0.20/0.51 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))) | (~(a(Y!25, Y!25) <=> a(Y!25, Y!25)))) <=> (~![X: $i] : (~(a(X, X) <=> a(X, Y!25))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[301, 297])).
% 0.20/0.51 tff(303,plain,
% 0.20/0.51 ((~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))) | (~(a(Y!25, Y!25) <=> a(Y!25, Y!25)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(304,plain,
% 0.20/0.51 (~![X: $i] : (~(a(X, X) <=> a(X, Y!25)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.20/0.51 tff(305,assumption,(~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))), introduced(assumption)).
% 0.20/0.51 tff(306,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))) | ![Y: $i] : (~p1(Y))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(307,plain,
% 0.20/0.51 (![Y: $i] : (~p1(Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.20/0.51 tff(308,plain,
% 0.20/0.51 (~p1(X!35)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[13, 307])).
% 0.20/0.51 tff(309,plain,
% 0.20/0.51 (((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))) | ![X: $i] : p1(X)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(310,plain,
% 0.20/0.51 (![X: $i] : p1(X)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[309, 305])).
% 0.20/0.51 tff(311,plain,
% 0.20/0.51 ((~![X: $i] : p1(X)) | p1(X!35)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(312,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[311, 310, 308])).
% 0.20/0.51 tff(313,plain,((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(314,assumption,(~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))), introduced(assumption)).
% 0.20/0.51 tff(315,plain,
% 0.20/0.51 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) | ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(316,plain,
% 0.20/0.51 (![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.20/0.51 tff(317,plain,
% 0.20/0.51 ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~(r1(B!42) | p1(tptp_fun_Y_15(B!42))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(318,plain,
% 0.20/0.51 (~(r1(B!42) | p1(tptp_fun_Y_15(B!42)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[317, 316])).
% 0.20/0.51 tff(319,plain,
% 0.20/0.51 ((r1(B!42) | p1(tptp_fun_Y_15(B!42))) | (~p1(tptp_fun_Y_15(B!42)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(320,plain,
% 0.20/0.51 (~p1(tptp_fun_Y_15(B!42))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.20/0.51 tff(321,plain,
% 0.20/0.51 (((~p1(tptp_fun_Y_15(B!42))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(B!42))))) | p1(tptp_fun_Y_15(B!42))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(322,plain,
% 0.20/0.51 ((~p1(tptp_fun_Y_15(B!42))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(B!42))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.20/0.51 tff(323,plain,
% 0.20/0.51 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) | ![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(324,plain,
% 0.20/0.51 (![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[323, 314])).
% 0.20/0.51 tff(325,plain,
% 0.20/0.51 ((~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))) | (~((~p1(tptp_fun_Y_15(B!42))) | (~q1(tptp_fun_Y_16(tptp_fun_Y_15(B!42))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(326,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[325, 324, 322])).
% 0.20/0.51 tff(327,plain,((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(328,assumption,(~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))), introduced(assumption)).
% 0.20/0.51 tff(329,plain,
% 0.20/0.51 (((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))) | ![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(330,plain,
% 0.20/0.51 (![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.20/0.51 tff(331,plain,
% 0.20/0.51 ((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~((~a(elem!57, tptp_fun_Y_17(elem!57))) | (~a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(332,plain,
% 0.20/0.51 (~((~a(elem!57, tptp_fun_Y_17(elem!57))) | (~a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[331, 330])).
% 0.20/0.51 tff(333,plain,
% 0.20/0.51 (((~a(elem!57, tptp_fun_Y_17(elem!57))) | (~a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57)))) | a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(334,plain,
% 0.20/0.51 (a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[333, 332])).
% 0.20/0.51 tff(335,plain,
% 0.20/0.51 (((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))) | ![Z: $i] : (~a(Z, Z))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(336,plain,
% 0.20/0.51 (![Z: $i] : (~a(Z, Z))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[335, 328])).
% 0.20/0.51 tff(337,plain,
% 0.20/0.51 ((~![Z: $i] : (~a(Z, Z))) | (~a(tptp_fun_Y_17(elem!57), tptp_fun_Y_17(elem!57)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(338,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[337, 336, 334])).
% 0.20/0.51 tff(339,plain,((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(340,assumption,(~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))), introduced(assumption)).
% 0.20/0.51 tff(341,plain,
% 0.20/0.51 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | ![X: $i] : (p1(X) | (~s1(X)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(342,plain,
% 0.20/0.51 (![X: $i] : (p1(X) | (~s1(X)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[341, 340])).
% 0.20/0.51 tff(343,plain,
% 0.20/0.51 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | s1(B!10)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(344,plain,
% 0.20/0.51 (s1(B!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[343, 340])).
% 0.20/0.51 tff(345,plain,
% 0.20/0.51 (((~![X: $i] : (p1(X) | (~s1(X)))) | (p1(B!10) | (~s1(B!10)))) <=> ((~![X: $i] : (p1(X) | (~s1(X)))) | p1(B!10) | (~s1(B!10)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(346,plain,
% 0.20/0.51 ((~![X: $i] : (p1(X) | (~s1(X)))) | (p1(B!10) | (~s1(B!10)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(347,plain,
% 0.20/0.51 ((~![X: $i] : (p1(X) | (~s1(X)))) | p1(B!10) | (~s1(B!10))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.20/0.51 tff(348,plain,
% 0.20/0.51 (p1(B!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[347, 344, 342])).
% 0.20/0.51 tff(349,plain,
% 0.20/0.51 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(350,plain,
% 0.20/0.51 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[349, 340])).
% 0.20/0.51 tff(351,plain,
% 0.20/0.51 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | r(B!10, C!9)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(352,plain,
% 0.20/0.51 (r(B!10, C!9)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[351, 340])).
% 0.20/0.51 tff(353,plain,
% 0.20/0.51 (((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!10, C!9)) | q(B!10, C!9))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!10, C!9)) | q(B!10, C!9))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(354,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!10, C!9)) | q(B!10, C!9))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(355,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!10, C!9)) | q(B!10, C!9)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.20/0.51 tff(356,plain,
% 0.20/0.51 (q(B!10, C!9)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[355, 352, 350])).
% 0.20/0.51 tff(357,plain,
% 0.20/0.51 (((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))) | ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(358,plain,
% 0.20/0.51 (![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[357, 340])).
% 0.20/0.52 tff(359,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | ((~p1(B!10)) | (~q(B!10, C!9)))) <=> ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | (~p1(B!10)) | (~q(B!10, C!9)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(360,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | ((~p1(B!10)) | (~q(B!10, C!9)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(361,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) | (~p1(B!10)) | (~q(B!10, C!9))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.20/0.52 tff(362,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[361, 358, 356, 348])).
% 0.20/0.52 tff(363,plain,((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(364,assumption,(~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))), introduced(assumption)).
% 0.20/0.52 tff(365,plain,
% 0.20/0.52 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | ![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(366,plain,
% 0.20/0.52 (![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.20/0.52 tff(367,plain,
% 0.20/0.52 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | a1(X!7)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(368,plain,
% 0.20/0.52 (a1(X!7)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[367, 364])).
% 0.20/0.52 tff(369,plain,
% 0.20/0.52 (((~![X: $i] : ((~a1(X)) | (~c(X)))) | ((~a1(X!7)) | (~c(X!7)))) <=> ((~![X: $i] : ((~a1(X)) | (~c(X)))) | (~a1(X!7)) | (~c(X!7)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(370,plain,
% 0.20/0.52 ((~![X: $i] : ((~a1(X)) | (~c(X)))) | ((~a1(X!7)) | (~c(X!7)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(371,plain,
% 0.20/0.52 ((~![X: $i] : ((~a1(X)) | (~c(X)))) | (~a1(X!7)) | (~c(X!7))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.52 tff(372,plain,
% 0.20/0.52 (~c(X!7)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[371, 368, 366])).
% 0.20/0.52 tff(373,plain,
% 0.20/0.52 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | ![X: $i] : (c(X) | b(X) | (~a1(X)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(374,plain,
% 0.20/0.52 (![X: $i] : (c(X) | b(X) | (~a1(X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[373, 364])).
% 0.20/0.52 tff(375,plain,
% 0.20/0.52 ((b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))) | (~b(X!7))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(376,plain,
% 0.20/0.52 (~b(X!7)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[375, 364])).
% 0.20/0.52 tff(377,plain,
% 0.20/0.52 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (b(X!7) | (~a1(X!7)) | c(X!7))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(378,plain,
% 0.20/0.52 ((c(X!7) | b(X!7) | (~a1(X!7))) <=> (b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(379,plain,
% 0.20/0.52 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (b(X!7) | (~a1(X!7)) | c(X!7)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[378])).
% 0.20/0.52 tff(380,plain,
% 0.20/0.52 (((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))) <=> ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7))),
% 0.20/0.52 inference(transitivity,[status(thm)],[379, 377])).
% 0.20/0.52 tff(381,plain,
% 0.20/0.52 ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (c(X!7) | b(X!7) | (~a1(X!7)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(382,plain,
% 0.20/0.52 ((~![X: $i] : (c(X) | b(X) | (~a1(X)))) | b(X!7) | (~a1(X!7)) | c(X!7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.20/0.52 tff(383,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[382, 376, 368, 374, 372])).
% 0.20/0.52 tff(384,plain,(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(385,assumption,(~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))), introduced(assumption)).
% 0.20/0.52 tff(386,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)) | (~p(X!47, X!47))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(387,plain,
% 0.20/0.52 (~p(X!47, X!47)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[386, 385])).
% 0.20/0.52 tff(388,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)) | ![X: $i, Y: $i] : p(X, Y)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(389,plain,
% 0.20/0.52 (![X: $i, Y: $i] : p(X, Y)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[388, 385])).
% 0.20/0.52 tff(390,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(391,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[390, 389, 387])).
% 0.20/0.52 tff(392,plain,((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(393,assumption,(~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))), introduced(assumption)).
% 0.20/0.52 tff(394,plain,
% 0.20/0.52 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) | ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(395,plain,
% 0.20/0.52 (![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.20/0.52 tff(396,plain,
% 0.20/0.52 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) | ![Z: $i] : (p1(Z) | (~q1(Z)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(397,plain,
% 0.20/0.52 (![Z: $i] : (p1(Z) | (~q1(Z)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[396, 393])).
% 0.20/0.52 tff(398,assumption,(~p1(B!21)), introduced(assumption)).
% 0.20/0.52 tff(399,plain,
% 0.20/0.52 ((p1(A!22) | (~p1(B!21))) | p1(B!21)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(400,plain,
% 0.20/0.52 (p1(A!22) | (~p1(B!21))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[399, 398])).
% 0.20/0.52 tff(401,assumption,(![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))), introduced(assumption)).
% 0.20/0.52 tff(402,plain,
% 0.20/0.52 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(403,plain,
% 0.20/0.52 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(404,plain,
% 0.20/0.52 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(A!22) | (~p1(B!21)))) | (~(p1(B!21) | (~q1(B!21))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.20/0.52 tff(405,plain,
% 0.20/0.52 (~(p1(B!21) | (~q1(B!21)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[404, 401, 400])).
% 0.20/0.52 tff(406,assumption,(![Z: $i] : (p1(Z) | (~q1(Z)))), introduced(assumption)).
% 0.20/0.52 tff(407,plain,
% 0.20/0.52 (((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(B!21) | (~q1(B!21)))) <=> ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(B!21) | (~q1(B!21)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(408,plain,
% 0.20/0.52 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (p1(B!21) | (~q1(B!21)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(409,plain,
% 0.20/0.52 ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | p1(B!21) | (~q1(B!21))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.20/0.52 tff(410,plain,
% 0.20/0.52 (~q1(B!21)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[409, 406, 398])).
% 0.20/0.52 tff(411,plain,
% 0.20/0.52 ((p1(B!21) | (~q1(B!21))) | q1(B!21)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(412,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[411, 410, 405])).
% 0.20/0.52 tff(413,plain,(p1(B!21) | (~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(414,plain,
% 0.20/0.52 (p1(B!21)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[413, 397, 395])).
% 0.20/0.52 tff(415,plain,
% 0.20/0.52 ((p1(B!21) | (~q1(A!22))) | (~p1(B!21))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(416,plain,
% 0.20/0.52 (p1(B!21) | (~q1(A!22))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.20/0.52 tff(417,plain,
% 0.20/0.52 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(418,plain,
% 0.20/0.52 (($false | (~(p1(B!21) | (~q1(A!22))))) <=> (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(419,plain,
% 0.20/0.52 ((p1(A!22) | (~p1(A!22))) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(420,plain,
% 0.20/0.52 ((~(p1(A!22) | (~p1(A!22)))) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[419])).
% 0.20/0.52 tff(421,plain,
% 0.20/0.52 ((~(p1(A!22) | (~p1(A!22)))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[420, 41])).
% 0.20/0.52 tff(422,plain,
% 0.20/0.52 (((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22))))) <=> ($false | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[421])).
% 0.20/0.52 tff(423,plain,
% 0.20/0.52 (((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22))))) <=> (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[422, 418])).
% 0.20/0.52 tff(424,plain,
% 0.20/0.52 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[423])).
% 0.20/0.52 tff(425,plain,
% 0.20/0.52 (((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))) <=> ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[424, 417])).
% 0.20/0.52 tff(426,plain,
% 0.20/0.52 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | ((~(p1(A!22) | (~p1(A!22)))) | (~(p1(B!21) | (~q1(A!22)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(427,plain,
% 0.20/0.52 ((~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) | (~(p1(B!21) | (~q1(A!22))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.20/0.52 tff(428,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[427, 395, 416])).
% 0.20/0.52 tff(429,plain,((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(430,assumption,(~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))), introduced(assumption)).
% 0.20/0.52 tff(431,plain,
% 0.20/0.52 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) | ![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(432,plain,
% 0.20/0.52 (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.20/0.52 tff(433,assumption,(~p(f(B!51), B!51)), introduced(assumption)).
% 0.20/0.52 tff(434,assumption,(![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))), introduced(assumption)).
% 0.20/0.52 tff(435,plain,
% 0.20/0.52 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | p(f(B!51), B!51)) <=> ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | p(f(B!51), B!51))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(436,plain,
% 0.20/0.52 (($false | p(f(B!51), B!51)) <=> p(f(B!51), B!51)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(437,plain,
% 0.20/0.52 ((r1(B!51) | (~r1(B!51))) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(438,plain,
% 0.20/0.52 ((~(r1(B!51) | (~r1(B!51)))) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[437])).
% 0.20/0.52 tff(439,plain,
% 0.20/0.52 ((~(r1(B!51) | (~r1(B!51)))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[438, 41])).
% 0.20/0.52 tff(440,plain,
% 0.20/0.52 (((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51)) <=> ($false | p(f(B!51), B!51))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[439])).
% 0.20/0.52 tff(441,plain,
% 0.20/0.52 (((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51)) <=> p(f(B!51), B!51)),
% 0.20/0.52 inference(transitivity,[status(thm)],[440, 436])).
% 0.20/0.52 tff(442,plain,
% 0.20/0.52 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | ((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51))) <=> ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | p(f(B!51), B!51))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[441])).
% 0.20/0.52 tff(443,plain,
% 0.20/0.52 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | ((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51))) <=> ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | p(f(B!51), B!51))),
% 0.20/0.52 inference(transitivity,[status(thm)],[442, 435])).
% 0.20/0.52 tff(444,plain,
% 0.20/0.52 ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | ((~(r1(B!51) | (~r1(B!51)))) | p(f(B!51), B!51))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(445,plain,
% 0.20/0.52 ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | p(f(B!51), B!51)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.20/0.52 tff(446,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[445, 434, 433])).
% 0.20/0.52 tff(447,plain,(p(f(B!51), B!51) | (~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(448,plain,
% 0.20/0.52 (p(f(B!51), B!51)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[447, 432])).
% 0.20/0.52 tff(449,plain,
% 0.20/0.52 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) | ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(450,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[449, 430])).
% 0.20/0.52 tff(451,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | (~p(f(B!51), B!51))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | (~p(f(B!51), B!51)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(452,plain,
% 0.20/0.52 (((~p(f(B!51), B!51)) | $false) <=> (~p(f(B!51), B!51))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(453,plain,
% 0.20/0.52 (((~q(f(B!51), B!51)) | q(f(B!51), B!51)) <=> $true),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(454,plain,
% 0.20/0.52 ((~((~q(f(B!51), B!51)) | q(f(B!51), B!51))) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[453])).
% 0.20/0.52 tff(455,plain,
% 0.20/0.52 ((~((~q(f(B!51), B!51)) | q(f(B!51), B!51))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[454, 41])).
% 0.20/0.52 tff(456,plain,
% 0.20/0.52 (((~p(f(B!51), B!51)) | (~((~q(f(B!51), B!51)) | q(f(B!51), B!51)))) <=> ((~p(f(B!51), B!51)) | $false)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[455])).
% 0.20/0.52 tff(457,plain,
% 0.20/0.52 (((~p(f(B!51), B!51)) | (~((~q(f(B!51), B!51)) | q(f(B!51), B!51)))) <=> (~p(f(B!51), B!51))),
% 0.20/0.52 inference(transitivity,[status(thm)],[456, 452])).
% 0.20/0.52 tff(458,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | ((~p(f(B!51), B!51)) | (~((~q(f(B!51), B!51)) | q(f(B!51), B!51))))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | (~p(f(B!51), B!51)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[457])).
% 0.20/0.52 tff(459,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | ((~p(f(B!51), B!51)) | (~((~q(f(B!51), B!51)) | q(f(B!51), B!51))))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | (~p(f(B!51), B!51)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[458, 451])).
% 0.20/0.52 tff(460,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | ((~p(f(B!51), B!51)) | (~((~q(f(B!51), B!51)) | q(f(B!51), B!51))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(461,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) | (~p(f(B!51), B!51))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.20/0.52 tff(462,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[461, 450, 448])).
% 0.20/0.52 tff(463,plain,((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(464,assumption,(~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))), introduced(assumption)).
% 0.20/0.52 tff(465,plain,
% 0.20/0.52 (((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))) | b(X!26)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(466,plain,
% 0.20/0.52 (b(X!26)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[465, 464])).
% 0.20/0.52 tff(467,plain,
% 0.20/0.52 ((a1(X!26) | b(X!26)) | (~b(X!26))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(468,plain,
% 0.20/0.52 (a1(X!26) | b(X!26)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[467, 466])).
% 0.20/0.52 tff(469,plain,
% 0.20/0.52 (((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))) | ![X: $i] : (~(a1(X) | b(X)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(470,plain,
% 0.20/0.52 (![X: $i] : (~(a1(X) | b(X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[469, 464])).
% 0.20/0.52 tff(471,plain,
% 0.20/0.52 ((~![X: $i] : (~(a1(X) | b(X)))) | (~(a1(X!26) | b(X!26)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(472,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[471, 470, 468])).
% 0.20/0.52 tff(473,plain,((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(474,assumption,(~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))), introduced(assumption)).
% 0.20/0.52 tff(475,plain,
% 0.20/0.52 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | (b(X!24) | (~a1(X!24)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(476,plain,
% 0.20/0.52 (b(X!24) | (~a1(X!24))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[475, 474])).
% 0.20/0.52 tff(477,plain,
% 0.20/0.52 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | ![X: $i] : a1(X)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(478,plain,
% 0.20/0.52 (![X: $i] : a1(X)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[477, 474])).
% 0.20/0.52 tff(479,assumption,(![X: $i] : a1(X)), introduced(assumption)).
% 0.20/0.52 tff(480,assumption,(~a1(X!24)), introduced(assumption)).
% 0.20/0.52 tff(481,plain,
% 0.20/0.52 ((~![X: $i] : a1(X)) | a1(X!24)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(482,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[481, 480, 479])).
% 0.20/0.52 tff(483,plain,(a1(X!24) | (~![X: $i] : a1(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(484,plain,
% 0.20/0.52 (a1(X!24)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[483, 478])).
% 0.20/0.52 tff(485,plain,
% 0.20/0.52 ((~(b(X!24) | (~a1(X!24)))) | b(X!24) | (~a1(X!24))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(486,plain,
% 0.20/0.52 (b(X!24)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[485, 484, 476])).
% 0.20/0.52 tff(487,plain,
% 0.20/0.52 (((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))) | ![X: $i] : (~b(X))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(488,plain,
% 0.20/0.52 (![X: $i] : (~b(X))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[487, 474])).
% 0.20/0.52 tff(489,plain,
% 0.20/0.52 ((~![X: $i] : (~b(X))) | (~b(X!24))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(490,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[489, 488, 486])).
% 0.20/0.52 tff(491,plain,((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(492,assumption,(~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))), introduced(assumption)).
% 0.20/0.52 tff(493,plain,
% 0.20/0.52 ((q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))) | (~q1(A!48))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(494,plain,
% 0.20/0.52 (~q1(A!48)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[493, 492])).
% 0.20/0.52 tff(495,plain,
% 0.20/0.52 (((~p1(A!48)) | (~q1(A!48))) | q1(A!48)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(496,plain,
% 0.20/0.52 ((~p1(A!48)) | (~q1(A!48))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[495, 494])).
% 0.20/0.52 tff(497,plain,
% 0.20/0.52 ((q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))) | ![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(498,plain,
% 0.20/0.52 (![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[497, 492])).
% 0.20/0.52 tff(499,plain,
% 0.20/0.52 ((~![X: $i] : (~((~p1(X)) | (~q1(X))))) | (~((~p1(A!48)) | (~q1(A!48))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(500,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[499, 498, 496])).
% 0.20/0.52 tff(501,plain,(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(502,assumption,(~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))), introduced(assumption)).
% 0.20/0.52 tff(503,plain,
% 0.20/0.52 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | ![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(504,plain,
% 0.20/0.52 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[503, 502])).
% 0.20/0.52 tff(505,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))) | (~((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | (~(a_member_of(tptp_fun_Z_38(B!39, A!40), A!40) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(506,plain,
% 0.20/0.52 (~((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | (~(a_member_of(tptp_fun_Z_38(B!39, A!40), A!40) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[505, 504])).
% 0.20/0.52 tff(507,plain,
% 0.20/0.52 (((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~(eq(A!40, B!39) | (~(a_member_of(tptp_fun_Z_38(B!39, A!40), A!40) <=> a_member_of(tptp_fun_Z_38(B!39, A!40), B!39)))))) | ((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(508,plain,
% 0.20/0.52 ((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[507, 506])).
% 0.20/0.52 tff(509,plain,
% 0.20/0.52 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | eq(A!40, B!39)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(510,plain,
% 0.20/0.52 (eq(A!40, B!39)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[509, 502])).
% 0.20/0.52 tff(511,plain,
% 0.20/0.52 ((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | (~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(512,plain,
% 0.20/0.52 ((~((~eq(A!40, B!39)) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39)))) | ![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[511, 510])).
% 0.20/0.52 tff(513,plain,
% 0.20/0.52 (![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[512, 508])).
% 0.20/0.52 tff(514,plain,
% 0.20/0.52 ((~![Z: $i] : (a_member_of(Z, A!40) <=> a_member_of(Z, B!39))) | (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(515,plain,
% 0.20/0.52 (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.20/0.52 tff(516,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))) | (~((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(517,plain,
% 0.20/0.53 (~((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[516, 504])).
% 0.20/0.53 tff(518,plain,
% 0.20/0.53 (((~((~eq(B!39, A!40)) | ![Z: $i] : (a_member_of(Z, B!39) <=> a_member_of(Z, A!40)))) | (~(eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))))) | (eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(519,plain,
% 0.20/0.53 (eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[518, 517])).
% 0.20/0.53 tff(520,plain,
% 0.20/0.53 (((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))) | (~eq(B!39, A!40))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(521,plain,
% 0.20/0.53 (~eq(B!39, A!40)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[520, 502])).
% 0.20/0.53 tff(522,plain,
% 0.20/0.53 ((~(eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))) | eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(523,plain,
% 0.20/0.53 ((~(eq(B!39, A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))))) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[522, 521])).
% 0.20/0.53 tff(524,plain,
% 0.20/0.53 (~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[523, 519])).
% 0.20/0.53 tff(525,assumption,(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)), introduced(assumption)).
% 0.20/0.53 tff(526,assumption,(~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)), introduced(assumption)).
% 0.20/0.53 tff(527,assumption,(~(a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))), introduced(assumption)).
% 0.20/0.53 tff(528,plain,
% 0.20/0.53 ((a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)) | a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) | a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(529,plain,
% 0.20/0.53 (a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[528, 526, 527])).
% 0.20/0.53 tff(530,plain,
% 0.20/0.53 ((~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(531,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[530, 529, 526, 525])).
% 0.20/0.53 tff(532,plain,(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) | (~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | (a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(533,plain,
% 0.20/0.53 (a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[532, 515, 524])).
% 0.20/0.53 tff(534,plain,
% 0.20/0.53 ((a_member_of(tptp_fun_Z_38(A!40, B!39), B!39) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(535,plain,
% 0.20/0.53 (~a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[534, 533, 524])).
% 0.20/0.53 tff(536,plain,
% 0.20/0.53 ((~(a_member_of(tptp_fun_Z_38(A!40, B!39), A!40) <=> a_member_of(tptp_fun_Z_38(A!40, B!39), B!39))) | (~a_member_of(tptp_fun_Z_38(A!40, B!39), A!40)) | a_member_of(tptp_fun_Z_38(A!40, B!39), B!39)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(537,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[536, 535, 533, 515])).
% 0.20/0.53 tff(538,plain,((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(539,assumption,(~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))), introduced(assumption)).
% 0.20/0.53 tff(540,plain,
% 0.20/0.53 (((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))) | (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(541,plain,
% 0.20/0.53 (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[540, 539])).
% 0.20/0.53 tff(542,plain,
% 0.20/0.53 (((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))) | (a(X!28, Y!27) | a(X!29, Y!30))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(543,plain,
% 0.20/0.53 (a(X!28, Y!27) | a(X!29, Y!30)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[542, 539])).
% 0.20/0.53 tff(544,assumption,(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))), introduced(assumption)).
% 0.20/0.53 tff(545,assumption,(a(X!29, Y!30)), introduced(assumption)).
% 0.20/0.53 tff(546,assumption,(![X: $i, Y: $i] : (~a(X, Y))), introduced(assumption)).
% 0.20/0.53 tff(547,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!29, Y!30))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(548,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[547, 545, 546])).
% 0.20/0.53 tff(549,plain,((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!29, Y!30))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(550,plain,
% 0.20/0.53 (~![X: $i, Y: $i] : (~a(X, Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[549, 545])).
% 0.20/0.53 tff(551,plain,
% 0.20/0.53 ((~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | ![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(552,plain,
% 0.20/0.53 (![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[551, 550, 544])).
% 0.20/0.53 tff(553,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!29, Y!30))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(554,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[553, 545, 552])).
% 0.20/0.53 tff(555,plain,((~a(X!29, Y!30)) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(556,plain,
% 0.20/0.53 (~a(X!29, Y!30)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[555, 541])).
% 0.20/0.53 tff(557,plain,
% 0.20/0.53 ((~(a(X!28, Y!27) | a(X!29, Y!30))) | a(X!28, Y!27) | a(X!29, Y!30)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(558,plain,
% 0.20/0.53 (a(X!28, Y!27)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[557, 556, 543])).
% 0.20/0.53 tff(559,assumption,(![Y: $i, X: $i] : (~a(X, Y))), introduced(assumption)).
% 0.20/0.53 tff(560,assumption,(a(X!28, Y!27)), introduced(assumption)).
% 0.20/0.53 tff(561,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!28, Y!27))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(562,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[561, 560, 559])).
% 0.20/0.53 tff(563,plain,((~![Y: $i, X: $i] : (~a(X, Y))) | (~a(X!28, Y!27))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(564,plain,
% 0.20/0.53 (~![Y: $i, X: $i] : (~a(X, Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[563, 558])).
% 0.20/0.53 tff(565,plain,
% 0.20/0.53 (![X: $i, Y: $i] : (~a(X, Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[551, 564, 541])).
% 0.20/0.53 tff(566,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : (~a(X, Y))) | (~a(X!28, Y!27))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(567,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[566, 558, 565])).
% 0.20/0.53 tff(568,plain,((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(569,assumption,(~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))), introduced(assumption)).
% 0.20/0.53 tff(570,plain,
% 0.20/0.53 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | ![Y: $i] : (p1(Y) | (~r1(Y)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(571,plain,
% 0.20/0.53 (![Y: $i] : (p1(Y) | (~r1(Y)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[570, 569])).
% 0.20/0.53 tff(572,plain,
% 0.20/0.53 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | r1(B!42)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(573,plain,
% 0.20/0.53 (r1(B!42)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[572, 569])).
% 0.20/0.53 tff(574,plain,
% 0.20/0.53 (((~![Y: $i] : (p1(Y) | (~r1(Y)))) | (p1(B!42) | (~r1(B!42)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | p1(B!42) | (~r1(B!42)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(575,plain,
% 0.20/0.53 ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | (p1(B!42) | (~r1(B!42)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(576,plain,
% 0.20/0.53 ((~![Y: $i] : (p1(Y) | (~r1(Y)))) | p1(B!42) | (~r1(B!42))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.20/0.53 tff(577,plain,
% 0.20/0.53 (p1(B!42)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[576, 573, 571])).
% 0.20/0.53 tff(578,plain,
% 0.20/0.53 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | (~q1(B!42))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(579,plain,
% 0.20/0.53 (~q1(B!42)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[578, 569])).
% 0.20/0.53 tff(580,plain,
% 0.20/0.53 ((q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))) | ![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(581,plain,
% 0.20/0.53 (![X: $i] : (q1(X) | (~p1(X)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[580, 569])).
% 0.20/0.53 tff(582,plain,
% 0.20/0.53 (((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(B!42) | (~p1(B!42)))) <=> ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(B!42) | (~p1(B!42)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(583,plain,
% 0.20/0.53 ((~![X: $i] : (q1(X) | (~p1(X)))) | (q1(B!42) | (~p1(B!42)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(584,plain,
% 0.20/0.53 ((~![X: $i] : (q1(X) | (~p1(X)))) | q1(B!42) | (~p1(B!42))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.20/0.53 tff(585,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[584, 581, 579, 577])).
% 0.20/0.53 tff(586,plain,(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(587,assumption,(~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))), introduced(assumption)).
% 0.20/0.53 tff(588,plain,
% 0.20/0.53 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | (p1(X!35) | p1(Y!36))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(589,plain,
% 0.20/0.53 (p1(X!35) | p1(Y!36)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[588, 587])).
% 0.20/0.53 tff(590,plain,
% 0.20/0.53 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) | (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(591,plain,
% 0.20/0.53 (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[590, 587])).
% 0.20/0.53 tff(592,assumption,(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))), introduced(assumption)).
% 0.20/0.53 tff(593,plain,
% 0.20/0.53 (~![Y: $i] : (~p1(Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[13, 9])).
% 0.20/0.53 tff(594,plain,
% 0.20/0.53 ((~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | ![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(595,plain,
% 0.20/0.53 (![X: $i] : (~p1(X))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[594, 593, 592])).
% 0.20/0.53 tff(596,plain,
% 0.20/0.53 ((~![X: $i] : (~p1(X))) | (~p1(X!35))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(597,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[596, 9, 595])).
% 0.20/0.53 tff(598,plain,((~p1(X!35)) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(599,plain,
% 0.20/0.53 (~p1(X!35)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[598, 591])).
% 0.20/0.53 tff(600,plain,
% 0.20/0.53 ((~(p1(X!35) | p1(Y!36))) | p1(X!35) | p1(Y!36)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(601,plain,
% 0.20/0.53 (p1(Y!36)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[600, 599, 589])).
% 0.20/0.53 tff(602,assumption,(![X: $i] : (~p1(X))), introduced(assumption)).
% 0.20/0.53 tff(603,assumption,(p1(Y!36)), introduced(assumption)).
% 0.20/0.53 tff(604,plain,
% 0.20/0.53 ((~![X: $i] : (~p1(X))) | (~p1(Y!36))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(605,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[604, 603, 602])).
% 0.20/0.53 tff(606,plain,((~![X: $i] : (~p1(X))) | (~p1(Y!36))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(607,plain,
% 0.20/0.53 (~![X: $i] : (~p1(X))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[606, 601])).
% 0.20/0.53 tff(608,plain,
% 0.20/0.53 (![Y: $i] : (~p1(Y))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[594, 607, 591])).
% 0.20/0.53 tff(609,plain,
% 0.20/0.53 ((~![Y: $i] : (~p1(Y))) | (~p1(Y!36))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(610,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[609, 608, 601])).
% 0.20/0.53 tff(611,plain,((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(612,assumption,(~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))), introduced(assumption)).
% 0.20/0.53 tff(613,plain,
% 0.20/0.53 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) | ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(614,plain,
% 0.20/0.53 (![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[613, 612])).
% 0.20/0.53 tff(615,plain,
% 0.20/0.53 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) | ![Y: $i] : (p1(Y) | (~q1(Y)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(616,plain,
% 0.20/0.53 (![Y: $i] : (p1(Y) | (~q1(Y)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[615, 612])).
% 0.20/0.53 tff(617,assumption,(![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))), introduced(assumption)).
% 0.20/0.53 tff(618,plain,
% 0.20/0.53 (((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(B!18) | (~q1(A!19))))) <=> ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(B!18) | (~q1(A!19)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(619,plain,
% 0.20/0.53 (($false | (~(p1(B!18) | (~q1(A!19))))) <=> (~(p1(B!18) | (~q1(A!19))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(620,plain,
% 0.20/0.53 ((p1(A!19) | (~p1(A!19))) <=> $true),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(621,plain,
% 0.20/0.53 ((~(p1(A!19) | (~p1(A!19)))) <=> (~$true)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[620])).
% 0.20/0.53 tff(622,plain,
% 0.20/0.53 ((~(p1(A!19) | (~p1(A!19)))) <=> $false),
% 0.20/0.53 inference(transitivity,[status(thm)],[621, 41])).
% 0.20/0.53 tff(623,plain,
% 0.20/0.53 (((~(p1(A!19) | (~p1(A!19)))) | (~(p1(B!18) | (~q1(A!19))))) <=> ($false | (~(p1(B!18) | (~q1(A!19)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[622])).
% 0.20/0.53 tff(624,plain,
% 0.20/0.53 (((~(p1(A!19) | (~p1(A!19)))) | (~(p1(B!18) | (~q1(A!19))))) <=> (~(p1(B!18) | (~q1(A!19))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[623, 619])).
% 0.20/0.53 tff(625,plain,
% 0.20/0.53 (((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | ((~(p1(A!19) | (~p1(A!19)))) | (~(p1(B!18) | (~q1(A!19)))))) <=> ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(B!18) | (~q1(A!19)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[624])).
% 0.20/0.53 tff(626,plain,
% 0.20/0.53 (((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | ((~(p1(A!19) | (~p1(A!19)))) | (~(p1(B!18) | (~q1(A!19)))))) <=> ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(B!18) | (~q1(A!19)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[625, 618])).
% 0.20/0.53 tff(627,plain,
% 0.20/0.53 ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | ((~(p1(A!19) | (~p1(A!19)))) | (~(p1(B!18) | (~q1(A!19)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(628,plain,
% 0.20/0.53 ((~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) | (~(p1(B!18) | (~q1(A!19))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.20/0.53 tff(629,plain,
% 0.20/0.53 (~(p1(B!18) | (~q1(A!19)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[628, 617])).
% 0.20/0.53 tff(630,assumption,(~p1(A!19)), introduced(assumption)).
% 0.20/0.53 tff(631,assumption,(![Y: $i] : (p1(Y) | (~q1(Y)))), introduced(assumption)).
% 0.20/0.53 tff(632,plain,
% 0.20/0.53 (((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (p1(A!19) | (~q1(A!19)))) <=> ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | p1(A!19) | (~q1(A!19)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(633,plain,
% 0.20/0.53 ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (p1(A!19) | (~q1(A!19)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(634,plain,
% 0.20/0.53 ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | p1(A!19) | (~q1(A!19))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.20/0.53 tff(635,plain,
% 0.20/0.53 (~q1(A!19)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[634, 631, 630])).
% 0.20/0.53 tff(636,plain,
% 0.20/0.53 ((p1(B!18) | (~q1(A!19))) | q1(A!19)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(637,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[636, 635, 629])).
% 0.20/0.53 tff(638,plain,(p1(A!19) | (~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(639,plain,
% 0.20/0.53 (p1(A!19)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[638, 616, 614])).
% 0.20/0.53 tff(640,plain,
% 0.20/0.53 ((p1(A!19) | (~p1(B!18))) | (~p1(A!19))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(641,plain,
% 0.20/0.53 (p1(A!19) | (~p1(B!18))),
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(~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(681,plain,
% 0.20/0.54 ((~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))) <=> (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(682,plain,
% 0.20/0.54 ((~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(683,plain,
% 0.20/0.54 (^[Z: $i, Y: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~![W: $i] : (~p(W, Y))) <=> (~![W: $i] : (~p(W, Y)))), (((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))) <=> ((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))), ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) <=> (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), rewrite((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) <=> (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))), (((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))))), rewrite(((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))), (((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(684,plain,
% 0.20/0.54 (![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[683])).
% 0.20/0.54 tff(685,plain,
% 0.20/0.54 ((~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) <=> (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(686,plain,
% 0.20/0.54 ((~![X: $i] : ((~a1(X)) | (~b(X)))) <=> (~![X: $i] : ((~a1(X)) | (~b(X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(687,plain,
% 0.20/0.54 ((~![X: $i] : b(X)) <=> (~![X: $i] : b(X))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(688,plain,
% 0.20/0.54 (((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))) <=> ((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[687, 686])).
% 0.20/0.54 tff(689,plain,
% 0.20/0.54 ((~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[688])).
% 0.20/0.54 tff(690,plain,
% 0.20/0.54 ((~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))) <=> (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(691,plain,
% 0.20/0.54 ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(692,plain,
% 0.20/0.54 (((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))) <=> ((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[691, 690])).
% 0.20/0.54 tff(693,plain,
% 0.20/0.54 ((~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[692])).
% 0.20/0.54 tff(694,plain,
% 0.20/0.54 ((~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) <=> (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(695,plain,
% 0.20/0.54 ((~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(696,plain,
% 0.20/0.54 ((~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(697,plain,
% 0.20/0.54 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(698,plain,
% 0.20/0.54 ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) <=> (~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(699,plain,
% 0.20/0.54 (((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) <=> ((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[698, 697])).
% 0.20/0.54 tff(700,plain,
% 0.20/0.54 ((~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) <=> (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[699])).
% 0.20/0.54 tff(701,plain,
% 0.20/0.54 ((~((~b0) | (a0 <=> b0) | (~a0))) <=> (~((~b0) | (a0 <=> b0) | (~a0)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(702,plain,
% 0.20/0.54 ((~![X: $i, Y: $i] : p(X, Y)) <=> (~![X: $i, Y: $i] : p(X, Y))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(703,plain,
% 0.20/0.54 (((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)) <=> ((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[702])).
% 0.20/0.54 tff(704,plain,
% 0.20/0.54 ((~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) <=> (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[703])).
% 0.20/0.54 tff(705,plain,
% 0.20/0.54 ((~![Y: $i] : (~p1(Y))) <=> (~![Y: $i] : (~p1(Y)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(706,plain,
% 0.20/0.54 (((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))) <=> ((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[705])).
% 0.20/0.54 tff(707,plain,
% 0.20/0.54 ((~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) <=> (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[706])).
% 0.20/0.54 tff(708,plain,
% 0.20/0.54 ((~![X: $i] : (~p(X, Y!46))) <=> (~![X: $i] : (~p(X, Y!46)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(709,plain,
% 0.20/0.54 ((~![Y: $i] : p(X!45, Y)) <=> (~![Y: $i] : p(X!45, Y))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(710,plain,
% 0.20/0.54 (((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))) <=> ((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[709, 708])).
% 0.20/0.54 tff(711,plain,
% 0.20/0.54 ((~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) <=> (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[710])).
% 0.20/0.54 tff(712,plain,
% 0.20/0.54 ((~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(713,plain,
% 0.20/0.54 ((~![Z: $i] : (~p1(Z))) <=> (~![Z: $i] : (~p1(Z)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(714,plain,
% 0.20/0.54 (((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))) <=> ((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[713])).
% 0.20/0.54 tff(715,plain,
% 0.20/0.54 ((~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) <=> (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[714])).
% 0.20/0.54 tff(716,plain,
% 0.20/0.54 ((![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))) <=> (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(717,plain,
% 0.20/0.54 ((~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[716])).
% 0.20/0.54 tff(718,plain,
% 0.20/0.54 (((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))) <=> ((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[717])).
% 0.20/0.54 tff(719,plain,
% 0.20/0.54 ((~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[718])).
% 0.20/0.54 tff(720,plain,
% 0.20/0.54 ((~![X: $i] : p1(X)) <=> (~![X: $i] : p1(X))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(721,plain,
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% 0.20/0.54 inference(monotonicity,[status(thm)],[720])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[721])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[720])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[723])).
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% 0.20/0.54 inference(rewrite,[status(thm)],[])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[725])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[726])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[727])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[729])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[730])).
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% 0.20/0.54 inference(monotonicity,[status(thm)],[720, 705])).
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Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> ((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))) | (~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[759, 756, 752, 749, 747, 746, 742, 740, 737, 733, 732, 731, 728, 724, 722, 719, 715, 712, 711, 707, 704, 701, 700, 696, 695, 694, 693, 689, 685, 684, 682, 681])).
% 0.20/0.55 tff(761,plain,
% 0.20/0.55 (((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> ((~((~b0) | (a0 <=> b0) | (~a0))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : 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| (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~a1(X!23)) | (~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))))) | (~((~(b(X!24) | (~a1(X!24)))) | (~![X: $i] : (~b(X))) | (~![X: $i] : a1(X)))) | (~((~q1(Y!14)) | (~![X: $i] : p1(X)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~(q1(B!42) | (~r1(B!42)) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))) | (~((~(r1(Y!52) | (~q1(Y!52)))) | (~![X: $i] : (q1(X) | (~p1(X)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[760, 680])).
% 0.20/0.55 tff(762,plain,
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Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | 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p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(763,plain,
% 0.20/0.56 (((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))) <=> ((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(764,plain,
% 0.41/0.56 ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))) <=> (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z)))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(765,plain,
% 0.41/0.56 (((~q1(A!48)) & k!0 & ![X: $i] : (~((~p1(X)) | (~q1(X))))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(766,plain,
% 0.41/0.56 (^[X: $i] : rewrite((p1(X) & q1(X)) <=> (~((~p1(X)) | (~q1(X)))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(767,plain,
% 0.41/0.56 (![X: $i] : (p1(X) & q1(X)) <=> ![X: $i] : (~((~p1(X)) | (~q1(X))))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[766])).
% 0.41/0.56 tff(768,plain,
% 0.41/0.56 (((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (~((~p1(X)) | (~q1(X)))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[767])).
% 0.41/0.56 tff(769,plain,
% 0.41/0.56 (((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) <=> (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X)))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[768, 765])).
% 0.41/0.56 tff(770,plain,
% 0.41/0.56 (((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) <=> (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(771,plain,
% 0.41/0.56 (^[Z: $i, Y: $i] : trans(monotonicity(rewrite((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) <=> (~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y)))))), rewrite((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))) <=> (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))), (((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))))), rewrite(((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) <=> ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))))), (((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(772,plain,
% 0.41/0.56 (![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y)))))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[771])).
% 0.41/0.56 tff(773,plain,
% 0.41/0.56 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : ((~a1(X)) | (~b(X)))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(774,plain,
% 0.41/0.56 (^[X: $i] : trans(monotonicity(rewrite((a1(X) & b(X)) <=> (~((~a1(X)) | (~b(X))))), ((~(a1(X) & b(X))) <=> (~(~((~a1(X)) | (~b(X))))))), rewrite((~(~((~a1(X)) | (~b(X))))) <=> ((~a1(X)) | (~b(X)))), ((~(a1(X) & b(X))) <=> ((~a1(X)) | (~b(X)))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(775,plain,
% 0.41/0.56 (![X: $i] : (~(a1(X) & b(X))) <=> ![X: $i] : ((~a1(X)) | (~b(X)))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[774])).
% 0.41/0.56 tff(776,plain,
% 0.41/0.56 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : ((~a1(X)) | (~b(X))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[775])).
% 0.41/0.56 tff(777,plain,
% 0.41/0.56 ((a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) <=> (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[776, 773])).
% 0.41/0.56 tff(778,plain,
% 0.41/0.56 ((![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(779,plain,
% 0.41/0.56 (^[X: $i] : rewrite((p1(X) & q1(tptp_fun_Y_16(X))) <=> (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(780,plain,
% 0.41/0.56 (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) <=> ![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[779])).
% 0.41/0.56 tff(781,plain,
% 0.41/0.56 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[780])).
% 0.41/0.56 tff(782,plain,
% 0.41/0.56 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X))))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[781, 778])).
% 0.41/0.56 tff(783,plain,
% 0.41/0.56 ((![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(784,plain,
% 0.41/0.56 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(785,plain,
% 0.41/0.56 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p1(X) & q(X, Y)) <=> (~((~p1(X)) | (~q(X, Y))))), ((~(p1(X) & q(X, Y))) <=> (~(~((~p1(X)) | (~q(X, Y))))))), rewrite((~(~((~p1(X)) | (~q(X, Y))))) <=> ((~p1(X)) | (~q(X, Y)))), ((~(p1(X) & q(X, Y))) <=> ((~p1(X)) | (~q(X, Y)))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(786,plain,
% 0.41/0.56 (![X: $i, Y: $i] : (~(p1(X) & q(X, Y))) <=> ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[785])).
% 0.41/0.56 tff(787,plain,
% 0.41/0.56 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[786])).
% 0.41/0.56 tff(788,plain,
% 0.41/0.56 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[787, 784])).
% 0.41/0.56 tff(789,plain,
% 0.41/0.56 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : ((~a1(X)) | (~c(X)))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(790,plain,
% 0.41/0.56 (^[X: $i] : trans(monotonicity(rewrite((a1(X) & c(X)) <=> (~((~a1(X)) | (~c(X))))), ((~(a1(X) & c(X))) <=> (~(~((~a1(X)) | (~c(X))))))), rewrite((~(~((~a1(X)) | (~c(X))))) <=> ((~a1(X)) | (~c(X)))), ((~(a1(X) & c(X))) <=> ((~a1(X)) | (~c(X)))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(791,plain,
% 0.41/0.56 (![X: $i] : (~(a1(X) & c(X))) <=> ![X: $i] : ((~a1(X)) | (~c(X)))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[790])).
% 0.41/0.56 tff(792,plain,
% 0.41/0.56 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : ((~a1(X)) | (~c(X))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[791])).
% 0.41/0.56 tff(793,plain,
% 0.41/0.56 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[792, 789])).
% 0.41/0.56 tff(794,plain,
% 0.41/0.56 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(795,plain,
% 0.41/0.56 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))) <=> (~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))), ((~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> (~(~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))), rewrite((~(~((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))) <=> ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))), ((~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(796,plain,
% 0.41/0.56 (![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))) <=> ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[795])).
% 0.41/0.56 tff(797,plain,
% 0.41/0.56 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[796])).
% 0.41/0.56 tff(798,plain,
% 0.41/0.56 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y)))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[797, 794])).
% 0.41/0.56 tff(799,plain,
% 0.41/0.56 (^[X: $i, Y: $i] : rewrite((~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) <=> (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(800,plain,
% 0.41/0.56 (![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) <=> ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[799])).
% 0.41/0.57 tff(801,plain,
% 0.41/0.57 ((~((~(a0 & b0)) | (a0 <=> b0))) <=> (~((~b0) | (a0 <=> b0) | (~a0)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(802,plain,
% 0.41/0.57 ((![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) <=> (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(803,plain,
% 0.41/0.57 ((p1(X!35) & ![Y: $i] : (~p1(Y))) <=> (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(804,plain,
% 0.41/0.57 ((![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) <=> (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(805,plain,
% 0.41/0.57 (^[Y: $i] : rewrite(((~p1(Y)) & p1(X!35)) <=> (~(p1(Y) | (~p1(X!35)))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(806,plain,
% 0.41/0.57 (![Y: $i] : ((~p1(Y)) & p1(X!35)) <=> ![Y: $i] : (~(p1(Y) | (~p1(X!35))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[805])).
% 0.41/0.57 tff(807,plain,
% 0.41/0.57 ((![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(808,plain,
% 0.41/0.57 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))), trans(monotonicity(rewrite((~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))) <=> (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))), ((eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))), rewrite((eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))), ((eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))) <=> (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) <=> (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))), rewrite((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(809,plain,
% 0.41/0.57 (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[808])).
% 0.41/0.57 tff(810,plain,
% 0.41/0.57 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[809])).
% 0.41/0.57 tff(811,plain,
% 0.41/0.57 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[810, 807])).
% 0.41/0.57 tff(812,plain,
% 0.41/0.57 ((p1(X!35) & ![Z: $i] : (~p1(Z))) <=> (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(813,plain,
% 0.41/0.57 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(814,plain,
% 0.41/0.57 ((![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))) <=> (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(815,plain,
% 0.41/0.57 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[814])).
% 0.41/0.57 tff(816,plain,
% 0.41/0.57 (((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) <=> (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[815, 813])).
% 0.41/0.57 tff(817,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(818,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & ((~p1(A!32)) | (~p1(B!31)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(819,plain,
% 0.41/0.57 ((~(~((~p1(A!32)) | (~p1(B!31))))) <=> ((~p1(A!32)) | (~p1(B!31)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(820,plain,
% 0.41/0.57 ((p1(A!32) & p1(B!31)) <=> (~((~p1(A!32)) | (~p1(B!31))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(821,plain,
% 0.41/0.57 ((~(p1(A!32) & p1(B!31))) <=> (~(~((~p1(A!32)) | (~p1(B!31)))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[820])).
% 0.41/0.57 tff(822,plain,
% 0.41/0.57 ((~(p1(A!32) & p1(B!31))) <=> ((~p1(A!32)) | (~p1(B!31)))),
% 0.41/0.57 inference(transitivity,[status(thm)],[821, 819])).
% 0.41/0.57 tff(823,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) <=> (![X: $i] : p1(X) & ((~p1(A!32)) | (~p1(B!31))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[822])).
% 0.41/0.57 tff(824,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[823, 818])).
% 0.41/0.57 tff(825,plain,
% 0.41/0.57 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(826,plain,
% 0.41/0.57 ((![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))) <=> (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(827,plain,
% 0.41/0.57 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[826])).
% 0.41/0.57 tff(828,plain,
% 0.41/0.57 (((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) <=> (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[827, 825])).
% 0.41/0.57 tff(829,plain,
% 0.41/0.57 ((b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) <=> (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(830,plain,
% 0.41/0.57 ((![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) <=> (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(831,plain,
% 0.41/0.57 ((![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) <=> (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(832,plain,
% 0.41/0.57 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))) <=> (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(833,plain,
% 0.41/0.57 (^[X: $i] : trans(monotonicity(rewrite(((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))) <=> (~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))), ((~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> (~(~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))), rewrite((~(~((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))) <=> ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))), ((~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(834,plain,
% 0.41/0.57 (![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))) <=> ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[833])).
% 0.41/0.57 tff(835,plain,
% 0.41/0.57 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[834])).
% 0.41/0.57 tff(836,plain,
% 0.41/0.57 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[835, 832])).
% 0.41/0.57 tff(837,plain,
% 0.41/0.57 (((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) <=> (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(838,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) <=> (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(839,plain,
% 0.41/0.57 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))) <=> (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(840,plain,
% 0.41/0.57 (^[X: $i] : trans(monotonicity(rewrite(((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))) <=> (~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))), ((~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> (~(~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))), rewrite((~(~((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))) <=> ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))), ((~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(841,plain,
% 0.41/0.57 (![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))) <=> ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[840])).
% 0.41/0.57 tff(842,plain,
% 0.41/0.57 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[841])).
% 0.41/0.57 tff(843,plain,
% 0.41/0.57 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[842, 839])).
% 0.41/0.57 tff(844,plain,
% 0.41/0.57 ((![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))) & ![Z: $i] : (~a(Z, Z))) <=> (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(845,plain,
% 0.41/0.57 (^[X: $i] : rewrite((a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) <=> (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(846,plain,
% 0.41/0.57 (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) <=> ![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[845])).
% 0.41/0.57 tff(847,plain,
% 0.41/0.57 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))))) & ![Z: $i] : (~a(Z, Z)))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[846])).
% 0.41/0.57 tff(848,plain,
% 0.41/0.57 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[847, 844])).
% 0.41/0.57 tff(849,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & ((~p1(A!13)) | (~p1(B!12)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(850,plain,
% 0.41/0.57 ((~(~((~p1(A!13)) | (~p1(B!12))))) <=> ((~p1(A!13)) | (~p1(B!12)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(851,plain,
% 0.41/0.57 ((p1(A!13) & p1(B!12)) <=> (~((~p1(A!13)) | (~p1(B!12))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(852,plain,
% 0.41/0.57 ((~(p1(A!13) & p1(B!12))) <=> (~(~((~p1(A!13)) | (~p1(B!12)))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[851])).
% 0.41/0.57 tff(853,plain,
% 0.41/0.57 ((~(p1(A!13) & p1(B!12))) <=> ((~p1(A!13)) | (~p1(B!12)))),
% 0.41/0.57 inference(transitivity,[status(thm)],[852, 850])).
% 0.41/0.57 tff(854,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) <=> (![X: $i] : p1(X) & ((~p1(A!13)) | (~p1(B!12))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[853])).
% 0.41/0.57 tff(855,plain,
% 0.41/0.57 ((![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) <=> (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[854, 849])).
% 0.41/0.57 tff(856,plain,
% 0.41/0.57 (^[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : rewrite((~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) <=> (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(857,plain,
% 0.41/0.57 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) <=> ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[856])).
% 0.41/0.57 tff(858,plain,
% 0.41/0.57 ((q1(f(B!6)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))) <=> (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(859,plain,
% 0.41/0.57 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) <=> ((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)) <=> (((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))) & q1(X)))), rewrite((((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)) <=> (~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> (~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))), rewrite((~(~((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(860,plain,
% 0.41/0.57 (![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))) <=> ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[859])).
% 0.41/0.57 tff(861,plain,
% 0.41/0.57 ((q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (q1(f(B!6)) & ![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[860])).
% 0.41/0.57 tff(862,plain,
% 0.41/0.57 ((q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5))))))))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[861, 858])).
% 0.41/0.57 tff(863,plain,
% 0.41/0.57 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(864,plain,
% 0.41/0.57 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) <=> ((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)) <=> (((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))) & q1(X)))), rewrite((((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3))))))))) & q1(X)) <=> (~((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))), ((((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)) <=> (~((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> (~(~((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))))), rewrite((~(~((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))) <=> ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))), ((~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(865,plain,
% 0.41/0.57 (![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))) <=> ![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[864])).
% 0.41/0.57 tff(866,plain,
% 0.41/0.57 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[865])).
% 0.41/0.57 tff(867,plain,
% 0.41/0.57 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[866, 863])).
% 0.41/0.57 tff(868,plain,
% 0.41/0.57 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(869,plain,
% 0.41/0.58 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r1(Y)) | (r1(B!1) & r1(C!2))) <=> ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))), (((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)) <=> ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))) & q1(X)))), rewrite(((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2))))) & q1(X)) <=> (~((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))), (((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)) <=> (~((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))), ((~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> (~(~((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))))), rewrite((~(~((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))) <=> ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))), ((~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(870,plain,
% 0.41/0.58 (![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))) <=> ![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[869])).
% 0.41/0.58 tff(871,plain,
% 0.41/0.58 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[870])).
% 0.41/0.58 tff(872,plain,
% 0.41/0.58 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X))))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[871, 868])).
% 0.41/0.58 tff(873,plain,
% 0.41/0.58 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[872, 867, 862, 857, 855, 848, 843, 838, 837, 836, 831, 830, 829, 828, 824, 817, 816, 812, 811, 806, 804, 803, 802, 801, 800, 798, 793, 788, 783, 782, 777, 772, 770, 769, 764])).
% 0.43/0.58 tff(874,plain,
% 0.43/0.58 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~(p1(X) | (~p1(f(Y))))) | (~((~r1(Y)) | (~((~r1(B!1)) | (~r1(C!2)))))) | (~q1(X)))))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | (~((~![Z: $i] : q1(f(Z))) | (~![X: $i, Y: $i] : ((~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!4)) | (~r1(C!3)))))))))) | (~q1(X)))))) | (~((~q1(f(B!6))) | (~![X: $i, Y: $i] : ((~q1(X)) | (~((~p1(f(Y))) | (~((~p1(X)) | (~((~r1(Y)) | (~((~r1(B!6)) | (~r1(C!5)))))))))))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!13)) | (~p1(B!12)))))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p1(X4)) | (~c(X4)))) | (~((~p1(X3)) | (~g(X3)))) | (~p1(A!8)) | (~e(A!8)) | (~(s(X, f(X)) | g(X) | (~e(X)))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p1(Y) | (~s(A!8, Y)))))) | (~((~![X: $i] : (~((~a(X, tptp_fun_Y_17(X))) | (~a(tptp_fun_Y_17(X), tptp_fun_Y_17(X)))))) | (~![Z: $i] : (~a(Z, Z))))) | (~((~![Y: $i] : (p1(Y) | (~q1(Y)))) | (~![X: $i] : ((~(p1(A!19) | (~p1(X)))) | (~(p1(B!18) | (~q1(X)))))))) | (~((~![X: $i] : p1(X)) | (~![Y: $i] : (~p1(Y))))) | (~(q1(X!20) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X)))))) | (~((~![Z: $i] : (p1(Z) | (~q1(Z)))) | (~![X: $i] : ((~(p1(A!22) | (~p1(X)))) | (~(p1(B!21) | (~q1(X)))))))) | (~((~![X: $i] : (b(X) | (~a1(X)))) | (~![X: $i] : (~b(X))) | (~a1(X!23)))) | (~((~![X: $i] : a1(X)) | (~![X: $i] : (~b(X))) | (~(b(X!24) | (~a1(X!24)))))) | (~((~b(X!26)) | (~![X: $i] : (~(a1(X) | b(X)))))) | (~((~(a(X!28, Y!27) | a(X!29, Y!30))) | (~(![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(A!32)) | (~p1(B!31)))))) | (~((~![X: $i] : p1(X)) | (~((~p1(X!33)) | (~p1(Y!34)))))) | (~((~(p1(X!35) | p1(Y!36))) | (~(![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))))) | (~((~p1(X!35)) | (~![Z: $i] : (~p1(Z))))) | (~((~eq(A!40, B!39)) | eq(B!39, A!40) | (~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y)))))))))) | ![Y: $i] : (~(p1(Y) | (~p1(X!35)))) | (~((~![Y: $i] : p(X!45, Y)) | (~![X: $i] : (~p(X, Y!46))))) | (~((~p1(X!35)) | (~![Y: $i] : (~p1(Y))))) | (~((~![X: $i, Y: $i] : p(X, Y)) | p(X!47, X!47))) | (~((~b0) | (a0 <=> b0) | (~a0))) | ![X: $i, Y: $i] : (~((~s1(A!50)) | p(A!50, B!49) | (~((~q1(X)) | p(X, A!50))) | (~q1(A!50)) | (~q1(B!49)) | (~((~r1(Y)) | p(B!49, Y))) | (~r1(A!50)) | (~r1(B!49)) | (~((~s1(A!50)) | p(X, Y))))) | (~((~![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y))) | (~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!51), B!51)) | q(X, Y))))))) | (~(b(X!7) | (~a1(X!7)) | (~![X: $i] : (c(X) | b(X) | (~a1(X)))) | (~![X: $i] : ((~a1(X)) | (~c(X)))))) | (~((~s1(A!11)) | (~s1(B!10)) | (~r(B!10, C!9)) | (~![X: $i] : (p1(X) | (~s1(X)))) | (~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~![X: $i, Y: $i] : ((~p1(X)) | (~q(X, Y)))))) | (~((~![X: $i] : p1(X)) | (~q1(Y!14)) | (~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))))) | (~((~![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (~![X: $i] : (~((~p1(X)) | (~q1(tptp_fun_Y_16(X)))))))) | (~((~a1(X!23)) | (~![X: $i] : b(X)) | (~![X: $i] : ((~a1(X)) | (~b(X)))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | q1(B!42) | (~r1(B!42)))) | ![Z: $i, Y: $i] : ((~((~p(Y, tptp_fun_X_37(Z))) | (~![W: $i] : (~p(W, Y))))) | (~((~p(Y, Z)) | p(Y, tptp_fun_X_37(Z)) | (~p(Z, Y))))) | (~(q1(A!48) | (~k!0) | (~![X: $i] : (~((~p1(X)) | (~q1(X))))))) | (~((~![X: $i] : (q1(X) | (~p1(X)))) | (~(r1(Y!52) | (~q1(Y!52)))) | (~![Z: $i] : (~(r1(Z) | (~p1(Z))))))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[873, 763])).
% 0.43/0.58 tff(875,plain,
% 0.43/0.58 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(876,plain,
% 0.43/0.59 (((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))) <=> (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(877,plain,
% 0.43/0.59 ((![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) <=> (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(878,plain,
% 0.43/0.59 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(879,plain,
% 0.43/0.59 ((k!0 & ![X: $i] : (p1(X) & q1(X))) <=> (k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(880,plain,
% 0.43/0.59 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[879])).
% 0.43/0.59 tff(881,plain,
% 0.43/0.59 (((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) <=> ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[880, 878])).
% 0.43/0.59 tff(882,plain,
% 0.43/0.59 ((![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) <=> (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(883,plain,
% 0.43/0.59 (((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) <=> ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(884,plain,
% 0.43/0.59 (^[X: $i] : rewrite((~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) <=> (~((~p1(X)) | p1(tptp_fun_Y_41(X)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(885,plain,
% 0.43/0.59 (![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) <=> ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[884])).
% 0.43/0.59 tff(886,plain,
% 0.43/0.59 ((![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) <=> (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(887,plain,
% 0.43/0.59 (![Z: $i] : ![Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) <=> ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z)))))),
% 0.43/0.59 inference(pull_quant,[status(thm)],[])).
% 0.43/0.59 tff(888,plain,
% 0.43/0.59 ((p1(X!35) & ![Z: $i] : (~p1(Z))) <=> (p1(X!35) & ![Z: $i] : (~p1(Z)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(889,plain,
% 0.43/0.59 ((b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) <=> (b(X!26) & ![X: $i] : (~(a1(X) | b(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(890,plain,
% 0.43/0.59 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(891,plain,
% 0.43/0.59 ((a1(X!23) & ![X: $i] : b(X)) <=> (a1(X!23) & ![X: $i] : b(X))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(892,plain,
% 0.43/0.59 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[891])).
% 0.43/0.59 tff(893,plain,
% 0.43/0.59 (((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) <=> (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[892, 890])).
% 0.43/0.59 tff(894,plain,
% 0.43/0.59 ((![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) <=> (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(895,plain,
% 0.43/0.59 ((![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) <=> (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(896,plain,
% 0.43/0.59 ((![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) <=> (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(897,plain,
% 0.43/0.59 ((![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) <=> (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(898,plain,
% 0.43/0.59 ((![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) <=> (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(899,plain,
% 0.43/0.59 ((![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(900,plain,
% 0.43/0.59 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) <=> (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(901,plain,
% 0.43/0.59 (^[Z: $i] : rewrite((~(p1(tptp_fun_Y_15(Z)) | r1(Z))) <=> (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(902,plain,
% 0.43/0.59 (![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z))) <=> ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[901])).
% 0.43/0.59 tff(903,plain,
% 0.43/0.59 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[902])).
% 0.43/0.59 tff(904,plain,
% 0.43/0.59 (((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) <=> (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z)))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[903, 900])).
% 0.43/0.59 tff(905,plain,
% 0.43/0.59 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(906,plain,
% 0.43/0.59 ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(907,plain,
% 0.43/0.59 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[906])).
% 0.43/0.59 tff(908,plain,
% 0.43/0.59 (((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) <=> (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[907, 905])).
% 0.43/0.59 tff(909,plain,
% 0.43/0.59 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(910,plain,
% 0.43/0.59 ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(911,plain,
% 0.43/0.59 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[910])).
% 0.43/0.59 tff(912,plain,
% 0.43/0.59 (((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) <=> (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[911, 909])).
% 0.43/0.59 tff(913,plain,
% 0.43/0.59 ((q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) <=> (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(914,plain,
% 0.43/0.59 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(915,plain,
% 0.43/0.59 ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) <=> (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(916,plain,
% 0.43/0.59 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i] : ![Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[915, 914, 913, 912, 908, 904, 899, 898, 897, 896, 895, 894, 893, 889, 827, 815, 888, 887, 886, 885, 883, 882, 881, 877, 876])).
% 0.43/0.60 tff(917,plain,
% 0.43/0.60 (((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ((![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7))))) & ![X: $i] : (~(a1(X) & c(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | ((s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | ((![X: $i] : p1(X) & q1(Y!14)) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(p1(tptp_fun_Y_15(Z)) | r1(Z)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | ((a1(X!23) & ![X: $i] : b(X)) & ![X: $i] : (~(a1(X) & b(X)))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | ![Z: $i] : ![Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i] : (~(p1(tptp_fun_Y_41(X)) | (~p1(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & (![X: $i] : (q1(X) | (~p1(X))) & r1(B!42))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | ((~q1(A!48)) & (k!0 & ![X: $i] : (p1(X) & q1(X)))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | ((![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52)))) & ![Z: $i] : (~(r1(Z) | (~p1(Z)))))) <=> ((![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B!1) & r1(C!2))) & q1(X)))) | (![Z: $i] : q1(f(Z)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!4) & r1(C!3))))) & q1(X)))) | (q1(f(B!6)) & ![X: $i, Y: $i] : (~(((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B!6) & r1(C!5))))) & q1(X)))) | ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A!8) & e(A!8) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A!8, Y))))))) | (![X: $i] : p1(X) & (~(p1(A!13) & p1(B!12)))) | (![X: $i] : (a(X, tptp_fun_Y_17(X)) & a(tptp_fun_Y_17(X), tptp_fun_Y_17(X))) & ![Z: $i] : (~a(Z, Z))) | (![Y: $i] : (p1(Y) | (~q1(Y))) & ![X: $i] : (~((p1(A!19) | (~p1(X))) & (p1(B!18) | (~q1(X)))))) | (![X: $i] : p1(X) & ![Y: $i] : (~p1(Y))) | ((~q1(X!20)) & ![X: $i] : p1(X) & ![X: $i] : (q1(X) | (~p1(X)))) | (![Z: $i] : (p1(Z) | (~q1(Z))) & ![X: $i] : (~((p1(A!22) | (~p1(X))) & (p1(B!21) | (~q1(X)))))) | (![X: $i] : (~b(X)) & ![X: $i] : (b(X) | (~a1(X))) & a1(X!23)) | (![X: $i] : (~b(X)) & ![X: $i] : a1(X) & (b(X!24) | (~a1(X!24)))) | ![X: $i] : (~(a(X, X) <=> a(X, Y!25))) | (b(X!26) & ![X: $i] : (~(a1(X) | b(X)))) | ((a(X!28, Y!27) | a(X!29, Y!30)) & (![X: $i, Y: $i] : (~a(X, Y)) | ![Y: $i, X: $i] : (~a(X, Y)))) | (![X: $i] : p1(X) & (~(p1(A!32) & p1(B!31)))) | (![X: $i] : p1(X) & ((~p1(X!33)) | (~p1(Y!34)))) | ((p1(X!35) | p1(Y!36)) & (![X: $i] : (~p1(X)) | ![Y: $i] : (~p1(Y)))) | (p1(X!35) & ![Z: $i] : (~p1(Z))) | (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_38(Y, X), X) <=> a_member_of(tptp_fun_Z_38(Y, X), Y))))) & (~((~eq(A!40, B!39)) | eq(B!39, A!40)))) | ![X: $i, Y: $i] : (~(r1(B!43) | (~p1(A!44)) | (~(r1(Y) | (~p1(X)))))) | ![Y: $i] : ((~p1(Y)) & p1(X!35)) | (![Y: $i] : p(X!45, Y) & ![X: $i] : (~p(X, Y!46))) | (p1(X!35) & ![Y: $i] : (~p1(Y))) | (![X: $i, Y: $i] : p(X, Y) & (~p(X!47, X!47))) | (~((~(a0 & b0)) | (a0 <=> b0))) | ![X: $i, Y: $i] : (~((~(((~q1(X)) | p(X, A!50)) & q1(A!50) & q1(B!49) & ((~r1(Y)) | p(B!49, Y)) & r1(A!50) & r1(B!49) & ((~s1(A!50)) | p(X, Y)) & s1(A!50))) | p(A!50, B!49))) | (![Y: $i] : ((~(r1(Y) | (~r1(B!51)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!51), B!51)) | q(X, Y))))) | (![X: $i] : (c(X) | b(X) | (~a1(X))) & (~(b(X!7) | (~a1(X!7)))) & ![X: $i] : (~(a1(X) & c(X)))) | (s1(A!11) & s1(B!10) & r(B!10, C!9) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p1(X) & q(X, Y)))) | (![X: $i] : p1(X) & q1(Y!14) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (![X: $i] : (p1(X) & q1(tptp_fun_Y_16(X))) & ![Z: $i] : (~(r1(Z) | p1(tptp_fun_Y_15(Z))))) | (a1(X!23) & ![X: $i] : b(X) & ![X: $i] : (~(a1(X) & b(X)))) | ![Z: $i, Y: $i] : ((p(Y, tptp_fun_X_37(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_37(Z))))) | ![X: $i] : (~((~p1(X)) | p1(tptp_fun_Y_41(X)))) | ((~q1(B!42)) & ![Y: $i] : (p1(Y) | (~r1(Y))) & ![X: $i] : (q1(X) | (~p1(X))) & r1(B!42)) | ((~q1(A!48)) & k!0 & ![X: $i] : (p1(X) & q1(X))) | (![X: $i] : (q1(X) | (~p1(X))) & (r1(Y!52) | (~q1(Y!52))) & ![Z: $i] : (~(r1(Z) | (~p1(Z))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[916, 875])).
% 0.43/0.60 tff(918,plain,
% 0.43/0.60 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(919,plain,
% 0.43/0.60 ((![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))) <=> (![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(920,plain,
% 0.43/0.61 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[919])).
% 0.43/0.61 tff(921,plain,
% 0.43/0.61 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(922,plain,
% 0.43/0.61 ((![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))) <=> (![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(923,plain,
% 0.43/0.62 ((~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[922])).
% 0.43/0.62 tff(924,plain,
% 0.43/0.62 ((~((((((((((((((((((((((((((((((((((((((((((![C: $i, B: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : (((p1(f(Y)) => p1(X)) & (r1(Y) => (r1(B) & r1(C)))) & q1(X))) & ![B: $i, C: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ![B: $i, C: $i] : (q1(f(B)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ((![X: $i] : (a1(X) => (b(X) | c(X))) & (~![X: $i] : (a1(X) => b(X)))) => ?[X: $i] : (a1(X) & c(X)))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p1(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p1(Y))) => ((p1(X3) & g(X3)) | (p1(X4) & c(X4))))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & (![X: $i] : p1(X) => ![A: $i, B: $i] : (p1(A) & p1(B)))) & ((![X: $i] : p1(X) & ?[Y: $i] : q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (p1(X) & q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (?[X: $i] : p1(X) => (?[X: $i] : p1(X) & (a0 => ((b0 | (~b0)) & (q0 => q0)))))) & (![X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i] : (p1(X) => q1(X)) => (![X: $i] : p1(X) => ![X: $i] : q1(X)))) & ![A: $i, B: $i] : (![Z: $i] : (q1(Z) => p1(Z)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (![X: $i] : (a1(X) => b(X)) => (?[X: $i] : a1(X) => ?[X: $i] : b(X)))) & (?[X: $i] : (a1(X) => b(X)) => (![X: $i] : a1(X) => ?[X: $i] : b(X)))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) & ((?[X: $i] : a1(X) & ![X: $i] : b(X)) => ?[X: $i] : (a1(X) & b(X)))) & (?[X: $i] : b(X) => ?[X: $i] : (a1(X) | b(X)))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y))) & ![A: $i, B: $i] : (![X: $i] : p1(X) => (p1(A) & p1(B)))) & (![X: $i] : p1(X) => (![X: $i] : p1(X) & ![Y: $i] : p1(Y)))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y))) & (?[X: $i] : p1(X) => ?[Z: $i] : p1(Z))) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) & (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & ?[X: $i] : ![Y: $i] : (p1(X) => p1(Y))) & ![B: $i] : ((![X: $i] : (p1(X) => q1(X)) & r1(B)) => (![Y: $i] : (r1(Y) => p1(Y)) => q1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p1(X) => r1(Y)) => (p1(A) => r1(B)))) & ?[Y: $i] : (?[X: $i] : p1(X) => p1(Y))) & (?[X: $i] : ![Y: $i] : p(X, Y) => ![Y: $i] : ?[X: $i] : p(X, Y))) & (p1(z) => p1(z))) & (?[X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i, Y: $i] : p(X, Y) => ![X: $i] : p(X, X))) & ![A: $i] : (((f0 | g0) & ![X: $i] : (p1(X) & q1(X))) => q1(A))) & (((a0 <=> b0) | a0) | b0)) & ((a0 & b0) => (a0 <=> b0))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q1(X) => p(X, A)) & q1(A)) & q1(B)) & (r1(Y) => p(B, Y))) & r1(A)) & r1(B)) & (s1(A) => p(X, Y))) & s1(A)) => p(A, B))) & ![B: $i] : (![Y: $i] : ((r1(B) => r1(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))) & ((![X: $i] : (p1(X) => q1(X)) & ?[Y: $i] : (q1(Y) => r1(Y))) => ?[Z: $i] : (p1(Z) => r1(Z))))) <=> (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(925,axiom,(~((((((((((((((((((((((((((((((((((((((((((![C: $i, B: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : (((p1(f(Y)) => p1(X)) & (r1(Y) => (r1(B) & r1(C)))) & q1(X))) & ![B: $i, C: $i] : (![Z: $i] : q1(f(Z)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ![B: $i, C: $i] : (q1(f(B)) => ?[X: $i, Y: $i] : ((p1(f(Y)) => (p1(X) & (r1(Y) => (r1(B) & r1(C))))) & q1(X)))) & ((![X: $i] : (a1(X) => (b(X) | c(X))) & (~![X: $i] : (a1(X) => b(X)))) => ?[X: $i] : (a1(X) & c(X)))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p1(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p1(Y))) => ((p1(X3) & g(X3)) | (p1(X4) & c(X4))))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & (![X: $i] : p1(X) => ![A: $i, B: $i] : (p1(A) & p1(B)))) & ((![X: $i] : p1(X) & ?[Y: $i] : q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (p1(X) & q1(Y)) => ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z)))) & (![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y)) => ?[Z: $i] : a(Z, Z))) & ![A: $i, B: $i, C: $i] : (((((s1(A) & s1(B)) & r(B, C)) & ![X: $i] : (s1(X) => p1(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p1(X) & q(X, Y)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (?[X: $i] : p1(X) => (?[X: $i] : p1(X) & (a0 => ((b0 | (~b0)) & (q0 => q0)))))) & (![X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i] : (p1(X) => q1(X)) => (![X: $i] : p1(X) => ![X: $i] : q1(X)))) & ![A: $i, B: $i] : (![Z: $i] : (q1(Z) => p1(Z)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & (![X: $i] : (a1(X) => b(X)) => (?[X: $i] : a1(X) => ?[X: $i] : b(X)))) & (?[X: $i] : (a1(X) => b(X)) => (![X: $i] : a1(X) => ?[X: $i] : b(X)))) & (~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) & ((?[X: $i] : a1(X) & ![X: $i] : b(X)) => ?[X: $i] : (a1(X) & b(X)))) & (?[X: $i] : b(X) => ?[X: $i] : (a1(X) | b(X)))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y))) & ![A: $i, B: $i] : (![X: $i] : p1(X) => (p1(A) & p1(B)))) & (![X: $i] : p1(X) => (![X: $i] : p1(X) & ![Y: $i] : p1(Y)))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y))) & (?[X: $i] : p1(X) => ?[Z: $i] : p1(Z))) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) & (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))) & ![A: $i, B: $i] : (![Y: $i] : (q1(Y) => p1(Y)) => ?[X: $i] : ((p1(X) => p1(A)) & (q1(X) => p1(B))))) & ?[X: $i] : ![Y: $i] : (p1(X) => p1(Y))) & ![B: $i] : ((![X: $i] : (p1(X) => q1(X)) & r1(B)) => (![Y: $i] : (r1(Y) => p1(Y)) => q1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p1(X) => r1(Y)) => (p1(A) => r1(B)))) & ?[Y: $i] : (?[X: $i] : p1(X) => p1(Y))) & (?[X: $i] : ![Y: $i] : p(X, Y) => ![Y: $i] : ?[X: $i] : p(X, Y))) & (p1(z) => p1(z))) & (?[X: $i] : p1(X) => ?[Y: $i] : p1(Y))) & (![X: $i, Y: $i] : p(X, Y) => ![X: $i] : p(X, X))) & ![A: $i] : (((f0 | g0) & ![X: $i] : (p1(X) & q1(X))) => q1(A))) & (((a0 <=> b0) | a0) | b0)) & ((a0 & b0) => (a0 <=> b0))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q1(X) => p(X, A)) & q1(A)) & q1(B)) & (r1(Y) => p(B, Y))) & r1(A)) & r1(B)) & (s1(A) => p(X, Y))) & s1(A)) => p(A, B))) & ![B: $i] : (![Y: $i] : ((r1(B) => r1(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))) & ((![X: $i] : (p1(X) => q1(X)) & ?[Y: $i] : (q1(Y) => r1(Y))) => ?[Z: $i] : (p1(Z) => r1(Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.43/0.63 tff(926,plain,
% 0.43/0.63 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.43/0.63 tff(927,plain,
% 0.43/0.63 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & (a0 | b0 | (a0 <=> b0)) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[926, 923])).
% 0.48/0.63 tff(928,plain,
% 0.48/0.63 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[927, 921])).
% 0.48/0.63 tff(929,plain,
% 0.48/0.63 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~((f0 | g0) & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[928, 920])).
% 0.48/0.63 tff(930,plain,
% 0.48/0.63 (~(![C: $i, B: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : ((p1(X) | (~p1(f(Y)))) & ((~r1(Y)) | (r1(B) & r1(C))) & q1(X))) & ![B: $i, C: $i] : ((~![Z: $i] : q1(f(Z))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ![B: $i, C: $i] : ((~q1(f(B))) | ?[X: $i, Y: $i] : (((~p1(f(Y))) | (p1(X) & ((~r1(Y)) | (r1(B) & r1(C))))) & q1(X))) & ((~(![X: $i] : (c(X) | b(X) | (~a1(X))) & (~![X: $i] : (b(X) | (~a1(X)))))) | ?[X: $i] : (a1(X) & c(X))) & ![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p1(X4) & c(X4)) | (p1(X3) & g(X3)) | (~(p1(A) & e(A) & (s(X, f(X)) | g(X) | (~e(X))) & (c(f(X2)) | g(X2) | (~e(X2))) & (p1(Y) | (~s(A, Y)))))) & ![A: $i, B: $i, C: $i] : ((~(s1(A) & s1(B) & r(B, C) & ![X: $i] : (p1(X) | (~s1(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p1(X) & q(X, Y))) & ((~![X: $i] : p1(X)) | ![A: $i, B: $i] : (p1(A) & p1(B))) & ((~(![X: $i] : p1(X) & ?[Y: $i] : q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (p1(X) & q1(Y))) | ?[Z: $i] : ![Y: $i] : (p1(Y) | r1(Z))) & ((~![X: $i] : ?[Y: $i] : (a(X, Y) & a(Y, Y))) | ?[Z: $i] : a(Z, Z)) & ![A: $i, B: $i] : ((~![Y: $i] : (p1(Y) | (~q1(Y)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & ((~![X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & (![X: $i] : q1(X) | (~![X: $i] : p1(X)) | (~![X: $i] : (q1(X) | (~p1(X))))) & ![A: $i, B: $i] : ((~![Z: $i] : (p1(Z) | (~q1(Z)))) | ?[X: $i] : ((p1(A) | (~p1(X))) & (p1(B) | (~q1(X))))) & (?[X: $i] : b(X) | (~![X: $i] : (b(X) | (~a1(X)))) | (~?[X: $i] : a1(X))) & (?[X: $i] : b(X) | (~![X: $i] : a1(X)) | (~?[X: $i] : (b(X) | (~a1(X))))) & (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))) & ((~(?[X: $i] : a1(X) & ![X: $i] : b(X))) | ?[X: $i] : (a1(X) & b(X))) & ((~?[X: $i] : b(X)) | ?[X: $i] : (a1(X) | b(X))) & (?[X: $i, Y: $i] : a(X, Y) <=> ?[Y: $i, X: $i] : a(X, Y)) & ![A: $i, B: $i] : ((~![X: $i] : p1(X)) | (p1(A) & p1(B))) & ((~![X: $i] : p1(X)) | (![X: $i] : p1(X) & ![Y: $i] : p1(Y))) & (?[X: $i] : p1(X) <=> ?[Y: $i] : p1(Y)) & ((~?[X: $i] : p1(X)) | ?[Z: $i] : p1(Z)) & ?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))) & ((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) & ?[X: $i] : ![Y: $i] : (p1(Y) | (~p1(X))) & ![B: $i] : (q1(B) | (~![Y: $i] : (p1(Y) | (~r1(Y)))) | (~(![X: $i] : (q1(X) | (~p1(X))) & r1(B)))) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : (r1(B) | (~p1(A)) | (~(r1(Y) | (~p1(X))))) & ?[Y: $i] : (p1(Y) | (~?[X: $i] : p1(X))) & ((~?[X: $i] : ![Y: $i] : p(X, Y)) | ![Y: $i] : ?[X: $i] : p(X, Y)) & ((~?[X: $i] : p1(X)) | ?[Y: $i] : p1(Y)) & ((~![X: $i, Y: $i] : p(X, Y)) | ![X: $i] : p(X, X)) & ![A: $i] : (q1(A) | (~(k!0 & ![X: $i] : (p1(X) & q1(X))))) & ((~(a0 & b0)) | (a0 <=> b0)) & ![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q1(X)) | p(X, A)) & q1(A) & q1(B) & ((~r1(Y)) | p(B, Y)) & r1(A) & r1(B) & ((~s1(A)) | p(X, Y)) & s1(A))) | p(A, B)) & ![B: $i] : ((~![Y: $i] : ((~(r1(Y) | (~r1(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))) & ((~(![X: $i] : (q1(X) | (~p1(X))) & ?[Y: $i] : (r1(Y) | (~q1(Y))))) | ?[Z: $i] : (r1(Z) | (~p1(Z)))))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[929, 918])).
% 0.50/0.71 unexpected number of arguments: (let ((a!1 (forall ((C $i) (B $i))
% 0.50/0.71 (let ((a!1 (forall ((Z $i)) (q1 (f Z))))
% 0.50/0.71 (a!2 (exists ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.50/0.71 (and a!1
% 0.50/0.71 (or (not (r1 Y)) (and (r1 B) (r1 C)))
% 0.50/0.71 (q1 X))))))
% 0.50/0.71 (or (not a!1) a!2))))
% 0.50/0.71 (a!2 (forall ((Z $i)) (q1 (f Z))))
% 0.50/0.71 (a!3 (exists ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.50/0.71 (and a!1 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2))) (q1 X)))))
% 0.50/0.71 (a!5 (lambda ((Z $i)) (refl (~ (q1 (f Z)) (q1 (f Z))))))
% 0.50/0.71 (a!7 (lambda ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.50/0.71 (let ((a!2 (and a!1
% 0.50/0.71 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2)))
% 0.50/0.71 (q1 X))))
% 0.50/0.71 (refl (~ (not a!2) (not a!2)))))))
% 0.50/0.71 (a!8 (forall ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (or (p1 X) (not (p1 (f Y))))))
% 0.50/0.71 (let ((a!2 (and a!1
% 0.50/0.71 (or (not (r1 Y)) (and (r1 B!1) (r1 C!2)))
% 0.50/0.71 (q1 X))))
% 0.50/0.71 (not a!2)))))
% 0.50/0.71 (a!11 (forall ((B $i) (C $i))
% 0.50/0.71 (let ((a!1 (forall ((Z $i)) (q1 (f Z))))
% 0.50/0.71 (a!2 (exists ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (and (p1 X)
% 0.50/0.71 (or (not (r1 Y)) (and (r1 B) (r1 C))))))
% 0.50/0.71 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.50/0.71 (and a!2 (q1 X)))))))
% 0.50/0.71 (or (not a!1) a!2))))
% 0.50/0.71 (a!12 (exists ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (and (p1 X) (or (not (r1 Y)) (and (r1 B!4) (r1 C!3))))))
% 0.50/0.71 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.50/0.71 (and a!2 (q1 X))))))
% 0.50/0.71 (a!14 (forall ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (and (p1 X) (or (not (r1 Y)) (and (r1 B!4) (r1 C!3))))))
% 0.50/0.71 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.50/0.71 (not (and a!2 (q1 X)))))))
% 0.50/0.71 (a!17 (forall ((B $i) (C $i))
% 0.50/0.71 (let ((a!1 (exists ((X $i) (Y $i))
% 0.50/0.71 (let ((a!1 (and (p1 X)
% 0.50/0.71 (or (not (r1 Y)) (and (r1 B) (r1 C))))))
% 0.50/0.71 (let ((a!2 (or (not (p1 (f Y))) a!1)))
% 0.50/0.71 (and a!2 (q1 X)))))))
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% 0.50/0.71 (a!50 (monotonicity (refl (~ (s1 A!11) (s1 A!11)))
% 0.50/0.71 (refl (~ (s1 B!10) (s1 B!10)))
% 0.50/0.71 (refl (~ (r B!10 C!9) (r B!10 C!9)))
% 0.50/0.71 a!48
% 0.50/0.71 a!49
% 0.50/0.71 (~ a!45 a!45)))
% 0.50/0.71 (a!54 (~ (not (or (not a!45) a!46)) (and a!45 a!52)))
% 0.50/0.71 (a!61 (~ (not (or (not a!56) a!58)) a!60))
% 0.50/0.71 (a!69 (~ a!68 (and (and a!56 (q1 Y!14)) a!67)))
% 0.50/0.71 (a!74 (nnf-neg a!73 (~ (not (not a!71)) a!72)))
% 0.50/0.71 (a!85 (nnf-neg a!80 (nnf-neg (proof-bind a!81) (~ (not a!82) a!83)) a!84))
% 0.50/0.71 (a!91 (nnf-neg a!90 (~ (not (not a!87)) a!87)))
% 0.50/0.71 (a!100 (nnf-neg a!57 (nnf-neg (proof-bind a!96) (~ (not a!97) a!98)) a!99))
% 0.50/0.71 (a!105 (nnf-neg a!104 (~ (not (not a!103)) a!103)))
% 0.50/0.71 (a!112 (nnf-neg a!111 (~ (not (not a!108)) a!108)))
% 0.50/0.71 (a!121 (nnf-neg a!120 (~ (not (not a!28)) a!28)))
% 0.50/0.71 (a!133 (~ (not (or a!118 (not a!127) (not a!129))) a!132))
% 0.50/0.71 (a!138 (nnf-neg (trans (sk (~ a!135 a!136)) a!137 (~ a!135 a!136))
% 0.50/0.71 (~ (not (not a!135)) a!136)))
% 0.50/0.71 (a!147 (~ a!146 (and (and (a1 X!23) a!140) a!144)))
% 0.50/0.71 (a!160 (nnf-neg (sk (~ a!153 (a X!28 Y!27)))
% 0.50/0.71 (nnf-neg (proof-bind a!154) (~ (not a!153) a!155))
% 0.50/0.71 (sk (~ a!156 (a X!29 Y!30)))
% 0.50/0.71 (nnf-neg (proof-bind a!157) (~ (not a!156) a!158))
% 0.50/0.71 (~ (not (= a!153 a!156)) a!159)))
% 0.50/0.71 (a!165 (trans (sk (~ (not a!161) a!162))
% 0.50/0.71 (nnf-neg a!57 (refl a!163) (~ a!162 a!164))
% 0.50/0.71 (~ (not a!161) a!164)))
% 0.50/0.71 (a!171 (~ (not (or (not a!56) (and a!56 a!167))) a!170))
% 0.50/0.71 (a!176 (nnf-neg (sk (~ a!172 (p1 X!35)))
% 0.50/0.71 (nnf-neg (proof-bind a!173) (~ (not a!172) a!174))
% 0.50/0.71 (sk (~ a!97 (p1 Y!36)))
% 0.50/0.71 (nnf-neg (proof-bind a!96) (~ (not a!97) a!98))
% 0.50/0.71 a!175))
% 0.50/0.71 (a!182 (nnf-neg a!177
% 0.50/0.71 (nnf-neg (proof-bind a!178) (~ (not a!179) a!180))
% 0.50/0.71 a!181))
% 0.50/0.71 (a!193 (nnf-neg a!189 (sk (~ (not a!190) a!191)) a!192))
% 0.50/0.71 (a!202 (nnf-neg a!201 (~ (not (not a!198)) a!198)))
% 0.50/0.71 (a!203 (monotonicity a!104
% 0.50/0.71 (refl (~ (r1 B!42) (r1 B!42)))
% 0.50/0.71 (~ (and a!103 (r1 B!42)) (and a!103 (r1 B!42)))))
% 0.50/0.71 (a!206 (~ (not a!199) (and (not (q1 B!42)) a!198 (and a!103 (r1 B!42)))))
% 0.50/0.71 (a!227 (nnf-neg a!220
% 0.50/0.71 (trans (sk a!222)
% 0.50/0.71 (nnf-neg (proof-bind a!223) a!225)
% 0.50/0.71 (~ (not a!221) a!224))
% 0.50/0.71 a!226))
% 0.50/0.71 (a!229 (nnf-neg a!177
% 0.50/0.71 (nnf-neg (proof-bind a!96) (~ (not a!97) a!98))
% 0.50/0.71 a!228))
% 0.50/0.71 (a!242 (nnf-neg (monotonicity (refl (~ k!0 k!0))
% 0.50/0.71 (nnf-pos (proof-bind a!240) (~ a!237 a!237))
% 0.50/0.71 (~ (and k!0 a!237) (and k!0 a!237)))
% 0.50/0.71 a!241))
% 0.50/0.71 (a!243 (~ a!238 (and (not (q1 A!48)) (and k!0 a!237))))
% 0.50/0.71 (a!251 (trans (sk (~ (not a!247) a!248)) a!250 (~ (not a!247) a!249)))
% 0.50/0.71 (a!257 (nnf-neg a!256 (~ (not (not a!253)) a!253)))
% 0.50/0.71 (a!264 (~ (not (not (and a!103 a!261))) a!263))
% 0.50/0.71 (a!271 (and a!1
% 0.50/0.71 a!11
% 0.50/0.71 a!17
% 0.50/0.71 a!35
% 0.50/0.71 a!37
% 0.50/0.71 a!42
% 0.50/0.71 (or (not a!56) a!58)
% 0.50/0.71 (or (not (and a!56 a!62)) a!66)
% 0.50/0.71 (or (not a!71) a!66)
% 0.50/0.71 (or (not a!78) a!82)
% 0.50/0.71 a!86
% 0.50/0.71 (or (not a!56) a!97)
% 0.50/0.71 (or a!101 (not a!56) (not a!103))
% 0.50/0.71 a!107
% 0.50/0.71 (or a!118 (not a!28) (not a!122))
% 0.50/0.71 (or a!118 (not a!127) (not a!129))
% 0.50/0.71 (not a!135)
% 0.50/0.71 (or (not (and a!122 a!140)) a!143)
% 0.50/0.71 (or (not a!118) a!149)
% 0.50/0.71 (= a!153 a!156)
% 0.50/0.71 a!161
% 0.50/0.71 (or (not a!56) (and a!56 a!167))
% 0.50/0.71 (= a!172 a!97)
% 0.50/0.71 (or (not a!172) a!179)
% 0.50/0.71 a!184
% 0.50/0.71 (or (not a!187) a!190)
% 0.50/0.71 a!195
% 0.50/0.71 a!197
% 0.50/0.71 a!209
% 0.50/0.71 a!214
% 0.50/0.71 (or (not a!217) a!221)
% 0.50/0.71 (or (not a!172) a!97)
% 0.50/0.71 (or (not a!231) a!233)
% 0.50/0.71 a!236
% 0.50/0.71 (or (not (and a0 b0)) (= a0 b0))
% 0.50/0.71 a!247
% 0.50/0.71 a!252
% 0.50/0.71 (or (not (and a!103 a!261)) a!267)))
% 0.50/0.71 (a!272 (or (and a!2 a!8)
% 0.50/0.71 (and a!2 a!14)
% 0.50/0.71 (and (q1 (f B!6)) a!21)
% 0.50/0.71 (and (and a!26 a!29) a!33)
% 0.57/0.71 a!40
% 0.57/0.71 (and a!45 a!52)
% 0.57/0.71 a!60
% 0.57/0.71 (and (and a!56 (q1 Y!14)) a!67)
% 0.57/0.71 (and a!72 a!67)
% 0.57/0.71 (and a!79 a!83)
% 0.57/0.71 (and a!87 a!93)
% 0.57/0.71 (and a!56 a!98)
% 0.57/0.71 (and (not (q1 X!20)) a!56 a!103)
% 0.57/0.71 (and a!108 a!114)
% 0.57/0.71 (and a!119 a!28 (a1 X!23))
% 0.57/0.71 a!132
% 0.57/0.71 a!136
% 0.57/0.71 (and (and (a1 X!23) a!140) a!144)
% 0.57/0.71 (and (b X!26) a!150)
% 0.57/0.71 a!159
% 0.57/0.71 a!164
% 0.57/0.71 a!170
% 0.57/0.71 (and (or (p1 X!35) (p1 Y!36)) (or a!174 a!98))
% 0.57/0.71 (and (p1 X!35) a!180)
% 0.57/0.71 a!185
% 0.57/0.71 (and a!188 a!191)
% 0.57/0.71 a!196
% 0.57/0.71 (and (not (q1 B!42)) a!198 (and a!103 (r1 B!42)))
% 0.57/0.71 a!212
% 0.57/0.71 a!215
% 0.57/0.71 (and a!218 a!224)
% 0.57/0.71 (and (p1 X!35) a!98)
% 0.57/0.71 (and a!231 (not (p X!47 X!47)))
% 0.57/0.71 (and (not (q1 A!48)) (and k!0 a!237))
% 0.57/0.71 a!246
% 0.57/0.71 a!249
% 0.57/0.71 (and a!253 a!258)
% 0.57/0.71 (and a!263 a!268))))
% 0.57/0.71 (let ((a!25 (trans (sk (~ (not a!17) (not a!19))) (nnf-neg a!20 a!22 a!23) a!24))
% 0.57/0.71 (a!36 (nnf-neg (nnf-neg a!30 (~ a!31 (and a!26 a!29)))
% 0.57/0.71 a!34
% 0.57/0.71 (~ (not a!35) (and (and a!26 a!29) a!33))))
% 0.57/0.71 (a!51 (nnf-neg a!50 (~ (not (not a!45)) a!45)))
% 0.57/0.71 (a!70 (nnf-neg (nnf-neg a!63 a!64)
% 0.57/0.71 (nnf-neg (proof-bind a!65) (~ (not a!66) a!67))
% 0.57/0.71 a!69))
% 0.57/0.71 (a!76 (nnf-neg a!74 (nnf-neg (proof-bind a!65) (~ (not a!66) a!67)) a!75))
% 0.57/0.71 (a!95 (nnf-neg a!91 (nnf-neg (proof-bind a!92) (~ (not a!88) a!93)) a!94))
% 0.57/0.71 (a!116 (nnf-neg a!112
% 0.57/0.71 (nnf-neg (proof-bind a!113) (~ (not a!109) a!114))
% 0.57/0.71 a!115))
% 0.57/0.71 (a!125 (nnf-neg (nnf-neg (proof-bind a!117) (~ (not a!118) a!119))
% 0.57/0.71 a!121
% 0.57/0.71 a!123
% 0.57/0.71 a!124))
% 0.57/0.71 (a!134 (nnf-neg (nnf-neg (proof-bind a!117) (~ (not a!118) a!119))
% 0.57/0.71 a!128
% 0.57/0.71 (nnf-neg (sk a!130) a!131)
% 0.57/0.71 a!133))
% 0.57/0.71 (a!205 (nnf-neg a!203 (~ a!204 (and a!103 (r1 B!42)))))
% 0.57/0.71 (a!245 (trans (sk (~ (not a!236) a!238))
% 0.57/0.71 (nnf-neg a!239 a!242 a!243)
% 0.57/0.71 a!244))
% 0.57/0.71 (a!265 (nnf-neg (monotonicity a!104
% 0.57/0.71 (sk a!262)
% 0.57/0.71 (~ (and a!103 a!261) a!263))
% 0.57/0.71 a!264)))
% 0.57/0.71 (let ((a!208 (trans (sk (~ (not a!197) (not a!199)))
% 0.57/0.71 (nnf-neg a!200 a!202 a!205 a!206)
% 0.57/0.71 a!207))
% 0.57/0.71 (a!270 (nnf-neg a!265
% 0.57/0.71 (nnf-neg a!266 (~ (not a!267) a!268))
% 0.57/0.71 (~ a!269 (and a!263 a!268)))))
% 0.57/0.71 (nnf-neg (trans (sk a!4) a!10 (~ (not a!1) (and a!2 a!8)))
% 0.57/0.71 (trans (sk a!13)
% 0.57/0.71 (nnf-neg a!6 a!15 a!16)
% 0.57/0.71 (~ (not a!11) (and a!2 a!14)))
% 0.57/0.71 a!25
% 0.57/0.71 a!36
% 0.57/0.71 a!41
% 0.57/0.71 (trans (sk a!47)
% 0.57/0.71 (nnf-neg a!51 a!53 a!54)
% 0.57/0.71 (~ (not a!42) (and a!45 a!52)))
% 0.57/0.71 (nnf-neg a!57 (sk a!59) a!61)
% 0.57/0.71 a!70
% 0.57/0.71 a!76
% 0.57/0.71 a!85
% 0.57/0.71 (trans (sk a!89) a!95 (~ (not a!86) (and a!87 a!93)))
% 0.57/0.71 a!100
% 0.57/0.71 (nnf-neg a!102 a!57 a!105 a!106)
% 0.57/0.71 (trans (sk a!110) a!116 (~ (not a!107) (and a!108 a!114)))
% 0.57/0.71 a!125
% 0.57/0.71 a!134
% 0.57/0.71 a!138
% 0.57/0.71 (nnf-neg (nnf-neg a!141 a!142) a!145 a!147)
% 0.57/0.71 (nnf-neg a!148 a!151 a!152)
% 0.57/0.71 a!160
% 0.57/0.71 a!165
% 0.57/0.71 (nnf-neg a!57 (nnf-neg a!166 a!168 a!169) a!171)
% 0.57/0.71 a!176
% 0.57/0.71 a!182
% 0.57/0.71 (nnf-neg (proof-bind a!183) (~ (not a!184) a!185))
% 0.57/0.71 a!193
% 0.57/0.71 (nnf-neg (proof-bind a!194) (~ (not a!195) a!196))
% 0.57/0.71 a!208
% 0.57/0.71 a!213
% 0.57/0.71 a!216
% 0.57/0.71 a!227
% 0.57/0.71 a!229
% 0.57/0.71 (nnf-neg a!232 a!234 a!235)
% 0.57/0.71 a!245
% 0.57/0.71 (refl (~ a!246 a!246))
% 0.57/0.71 a!251
% 0.57/0.71 (trans (sk a!255)
% 0.57/0.71 (nnf-neg a!257 a!259 a!260)
% 0.57/0.71 (~ (not a!252) (and a!253 a!258)))
% 0.57/0.71 a!270
% 0.57/0.71 (~ (not a!271) a!272)))))))
% 0.57/0.71 Proof display could not be completed: unexpected number of arguments
% 0.57/0.72 % E exiting
%------------------------------------------------------------------------------