%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN575-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:36 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN575-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:39:50 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p3_type, type, (
% 0.12/0.38 p3: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f6_type, type, (
% 0.12/0.38 f6: $i > $i)).
% 0.12/0.38 tff(c14_type, type, (
% 0.12/0.38 c14: $i)).
% 0.12/0.38 tff(f5_type, type, (
% 0.12/0.38 f5: $i > $i)).
% 0.12/0.38 tff(p7_type, type, (
% 0.12/0.38 p7: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f8_type, type, (
% 0.12/0.38 f8: ( $i * $i ) > $i)).
% 0.12/0.38 tff(p2_type, type, (
% 0.12/0.38 p2: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p9_type, type, (
% 0.12/0.38 p9: ( $i * $i ) > $o)).
% 0.12/0.38 tff(c12_type, type, (
% 0.12/0.38 c12: $i)).
% 0.12/0.38 tff(c13_type, type, (
% 0.12/0.38 c13: $i)).
% 0.12/0.38 tff(p11_type, type, (
% 0.12/0.38 p11: ( $i * $i ) > $o)).
% 0.12/0.38 tff(c15_type, type, (
% 0.12/0.38 c15: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X20: $i] : refl(p3(f6(f5(X20)), f6(X20)) <=> p3(f6(f5(X20)), f6(X20)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X20: $i] : p3(f6(f5(X20)), f6(X20)) <=> ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X20: $i] : p3(f6(f5(X20)), f6(X20)) <=> ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X20: $i] : p3(f6(f5(X20)), f6(X20))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_8')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X20: $i] : p3(f6(f5(X20)), f6(X20))) | p3(f6(f5(c14)), f6(c14))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (p3(f6(f5(c14)), f6(c14))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,assumption,(~p2(c14, c14)), introduced(assumption)).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[X7: $i] : refl(p2(X7, X7) <=> p2(X7, X7))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(![X7: $i] : p2(X7, X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X7: $i] : p2(X7, X7)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 ![X7: $i] : p2(X7, X7)),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X7: $i] : p2(X7, X7)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![X7: $i] : p2(X7, X7)) | p2(c14, c14)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.12/0.38 tff(20,plain,(p2(c14, c14)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[X11: $i, X10: $i] : refl(((~p2(X10, X11)) | p2(f5(X10), f5(X11))) <=> ((~p2(X10, X11)) | p2(f5(X10), f5(X11))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11))) <=> ![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11))) <=> ![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[X11: $i, X10: $i] : rewrite((p2(f5(X10), f5(X11)) | (~p2(X10, X11))) <=> ((~p2(X10, X11)) | p2(f5(X10), f5(X11))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : (p2(f5(X10), f5(X11)) | (~p2(X10, X11))) <=> ![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,axiom,(![X11: $i, X10: $i] : (p2(f5(X10), f5(X11)) | (~p2(X10, X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_11')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.38 tff(29,plain,(
% 0.12/0.38 ![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((~![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))) | ((~p2(c14, c14)) | p2(f5(c14), f5(c14)))) <=> ((~![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))) | (~p2(c14, c14)) | p2(f5(c14), f5(c14)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))) | ((~p2(c14, c14)) | p2(f5(c14), f5(c14)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![X11: $i, X10: $i] : ((~p2(X10, X11)) | p2(f5(X10), f5(X11)))) | (~p2(c14, c14)) | p2(f5(c14), f5(c14))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (p2(f5(c14), f5(c14))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (^[X18: $i, X19: $i] : refl(((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ((~p2(X18, X19)) | p3(f6(X18), f6(X19))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[X18: $i, X19: $i] : rewrite((p3(f6(X18), f6(X19)) | (~p2(X18, X19))) <=> ((~p2(X18, X19)) | p3(f6(X18), f6(X19))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : (p3(f6(X18), f6(X19)) | (~p2(X18, X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,axiom,(![X18: $i, X19: $i] : (p3(f6(X18), f6(X19)) | (~p2(X18, X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_12')).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.38 tff(43,plain,(
% 0.12/0.38 ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[42])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c14, c14)) | p3(f6(c14), f6(c14)))) <=> ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c14, c14)) | p3(f6(c14), f6(c14)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c14, c14)) | p3(f6(c14), f6(c14)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c14, c14)) | p3(f6(c14), f6(c14))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~p2(c14, c14)) | p3(f6(c14), f6(c14))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (p3(f6(c14), f6(c14))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 20])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (^[X25: $i, X27: $i, X26: $i, X24: $i] : refl(((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))) <=> ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (^[X25: $i, X27: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p7(f8(X24, X25), f8(X26, X27)) | (~p2(X25, X27))) <=> ((~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))), (((p7(f8(X24, X25), f8(X26, X27)) | (~p2(X25, X27))) | (~p3(X24, X26))) <=> (((~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))) | (~p3(X24, X26))))), rewrite((((~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27))) | (~p3(X24, X26))) <=> ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))), (((p7(f8(X24, X25), f8(X26, X27)) | (~p2(X25, X27))) | (~p3(X24, X26))) <=> ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((p7(f8(X24, X25), f8(X26, X27)) | (~p2(X25, X27))) | (~p3(X24, X26))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.38 tff(55,axiom,(![X25: $i, X27: $i, X26: $i, X24: $i] : ((p7(f8(X24, X25), f8(X26, X27)) | (~p2(X25, X27))) | (~p3(X24, X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_20')).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.12/0.38 tff(58,plain,(
% 0.12/0.38 ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[57])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | ((~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (((~p3(f6(c14), f6(c14))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) <=> ((~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | ((~p3(f6(c14), f6(c14))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | ((~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[61])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | ((~p3(f6(c14), f6(c14))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[62, 60])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | ((~p3(f6(c14), f6(c14))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p3(X24, X26)) | (~p2(X25, X27)) | p7(f8(X24, X25), f8(X26, X27)))) | (~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))) | (~p3(f6(c14), f6(c14)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~p2(f5(c14), f5(c14))) | p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 34])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 59, 49, 34])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(f5(c14), f5(c14))) | p3(f6(f5(c14)), f6(f5(c14))))) <=> ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(f5(c14), f5(c14))) | p3(f6(f5(c14)), f6(f5(c14))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(f5(c14), f5(c14))) | p3(f6(f5(c14)), f6(f5(c14))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(f5(c14), f5(c14))) | p3(f6(f5(c14)), f6(f5(c14)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (p3(f6(f5(c14)), f6(f5(c14)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 44, 34])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (^[X14: $i, X12: $i, X13: $i] : refl(((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p3(X13, X14) | (~p3(X12, X13))) <=> ((~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> (((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))))), rewrite((((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.12/0.39 tff(78,axiom,(![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_16')).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.12/0.39 tff(81,plain,(
% 0.12/0.39 ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(skolemize,[status(sab)],[80])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14)))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (((~p3(f6(f5(c14)), f6(f5(c14)))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14)))) <=> ((~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(f5(c14)))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[84])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(f5(c14)))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[85, 83])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(f5(c14)))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(f5(c14)), f6(c14))) | p3(f6(c14), f6(f5(c14))) | (~p3(f6(f5(c14)), f6(f5(c14))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (p3(f6(c14), f6(f5(c14)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[88, 82, 9, 72])).
% 0.12/0.39 tff(90,assumption,(~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))), introduced(assumption)).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (^[X32: $i] : refl((p9(X32, f6(c14)) | (~p9(X32, c13))) <=> (p9(X32, f6(c14)) | (~p9(X32, c13))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(94,axiom,(![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_10')).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,(
% 0.12/0.39 ![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[95])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (p9(c12, c13) <=> p9(c12, c13)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(99,axiom,(p9(c12, c13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_5')).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (p9(c12, c13)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (((~![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))) | (p9(c12, f6(c14)) | (~p9(c12, c13)))) <=> ((~![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))) | p9(c12, f6(c14)) | (~p9(c12, c13)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))) | (p9(c12, f6(c14)) | (~p9(c12, c13)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 ((~![X32: $i] : (p9(X32, f6(c14)) | (~p9(X32, c13)))) | p9(c12, f6(c14)) | (~p9(c12, c13))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (p9(c12, f6(c14))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[103, 100, 97])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (^[X35: $i, X34: $i, X33: $i] : refl(((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 (^[X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) <=> (p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) <=> ((p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p11(X35, c15))))), rewrite(((p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p11(X35, c15))) <=> ((~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) <=> ((~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) <=> (((~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))))), rewrite((((~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)))), (((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> (((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p2(X34, f5(X35)))))), rewrite((((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), (((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (![X35: $i, X34: $i, X33: $i] : ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.39 tff(110,axiom,(![X35: $i, X34: $i, X33: $i] : ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_21')).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.12/0.39 tff(113,plain,(
% 0.12/0.39 ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.39 inference(skolemize,[status(sab)],[112])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (p11(c14, c15) <=> p11(c14, c15)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(116,axiom,(p11(c14, c15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_6')).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (p11(c14, c15)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 (((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14))) <=> ((~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[119])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[120, 118])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p2(f5(c14), f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p9(c12, f6(c14))) | (~p11(c14, c15))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (p9(f8(f6(c14), f5(c14)), f6(c14))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[123, 117, 114, 104, 34, 90])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (^[X31: $i, X30: $i, X29: $i, X28: $i] : refl(((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (^[X31: $i, X30: $i, X29: $i, X28: $i] : trans(monotonicity(trans(monotonicity(rewrite((p9(X28, X29) | (~p7(X31, X28))) <=> ((~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> (((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))))), rewrite((((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> (((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))))), rewrite((((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.12/0.40 tff(130,axiom,(![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_19')).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.12/0.40 tff(133,plain,(
% 0.12/0.40 ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(skolemize,[status(sab)],[132])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 (((~p3(f6(c14), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) <=> ((~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c14), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c14), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c14), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p3(f6(c14), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(f5(c14))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[140, 134, 124, 90, 89, 68])).
% 0.19/0.40 tff(142,plain,(p9(f8(f6(c14), f5(c14)), f6(f5(c14)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (^[X35: $i, X34: $i, X33: $i] : refl(((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (^[X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)))), (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) <=> (((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15))) | (~p9(f8(X33, X34), X33))))), rewrite((((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33)))), (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))))), ((((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> (((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))))), rewrite((((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))), ((((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (![X35: $i, X34: $i, X33: $i] : (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.41 tff(148,axiom,(![X35: $i, X34: $i, X33: $i] : (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_22')).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.41 tff(151,plain,(
% 0.19/0.41 ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[150])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 (((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14)))) <=> ((~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[155, 153])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~p2(f5(c14), f5(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[158, 117, 152, 104])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (~p9(f8(f6(c14), f5(c14)), f6(c14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 34, 142])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14))) <=> ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (~p3(f6(f5(c14)), f6(c14))) | (~p9(f8(f6(c14), f5(c14)), f6(f5(c14)))) | p9(f8(f6(c14), f5(c14)), f6(c14)) | (~p7(f8(f6(c14), f5(c14)), f8(f6(c14), f5(c14))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[166, 134, 160, 142, 67, 9])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------