%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN636-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:44 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN636-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n012.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:38:40 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p21_type, type, (
% 0.20/0.38 p21: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f12_type, type, (
% 0.20/0.38 f12: $i > $i)).
% 0.20/0.38 tff(f13_type, type, (
% 0.20/0.38 f13: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f20_type, type, (
% 0.20/0.38 f20: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(c29_type, type, (
% 0.20/0.38 c29: $i)).
% 0.20/0.38 tff(c28_type, type, (
% 0.20/0.38 c28: $i)).
% 0.20/0.38 tff(f6_type, type, (
% 0.20/0.38 f6: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f7_type, type, (
% 0.20/0.38 f7: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c26_type, type, (
% 0.20/0.38 c26: $i)).
% 0.20/0.38 tff(c23_type, type, (
% 0.20/0.38 c23: $i)).
% 0.20/0.38 tff(c25_type, type, (
% 0.20/0.38 c25: $i)).
% 0.20/0.38 tff(p22_type, type, (
% 0.20/0.38 p22: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f15_type, type, (
% 0.20/0.38 f15: $i > $i)).
% 0.20/0.38 tff(p3_type, type, (
% 0.20/0.38 p3: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f8_type, type, (
% 0.20/0.38 f8: $i > $i)).
% 0.20/0.38 tff(c24_type, type, (
% 0.20/0.38 c24: $i)).
% 0.20/0.38 tff(f4_type, type, (
% 0.20/0.38 f4: $i > $i)).
% 0.20/0.38 tff(p10_type, type, (
% 0.20/0.38 p10: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f11_type, type, (
% 0.20/0.38 f11: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(c27_type, type, (
% 0.20/0.38 c27: $i)).
% 0.20/0.38 tff(1,assumption,(p3(f4(f6(c25, f7(c23, c26))), f8(c24))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X80: $i, X81: $i, X82: $i] : refl(p3(f4(f6(X80, f7(X81, X82))), X81) <=> p3(f4(f6(X80, f7(X81, X82))), X81))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81) <=> ![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81) <=> ![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_8')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![X80: $i, X81: $i, X82: $i] : p3(f4(f6(X80, f7(X81, X82))), X81)) | p3(f4(f6(c25, f7(c23, c26))), c23)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (p3(f4(f6(c25, f7(c23, c26))), c23)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (^[X76: $i, X75: $i, X77: $i] : refl(((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77)) <=> ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77)) <=> ![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77)) <=> ![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (^[X76: $i, X75: $i, X77: $i] : trans(monotonicity(rewrite((p3(X76, X77) | (~p3(X75, X76))) <=> ((~p3(X75, X76)) | p3(X76, X77))), (((p3(X76, X77) | (~p3(X75, X76))) | (~p3(X75, X77))) <=> (((~p3(X75, X76)) | p3(X76, X77)) | (~p3(X75, X77))))), rewrite((((~p3(X75, X76)) | p3(X76, X77)) | (~p3(X75, X77))) <=> ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))), (((p3(X76, X77) | (~p3(X75, X76))) | (~p3(X75, X77))) <=> ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((p3(X76, X77) | (~p3(X75, X76))) | (~p3(X75, X77))) <=> ![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.38 tff(16,axiom,(![X76: $i, X75: $i, X77: $i] : ((p3(X76, X77) | (~p3(X75, X76))) | (~p3(X75, X77)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_17')).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.38 tff(19,plain,(
% 0.20/0.38 ![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(skolemize,[status(sab)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~p3(c23, f8(c24))) <=> (~p3(c23, f8(c24)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,axiom,(~p3(c23, f8(c24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p3_7')).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (~p3(c23, f8(c24))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | (p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24))))) <=> ((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~p3(f4(f6(c25, f7(c23, c26))), f8(c24))) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | p3(c23, f8(c24))) <=> (p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | ((~p3(f4(f6(c25, f7(c23, c26))), f8(c24))) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | p3(c23, f8(c24)))) <=> ((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | (p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | ((~p3(f4(f6(c25, f7(c23, c26))), f8(c24))) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | p3(c23, f8(c24)))) <=> ((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | ((~p3(f4(f6(c25, f7(c23, c26))), f8(c24))) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | p3(c23, f8(c24)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![X76: $i, X75: $i, X77: $i] : ((~p3(X75, X77)) | (~p3(X75, X76)) | p3(X76, X77))) | p3(c23, f8(c24)) | (~p3(f4(f6(c25, f7(c23, c26))), c23)) | (~p3(f4(f6(c25, f7(c23, c26))), f8(c24)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 23, 20, 10, 1])).
% 0.20/0.38 tff(31,plain,(~p3(f4(f6(c25, f7(c23, c26))), f8(c24))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (^[X18: $i, X20: $i, X19: $i] : refl((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) <=> (p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18)))), (((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) <=> ((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20))))), rewrite(((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))), (((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : ((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.38 tff(37,axiom,(![X18: $i, X20: $i, X19: $i] : ((p3(f4(X18), f8(c24)) | p22(f20(X18, X19, X20), f15(X18))) | p10(f11(X18, c27, X19), f11(X18, c27, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_34')).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.38 tff(40,plain,(
% 0.20/0.38 ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ((~p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29))) <=> (~p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(43,axiom,(~p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p10_25')).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (~p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))) <=> (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | p22(f20(X18, X19, X20), f15(X18)))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[50, 44, 41, 31])).
% 0.20/0.39 tff(52,assumption,(~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))), introduced(assumption)).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (^[X69: $i] : refl((p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26)))))) <=> (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26)))))) <=> ![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26)))))) <=> ![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(56,axiom,(![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p21_27')).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,(
% 0.20/0.39 ![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (((~![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))) | (p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))) | (~p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))))) <=> ((~![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))) | p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))) | (~p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))) | (p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))) | (~p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![X69: $i] : (p21(f12(f13(c28, c29)), f12(f13(c28, X69))) | (~p22(X69, f15(f6(c25, f7(c23, c26))))))) | p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))) | (~p22(f20(f6(c25, f7(c23, c26)), c28, c29), f15(f6(c25, f7(c23, c26)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 59, 52, 51])).
% 0.20/0.39 tff(64,plain,(p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (^[X18: $i, X20: $i, X19: $i] : refl((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)))), (((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> ((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))))), rewrite(((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))), (((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![X18: $i, X20: $i, X19: $i] : ((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20)))))) <=> ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.40 tff(70,axiom,(![X18: $i, X20: $i, X19: $i] : ((p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20))) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_37')).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.40 tff(73,plain,(
% 0.20/0.40 ![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))))) <=> (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | (p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | (p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~![X18: $i, X20: $i, X19: $i] : (p3(f4(X18), f8(c24)) | p10(f11(X18, c27, X19), f11(X18, c27, X20)) | (~p21(f12(f13(X19, X20)), f12(f13(X19, f20(X18, X19, X20))))))) | p10(f11(f6(c25, f7(c23, c26)), c27, c28), f11(f6(c25, f7(c23, c26)), c27, c29)) | p3(f4(f6(c25, f7(c23, c26))), f8(c24)) | (~p21(f12(f13(c28, c29)), f12(f13(c28, f20(f6(c25, f7(c23, c26)), c28, c29)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[80, 44, 74, 31, 64])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------