%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC102+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:30:10 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC102+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:19:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(frontsegP_type, type, (
% 0.20/0.43 frontsegP: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_U_45_type, type, (
% 0.20/0.43 tptp_fun_U_45: $i)).
% 0.20/0.43 tff(neq_type, type, (
% 0.20/0.43 neq: ( $i * $i ) > $o)).
% 0.20/0.43 tff(nil_type, type, (
% 0.20/0.43 nil: $i)).
% 0.20/0.43 tff(ssList_type, type, (
% 0.20/0.43 ssList: $i > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 ((~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U)))) <=> (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | (~neq(V, nil))) | (neq(U, nil) & frontsegP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(3,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | (~neq(V, nil))) | (neq(U, nil) & frontsegP(V, U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | (neq(U, nil) & frontsegP(U, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.43 tff(8,plain,(
% 0.20/0.43 ~((~ssList(U!45)) | (~neq(U!45, nil)) | (neq(U!45, nil) & frontsegP(U!45, U!45)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (neq(U!45, nil)),
% 0.20/0.43 inference(or_elim,[status(thm)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ((~(~((~neq(U!45, nil)) | (~frontsegP(U!45, U!45))))) <=> ((~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 ((neq(U!45, nil) & frontsegP(U!45, U!45)) <=> (~((~neq(U!45, nil)) | (~frontsegP(U!45, U!45))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~(neq(U!45, nil) & frontsegP(U!45, U!45))) <=> (~(~((~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((~(neq(U!45, nil) & frontsegP(U!45, U!45))) <=> ((~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[12, 10])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~(neq(U!45, nil) & frontsegP(U!45, U!45))),
% 0.20/0.43 inference(or_elim,[status(thm)],[8])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~neq(U!45, nil)) | (~frontsegP(U!45, U!45))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (~frontsegP(U!45, U!45)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[15, 9])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (ssList(U!45)),
% 0.20/0.43 inference(or_elim,[status(thm)],[8])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.43 tff(23,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.44 tff(26,plain,(
% 0.20/0.44 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.44 inference(skolemize,[status(sab)],[25])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[30, 27, 17, 16])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------