%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC131+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:30:15 AM UTC 2025
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC131+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 08:25:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(cyclefreeP_type, type, (
% 0.20/0.49 cyclefreeP: $i > $o)).
% 0.20/0.49 tff(nil_type, type, (
% 0.20/0.49 nil: $i)).
% 0.20/0.49 tff(tptp_fun_V_46_type, type, (
% 0.20/0.49 tptp_fun_V_46: $i)).
% 0.20/0.49 tff(neq_type, type, (
% 0.20/0.49 neq: ( $i * $i ) > $o)).
% 0.20/0.49 tff(ssList_type, type, (
% 0.20/0.49 ssList: $i > $o)).
% 0.20/0.49 tff(tptp_fun_U_45_type, type, (
% 0.20/0.49 tptp_fun_U_45: $i)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 ((ssList(U!45) & (~(cyclefreeP(V!46) | neq(V!46, nil) | (~ssList(V!46)) | (~ssList(U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | cyclefreeP(V!46) | neq(V!46, nil) | (~ssList(V!46)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | neq(X, nil)) | cyclefreeP(V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | neq(X, nil)) | cyclefreeP(V))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (cyclefreeP(V) | neq(V, nil) | (~ssList(V)) | (~ssList(U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (ssList(U!45) & (~((~ssList(U!45)) | cyclefreeP(V!46) | neq(V!46, nil) | (~ssList(V!46))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (~((~ssList(U!45)) | cyclefreeP(V!46) | neq(V!46, nil) | (~ssList(V!46)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (ssList(V!46)),
% 0.20/0.49 inference(or_elim,[status(thm)],[10])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.49 tff(20,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.49 tff(23,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[22])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (ssList(nil) <=> ssList(nil)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(30,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (ssList(nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[34, 31, 28])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (~neq(V!46, nil)),
% 0.20/0.49 inference(or_elim,[status(thm)],[10])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (((V!46 = nil) <=> neq(V!46, nil)) | (V!46 = nil) | neq(V!46, nil)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (((V!46 = nil) <=> neq(V!46, nil)) | (V!46 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (V!46 = nil),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (nil = V!46),
% 0.20/0.49 inference(symmetry,[status(thm)],[39])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (cyclefreeP(nil) <=> cyclefreeP(V!46)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (cyclefreeP(V!46) <=> cyclefreeP(nil)),
% 0.20/0.49 inference(symmetry,[status(thm)],[41])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 ((~cyclefreeP(V!46)) <=> (~cyclefreeP(nil))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (~cyclefreeP(V!46)),
% 0.20/0.49 inference(or_elim,[status(thm)],[10])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (~cyclefreeP(nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (cyclefreeP(nil) <=> cyclefreeP(nil)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(47,axiom,(cyclefreeP(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax60')).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (cyclefreeP(nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------