%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC037+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:29:59 AM UTC 2025
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC037+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:05:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(neq_type, type, (
% 0.20/0.50 neq: ( $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_Y_46_type, type, (
% 0.20/0.50 tptp_fun_Y_46: $i)).
% 0.20/0.50 tff(nil_type, type, (
% 0.20/0.50 nil: $i)).
% 0.20/0.50 tff(segmentP_type, type, (
% 0.20/0.50 segmentP: ( $i * $i ) > $o)).
% 0.20/0.50 tff(ssList_type, type, (
% 0.20/0.50 ssList: $i > $o)).
% 0.20/0.50 tff(tptp_fun_U_45_type, type, (
% 0.20/0.50 tptp_fun_U_45: $i)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) <=> (~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45)) <=> ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45))) <=> ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(6,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (![Y: $i] : ((~segmentP(U, Y)) | (~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(nil, Y))) & (~(nil = U))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 ((~(nil = U!45)) & ssList(U!45) & ssList(nil) & ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (~(nil = U!45)),
% 0.20/0.50 inference(and_elim,[status(thm)],[11])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 ((~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))) | (nil = U!45)),
% 0.20/0.50 inference(and_elim,[status(thm)],[11])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (~((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46))) | ssList(Y!46)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (ssList(Y!46)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.50 tff(22,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.50 tff(25,plain,(
% 0.20/0.50 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[24])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(Y!46)) | (segmentP(nil, Y!46) <=> (nil = Y!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(Y!46)) | (segmentP(nil, Y!46) <=> (nil = Y!46)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(Y!46)) | (segmentP(nil, Y!46) <=> (nil = Y!46)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(Y!46)) | (segmentP(nil, Y!46) <=> (nil = Y!46))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (segmentP(nil, Y!46) <=> (nil = Y!46)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46))) | segmentP(nil, Y!46)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (segmentP(nil, Y!46)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[31, 14])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 ((~(segmentP(nil, Y!46) <=> (nil = Y!46))) | (~segmentP(nil, Y!46)) | (nil = Y!46)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 ((~(segmentP(nil, Y!46) <=> (nil = Y!46))) | (nil = Y!46)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (nil = Y!46),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[34, 30])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (Y!46 = nil),
% 0.20/0.50 inference(symmetry,[status(thm)],[35])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (neq(nil, Y!46) <=> neq(Y!46, nil)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[35, 36])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (neq(Y!46, nil) <=> neq(nil, Y!46)),
% 0.20/0.50 inference(symmetry,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (((~segmentP(U!45, Y!46)) | (~neq(Y!46, nil)) | (~ssList(Y!46)) | (~segmentP(nil, Y!46))) | neq(Y!46, nil)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (neq(Y!46, nil)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[39, 14])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (neq(nil, Y!46)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (ssList(nil) <=> ssList(nil)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(43,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (ssList(nil)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.50 tff(53,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.50 tff(56,plain,(
% 0.20/0.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[55])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[60, 57, 44])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(Y!46)) | (~((nil = Y!46) <=> neq(nil, Y!46))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(Y!46)) | (~((nil = Y!46) <=> neq(nil, Y!46))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(Y!46)) | (~((nil = Y!46) <=> neq(nil, Y!46))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(Y!46)) | (~((nil = Y!46) <=> neq(nil, Y!46)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (~((nil = Y!46) <=> neq(nil, Y!46))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[64, 16, 61])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (((nil = Y!46) <=> neq(nil, Y!46)) | (~(nil = Y!46)) | (~neq(nil, Y!46))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 (((nil = Y!46) <=> neq(nil, Y!46)) | (~neq(nil, Y!46))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[66, 35])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (~neq(nil, Y!46)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[67, 65])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[68, 41])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------