%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC205+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:30 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC205+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:38:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(tptp_fun_U_45_type, type, (
% 0.20/0.48 tptp_fun_U_45: $i)).
% 0.20/0.48 tff(nil_type, type, (
% 0.20/0.48 nil: $i)).
% 0.20/0.48 tff(neq_type, type, (
% 0.20/0.48 neq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(ssList_type, type, (
% 0.20/0.48 ssList: $i > $o)).
% 0.20/0.48 tff(tptp_fun_V_46_type, type, (
% 0.20/0.48 tptp_fun_V_46: $i)).
% 0.20/0.48 tff(segmentP_type, type, (
% 0.20/0.48 segmentP: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((ssList(U!45) & (~(((~(nil = U!45)) & (nil = V!46)) | ((~(nil = V!46)) & (nil = U!45)) | (~ssList(V!46)) | (~ssList(U!45)) | neq(U!45, nil) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | neq(U!45, nil) | ((~(nil = U!45)) & (nil = V!46)) | ((~(nil = V!46)) & (nil = U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = X)) & (nil = W))) | ((~(nil = W)) & (nil = X)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = X)) & (nil = W))) | ((~(nil = W)) & (nil = X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (ssList(U!45) & (~((~ssList(U!45)) | neq(U!45, nil) | ((~(nil = U!45)) & (nil = V!46)) | ((~(nil = V!46)) & (nil = U!45)) | (~ssList(V!46)) | (~neq(V!46, nil))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (ssList(U!45)),
% 0.20/0.48 inference(and_elim,[status(thm)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[14, 12])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.48 tff(19,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.48 tff(22,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (ssList(nil) <=> ssList(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(29,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (ssList(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[33, 30, 27])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (~((~ssList(U!45)) | neq(U!45, nil) | ((~(nil = U!45)) & (nil = V!46)) | ((~(nil = V!46)) & (nil = U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[9])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (~neq(U!45, nil)),
% 0.20/0.48 inference(or_elim,[status(thm)],[35])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (U!45 = nil),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[38, 34])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (nil = U!45),
% 0.20/0.48 inference(symmetry,[status(thm)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (ssList(V!46)),
% 0.20/0.48 inference(or_elim,[status(thm)],[35])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.48 tff(47,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.48 tff(50,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[49])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (((~![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(57,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(58,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)],[57, 56])).
% 0.20/0.49 tff(59,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)],[58, 23, 41])).
% 0.20/0.49 tff(60,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(61,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(62,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)],[61, 60])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[62, 30, 59])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (neq(V!46, nil)),
% 0.20/0.49 inference(or_elim,[status(thm)],[35])).
% 0.20/0.49 tff(65,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(66,plain,
% 0.20/0.49 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (~(V!46 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.49 tff(78,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.49 tff(81,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[80])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[89, 83, 41])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.49 tff(96,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.49 tff(99,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(skolemize,[status(sab)],[98])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (segmentP(V!46, nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[103, 100, 41])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 30, 104, 90])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (~segmentP(nil, V!46)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[111, 67])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (~(nil = V!46)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[113, 112, 55])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ((~(~((~(nil = U!45)) | (nil = V!46)))) <=> ((~(nil = U!45)) | (nil = V!46))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (((~(nil = V!46)) & (nil = U!45)) <=> (~((~(nil = U!45)) | (nil = V!46)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ((~((~(nil = V!46)) & (nil = U!45))) <=> (~(~((~(nil = U!45)) | (nil = V!46))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 ((~((~(nil = V!46)) & (nil = U!45))) <=> ((~(nil = U!45)) | (nil = V!46))),
% 0.20/0.49 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (~((~(nil = V!46)) & (nil = U!45))),
% 0.20/0.49 inference(or_elim,[status(thm)],[35])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 ((~(nil = U!45)) | (nil = V!46)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (~(nil = U!45)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[120, 114])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[121, 40])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------