%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC369+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 05:31:02 AM UTC 2025
% Result : Theorem 0.47s 0.65s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC369+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.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 09:08:39 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.47/0.65 % SZS status Theorem
% 0.47/0.65 % SZS output start Proof
% 0.47/0.65 tff(tptp_fun_U_45_type, type, (
% 0.47/0.65 tptp_fun_U_45: $i)).
% 0.47/0.65 tff(nil_type, type, (
% 0.47/0.65 nil: $i)).
% 0.47/0.65 tff(segmentP_type, type, (
% 0.47/0.65 segmentP: ( $i * $i ) > $o)).
% 0.47/0.65 tff(ssList_type, type, (
% 0.47/0.65 ssList: $i > $o)).
% 0.47/0.65 tff(tptp_fun_V_46_type, type, (
% 0.47/0.65 tptp_fun_V_46: $i)).
% 0.47/0.65 tff(neq_type, type, (
% 0.47/0.65 neq: ( $i * $i ) > $o)).
% 0.47/0.65 tff(1,plain,
% 0.47/0.65 ((ssList(U!45) & (~(segmentP(V!46, U!45) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)) | (~ssList(U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(2,plain,
% 0.47/0.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(3,plain,
% 0.47/0.65 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (neq(X, nil) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.47/0.65 tff(5,plain,
% 0.47/0.65 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.47/0.65 tff(6,plain,
% 0.47/0.65 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.47/0.65 tff(7,plain,
% 0.47/0.65 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.47/0.65 tff(8,plain,
% 0.47/0.65 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (neq(V, nil) & ((~neq(U, nil)) | (~segmentP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.47/0.65 tff(9,plain,
% 0.47/0.65 (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.47/0.65 tff(10,plain,
% 0.47/0.65 (ssList(U!45)),
% 0.47/0.65 inference(and_elim,[status(thm)],[9])).
% 0.47/0.65 tff(11,plain,
% 0.47/0.65 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(12,plain,
% 0.47/0.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[11])).
% 0.47/0.65 tff(13,plain,
% 0.47/0.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(14,plain,
% 0.47/0.65 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(15,plain,
% 0.47/0.65 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[14])).
% 0.47/0.66 tff(16,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.47/0.66 tff(17,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.47/0.66 tff(18,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.47/0.66 tff(19,plain,(
% 0.47/0.66 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[18])).
% 0.47/0.66 tff(20,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.47/0.66 tff(21,plain,
% 0.47/0.66 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (segmentP(nil, U!45) <=> (nil = U!45)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (segmentP(nil, U!45) <=> (nil = U!45)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(22,plain,
% 0.47/0.66 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (segmentP(nil, U!45) <=> (nil = U!45)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(23,plain,
% 0.47/0.66 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (segmentP(nil, U!45) <=> (nil = U!45))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.47/0.66 tff(24,plain,
% 0.47/0.66 (segmentP(nil, U!45) <=> (nil = U!45)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.47/0.66 tff(25,plain,
% 0.47/0.66 (~((~ssList(U!45)) | segmentP(V!46, U!45) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)))),
% 0.47/0.66 inference(and_elim,[status(thm)],[9])).
% 0.47/0.66 tff(26,plain,
% 0.47/0.66 (ssList(V!46)),
% 0.47/0.66 inference(or_elim,[status(thm)],[25])).
% 0.47/0.66 tff(27,plain,
% 0.47/0.66 (^[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))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(28,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[27])).
% 0.47/0.66 tff(29,plain,
% 0.47/0.66 (^[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))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(30,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[29])).
% 0.47/0.66 tff(31,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[30, 28])).
% 0.47/0.66 tff(32,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(33,plain,
% 0.47/0.66 (^[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)))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(34,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[33])).
% 0.47/0.66 tff(35,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.47/0.66 tff(36,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.47/0.66 tff(37,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.47/0.66 tff(38,plain,(
% 0.47/0.66 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[37])).
% 0.47/0.66 tff(39,plain,
% 0.47/0.66 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.47/0.66 tff(40,plain,
% 0.47/0.66 (((~![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)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(41,plain,
% 0.47/0.66 ((~![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)))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(42,plain,
% 0.47/0.66 ((~![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))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.47/0.66 tff(43,plain,
% 0.47/0.66 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[42, 39, 26])).
% 0.47/0.66 tff(44,plain,
% 0.47/0.66 (ssList(nil) <=> ssList(nil)),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(45,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.47/0.66 tff(46,plain,
% 0.47/0.66 (ssList(nil)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.47/0.66 tff(47,plain,
% 0.47/0.66 (((~![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))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(48,plain,
% 0.47/0.66 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(49,plain,
% 0.47/0.66 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.47/0.66 tff(50,plain,
% 0.47/0.66 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[49, 46, 43])).
% 0.47/0.66 tff(51,plain,
% 0.47/0.66 (~segmentP(V!46, U!45)),
% 0.47/0.66 inference(or_elim,[status(thm)],[25])).
% 0.47/0.66 tff(52,plain,
% 0.47/0.66 (((~neq(U!45, nil)) | (~segmentP(V!46, U!45))) | segmentP(V!46, U!45)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(53,plain,
% 0.47/0.66 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.47/0.66 tff(54,plain,
% 0.47/0.66 ((~(~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))) <=> ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(55,plain,
% 0.47/0.66 ((neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) <=> (~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(56,plain,
% 0.47/0.66 ((~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> (~(~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[55])).
% 0.47/0.66 tff(57,plain,
% 0.47/0.66 ((~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[56, 54])).
% 0.47/0.66 tff(58,plain,
% 0.47/0.66 (~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.47/0.66 inference(or_elim,[status(thm)],[25])).
% 0.47/0.66 tff(59,plain,
% 0.47/0.66 ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.47/0.66 tff(60,plain,
% 0.47/0.66 (~neq(V!46, nil)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.47/0.66 tff(61,plain,
% 0.47/0.66 (((V!46 = nil) <=> neq(V!46, nil)) | (V!46 = nil) | neq(V!46, nil)),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(62,plain,
% 0.47/0.66 (((V!46 = nil) <=> neq(V!46, nil)) | (V!46 = nil)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.47/0.66 tff(63,plain,
% 0.47/0.66 (V!46 = nil),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[62, 50])).
% 0.47/0.66 tff(64,plain,
% 0.47/0.66 (nil = V!46),
% 0.47/0.66 inference(symmetry,[status(thm)],[63])).
% 0.47/0.66 tff(65,plain,
% 0.47/0.66 (segmentP(nil, U!45) <=> segmentP(V!46, U!45)),
% 0.47/0.66 inference(monotonicity,[status(thm)],[64])).
% 0.47/0.66 tff(66,plain,
% 0.47/0.66 (segmentP(V!46, U!45) <=> segmentP(nil, U!45)),
% 0.47/0.66 inference(symmetry,[status(thm)],[65])).
% 0.47/0.66 tff(67,plain,
% 0.47/0.66 ((~segmentP(V!46, U!45)) <=> (~segmentP(nil, U!45))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[66])).
% 0.47/0.66 tff(68,plain,
% 0.47/0.66 (~segmentP(nil, U!45)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[51, 67])).
% 0.47/0.66 tff(69,plain,
% 0.47/0.66 ((~(~((nil = U!45) | (~(nil = V!46))))) <=> ((nil = U!45) | (~(nil = V!46)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(70,plain,
% 0.47/0.66 (((~(nil = U!45)) & (nil = V!46)) <=> (~((nil = U!45) | (~(nil = V!46))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(71,plain,
% 0.47/0.66 ((~((~(nil = U!45)) & (nil = V!46))) <=> (~(~((nil = U!45) | (~(nil = V!46)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[70])).
% 0.47/0.66 tff(72,plain,
% 0.47/0.66 ((~((~(nil = U!45)) & (nil = V!46))) <=> ((nil = U!45) | (~(nil = V!46)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[71, 69])).
% 0.47/0.66 tff(73,plain,
% 0.47/0.66 (~((~(nil = U!45)) & (nil = V!46))),
% 0.47/0.66 inference(or_elim,[status(thm)],[25])).
% 0.47/0.66 tff(74,plain,
% 0.47/0.66 ((nil = U!45) | (~(nil = V!46))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.47/0.66 tff(75,plain,
% 0.47/0.66 (nil = U!45),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[74, 64])).
% 0.47/0.66 tff(76,plain,
% 0.47/0.66 ((~(segmentP(nil, U!45) <=> (nil = U!45))) | segmentP(nil, U!45) | (~(nil = U!45))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(77,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[76, 75, 68, 24])).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.67 % E exiting
%------------------------------------------------------------------------------