%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC086+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:30:07 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC086+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.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 08:16:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(segmentP_type, type, (
% 0.20/0.47 segmentP: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_U_45_type, type, (
% 0.20/0.47 tptp_fun_U_45: $i)).
% 0.20/0.47 tff(ssList_type, type, (
% 0.20/0.47 ssList: $i > $o)).
% 0.20/0.47 tff(tptp_fun_V_46_type, type, (
% 0.20/0.47 tptp_fun_V_46: $i)).
% 0.20/0.47 tff(neq_type, type, (
% 0.20/0.47 neq: ( $i * $i ) > $o)).
% 0.20/0.47 tff(nil_type, type, (
% 0.20/0.47 nil: $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 ((ssList(U!45) & ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (((~(((~(nil = V!46)) | (~(nil = U!45))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))) <=> ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 ((ssList(U!45) & ((~(((~(nil = V!46)) | (~(nil = U!45))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 ((ssList(U!45) & ((~(((~(nil = V!46)) | (~(nil = U!45))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (ssList(U!45) & (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) & ssList(V!46) & neq(V!46, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (ssList(U!45)),
% 0.20/0.47 inference(and_elim,[status(thm)],[12])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.47 tff(19,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.47 tff(22,plain,(
% 0.20/0.47 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(skolemize,[status(sab)],[21])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(U!45)) | segmentP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(U!45)) | segmentP(U!45, U!45))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(U!45)) | segmentP(U!45, U!45))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(U!45)) | segmentP(U!45, U!45)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (segmentP(U!45, U!45)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (ssList(V!46)),
% 0.20/0.47 inference(and_elim,[status(thm)],[12])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,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(33,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)],[32])).
% 0.20/0.48 tff(34,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(35,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.48 tff(37,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.48 tff(39,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(40,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(41,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)],[40, 39])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.20/0.48 tff(43,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(44,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)],[43])).
% 0.20/0.48 tff(45,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(46,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)],[45])).
% 0.20/0.48 tff(47,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)],[46, 44])).
% 0.20/0.48 tff(48,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(49,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(50,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)],[49])).
% 0.20/0.48 tff(51,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(52,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)],[51, 50])).
% 0.20/0.48 tff(53,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)],[52, 48])).
% 0.20/0.48 tff(54,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)],[53])).
% 0.20/0.48 tff(55,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)],[54, 47])).
% 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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(57,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)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(58,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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[58, 55, 28])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (ssList(nil) <=> ssList(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (ssList(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((~![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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (neq(V!46, nil)),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (~(V!46 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.48 tff(81,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')).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.48 tff(84,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[83])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~segmentP(V, V!46)) | (~ssList(V)) | (~segmentP(V!46, V)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~segmentP(V, V!46)) | (~ssList(V)) | (~segmentP(V!46, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~segmentP(V, V!46)) | (~ssList(V)) | (~segmentP(V!46, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~segmentP(V, V!46)) | (~ssList(V)) | (~segmentP(V!46, V))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[92, 86, 28])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.48 tff(99,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.48 tff(102,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(skolemize,[status(sab)],[101])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (segmentP(V!46, nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[106, 103, 28])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (((~ssList(nil)) | (~segmentP(V!46, nil)) | (V!46 = nil) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(V!46, nil)) | (V!46 = nil) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(V!46, nil)) | (V!46 = nil) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil))),
% 0.20/0.48 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(V!46, nil)) | (V!46 = nil) | (~segmentP(nil, V!46)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~segmentP(V!46, V)) | (V!46 = V) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[113, 62, 107, 93])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (~segmentP(nil, V!46)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[114, 70])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (~(nil = V!46)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[116, 115, 42])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((~(nil = U!45)) | (~(nil = V!46))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 ((((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) <=> (~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> (~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[121])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[125, 119])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (((~neq(U!45, nil)) | (~segmentP(V!46, U!45))) | neq(U!45, nil)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (neq(U!45, nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (((~neq(U!45, nil)) | (~segmentP(V!46, U!45))) | segmentP(V!46, U!45)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (segmentP(V!46, U!45)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~segmentP(V!46, U!45)) | (~segmentP(U!45, U!45)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~segmentP(V!46, U!45)) | (~segmentP(U!45, U!45)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~segmentP(V!46, U!45)) | (~segmentP(U!45, U!45)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!46, Y)) | (~segmentP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~segmentP(V!46, U!45)) | (~segmentP(U!45, U!45))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)) | (~segmentP(U!45, U!45))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[140, 13, 137])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[141, 130, 128, 27])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------