%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC415+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 05:31:10 AM UTC 2025
% Result : Theorem 0.57s 0.76s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC415+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:17:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.57/0.76 % SZS status Theorem
% 0.57/0.76 % SZS output start Proof
% 0.57/0.76 tff(neq_type, type, (
% 0.57/0.76 neq: ( $i * $i ) > $o)).
% 0.57/0.76 tff(tptp_fun_V_46_type, type, (
% 0.57/0.76 tptp_fun_V_46: $i)).
% 0.57/0.76 tff(nil_type, type, (
% 0.57/0.76 nil: $i)).
% 0.57/0.76 tff(ssList_type, type, (
% 0.57/0.76 ssList: $i > $o)).
% 0.57/0.76 tff(tl_type, type, (
% 0.57/0.76 tl: $i > $i)).
% 0.57/0.76 tff(tptp_fun_U_45_type, type, (
% 0.57/0.76 tptp_fun_U_45: $i)).
% 0.57/0.76 tff(segmentP_type, type, (
% 0.57/0.76 segmentP: ( $i * $i ) > $o)).
% 0.57/0.76 tff(1,plain,
% 0.57/0.76 (ssList(nil) <=> ssList(nil)),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(2,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.57/0.76 tff(3,plain,
% 0.57/0.76 (ssList(nil)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.57/0.76 tff(4,plain,
% 0.57/0.76 (^[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))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(5,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[4])).
% 0.57/0.76 tff(6,plain,
% 0.57/0.76 (^[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))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(7,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[6])).
% 0.57/0.76 tff(8,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[7, 5])).
% 0.57/0.76 tff(9,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(10,plain,
% 0.57/0.76 (^[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)))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(11,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[10])).
% 0.57/0.76 tff(12,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.57/0.76 tff(13,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.57/0.76 tff(14,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.57/0.76 tff(15,plain,(
% 0.57/0.76 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.76 inference(skolemize,[status(sab)],[14])).
% 0.60/0.76 tff(16,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.60/0.76 tff(17,plain,
% 0.60/0.76 (((~![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)))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(18,plain,
% 0.60/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(19,plain,
% 0.60/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.60/0.76 tff(20,plain,
% 0.60/0.76 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[19, 16, 3])).
% 0.60/0.76 tff(21,plain,
% 0.60/0.76 ((ssList(U!45) & (~((~ssList(V!46)) | (neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46)))) | (~ssList(U!45)) | (~neq(V!46, nil)) | (neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46)))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | (~ssList(V!46)) | (neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46)))) | (~neq(V!46, nil)) | (neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(22,plain,
% 0.60/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(23,plain,
% 0.60/0.76 ((~![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) & (~(W = Y))) & (tl(X) = Y)) & neq(nil, X))) | ?[Z: $i] : (((ssList(Z) & (tl(V) = Z)) & (U = Z)) & neq(nil, V))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(24,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) & (~(W = Y))) & (tl(X) = Y)) & neq(nil, X))) | ?[Z: $i] : (((ssList(Z) & (tl(V) = Z)) & (U = Z)) & neq(nil, V))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.60/0.76 tff(25,plain,
% 0.60/0.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.60/0.76 tff(26,plain,
% 0.60/0.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.60/0.76 tff(27,plain,
% 0.60/0.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.60/0.76 tff(28,plain,
% 0.60/0.76 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(nil, V) & ssList(tl(V)) & (~(U = tl(V)))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(tl(V)) & (U = tl(V)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.60/0.76 tff(29,plain,
% 0.60/0.76 (ssList(U!45) & (~((~ssList(U!45)) | (~ssList(V!46)) | (neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46)))) | (~neq(V!46, nil)) | (neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.60/0.76 tff(30,plain,
% 0.60/0.76 (~((~ssList(U!45)) | (~ssList(V!46)) | (neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46)))) | (~neq(V!46, nil)) | (neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46))))),
% 0.60/0.76 inference(and_elim,[status(thm)],[29])).
% 0.60/0.76 tff(31,plain,
% 0.60/0.76 (ssList(V!46)),
% 0.60/0.76 inference(or_elim,[status(thm)],[30])).
% 0.60/0.76 tff(32,plain,
% 0.60/0.76 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(33,plain,
% 0.60/0.76 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(34,plain,
% 0.60/0.76 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.60/0.76 tff(35,plain,
% 0.60/0.76 (~((nil = V!46) <=> neq(nil, V!46))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[34, 31, 20])).
% 0.60/0.76 tff(36,plain,
% 0.60/0.76 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(37,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[36])).
% 0.60/0.76 tff(38,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(39,plain,
% 0.60/0.76 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(40,plain,
% 0.60/0.76 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[39])).
% 0.60/0.76 tff(41,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.60/0.76 tff(42,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.60/0.76 tff(43,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.60/0.76 tff(44,plain,(
% 0.60/0.76 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[43])).
% 0.60/0.76 tff(45,plain,
% 0.60/0.76 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.60/0.76 tff(46,plain,
% 0.60/0.76 (((~![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)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(47,plain,
% 0.60/0.76 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(48,plain,
% 0.60/0.76 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.60/0.76 tff(49,plain,
% 0.60/0.76 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[48, 45, 31])).
% 0.60/0.76 tff(50,plain,
% 0.60/0.76 (((~![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)))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(51,plain,
% 0.60/0.76 ((~![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)))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(52,plain,
% 0.60/0.76 ((~![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))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.60/0.76 tff(53,plain,
% 0.60/0.76 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[52, 16, 31])).
% 0.60/0.76 tff(54,plain,
% 0.60/0.76 (((~![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))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(55,plain,
% 0.60/0.76 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(56,plain,
% 0.60/0.76 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.60/0.76 tff(57,plain,
% 0.60/0.76 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[56, 3, 53])).
% 0.60/0.76 tff(58,plain,
% 0.60/0.76 (neq(V!46, nil)),
% 0.60/0.76 inference(or_elim,[status(thm)],[30])).
% 0.60/0.76 tff(59,plain,
% 0.60/0.76 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(60,plain,
% 0.60/0.76 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.60/0.76 tff(61,plain,
% 0.60/0.76 (~(V!46 = nil)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.60/0.76 tff(62,plain,
% 0.60/0.76 (^[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)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(63,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[62])).
% 0.60/0.77 tff(64,plain,
% 0.60/0.77 (^[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)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(65,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[64])).
% 0.60/0.77 tff(66,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[65, 63])).
% 0.60/0.77 tff(67,plain,
% 0.60/0.77 (^[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)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(68,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[67])).
% 0.60/0.77 tff(69,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(70,plain,
% 0.60/0.77 (^[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)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(71,plain,
% 0.60/0.77 (![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)))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[70])).
% 0.60/0.77 tff(72,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.60/0.77 tff(73,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.60/0.77 tff(74,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.60/0.77 tff(75,plain,(
% 0.60/0.77 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[74])).
% 0.60/0.77 tff(76,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.60/0.77 tff(77,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.60/0.77 tff(78,plain,
% 0.60/0.77 (((~![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))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(79,plain,
% 0.60/0.77 (((~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))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(80,plain,
% 0.60/0.77 (((~![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)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[79])).
% 0.60/0.77 tff(81,plain,
% 0.60/0.77 (((~![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))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[80, 78])).
% 0.60/0.77 tff(82,plain,
% 0.60/0.77 ((~![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))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(83,plain,
% 0.60/0.77 ((~![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)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.60/0.77 tff(84,plain,
% 0.60/0.77 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[83, 77, 31])).
% 0.60/0.77 tff(85,plain,
% 0.60/0.77 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(86,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[85])).
% 0.60/0.77 tff(87,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(88,plain,
% 0.60/0.77 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(89,plain,
% 0.60/0.77 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[88])).
% 0.60/0.77 tff(90,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.60/0.77 tff(91,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.60/0.77 tff(92,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.60/0.77 tff(93,plain,(
% 0.60/0.77 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(skolemize,[status(sab)],[92])).
% 0.60/0.77 tff(94,plain,
% 0.60/0.77 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.60/0.77 tff(95,plain,
% 0.60/0.77 (((~![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))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(96,plain,
% 0.60/0.77 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(97,plain,
% 0.60/0.77 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.60/0.77 tff(98,plain,
% 0.60/0.77 (segmentP(V!46, nil)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[97, 94, 31])).
% 0.60/0.77 tff(99,plain,
% 0.60/0.77 (((~![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)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(100,plain,
% 0.60/0.77 (((~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)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(101,plain,
% 0.60/0.77 (((~![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))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[100])).
% 0.60/0.77 tff(102,plain,
% 0.60/0.77 (((~![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)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[101, 99])).
% 0.60/0.77 tff(103,plain,
% 0.60/0.77 ((~![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)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(104,plain,
% 0.60/0.77 ((~![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))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.60/0.77 tff(105,plain,
% 0.60/0.77 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[104, 3, 98, 84])).
% 0.60/0.77 tff(106,plain,
% 0.60/0.77 (~segmentP(nil, V!46)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[105, 61])).
% 0.60/0.77 tff(107,plain,
% 0.60/0.77 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(108,plain,
% 0.60/0.77 (~(nil = V!46)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[107, 106, 49])).
% 0.60/0.77 tff(109,plain,
% 0.60/0.77 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(110,plain,
% 0.60/0.77 (neq(nil, V!46)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[109, 108, 35])).
% 0.60/0.77 tff(111,plain,
% 0.60/0.77 (^[U: $i] : refl(((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(112,plain,
% 0.60/0.77 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[111])).
% 0.60/0.77 tff(113,plain,
% 0.60/0.77 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(114,plain,
% 0.60/0.77 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssList(tl(U))) <=> ((nil = U) | ssList(tl(U)))), ((ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> (ssList(U) => ((nil = U) | ssList(tl(U)))))), rewrite((ssList(U) => ((nil = U) | ssList(tl(U)))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(115,plain,
% 0.60/0.77 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[114])).
% 0.60/0.77 tff(116,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax24')).
% 0.60/0.77 tff(117,plain,
% 0.60/0.77 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.60/0.77 tff(118,plain,
% 0.60/0.77 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.60/0.77 tff(119,plain,(
% 0.60/0.77 ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[118])).
% 0.60/0.77 tff(120,plain,
% 0.60/0.77 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.60/0.77 tff(121,plain,
% 0.60/0.77 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(122,plain,
% 0.60/0.77 (((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(123,plain,
% 0.60/0.78 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[122])).
% 0.60/0.78 tff(124,plain,
% 0.60/0.78 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))),
% 0.60/0.78 inference(transitivity,[status(thm)],[123, 121])).
% 0.60/0.78 tff(125,plain,
% 0.60/0.78 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(126,plain,
% 0.60/0.78 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.60/0.78 tff(127,plain,
% 0.60/0.78 (ssList(tl(V!46))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[126, 120, 31, 108])).
% 0.60/0.78 tff(128,plain,
% 0.60/0.78 ((~(~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46))))) <=> ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(129,plain,
% 0.60/0.78 ((neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46)))) <=> (~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(130,plain,
% 0.60/0.78 ((~(neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46))))) <=> (~(~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46)))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[129])).
% 0.60/0.78 tff(131,plain,
% 0.60/0.78 ((~(neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46))))) <=> ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[130, 128])).
% 0.60/0.78 tff(132,plain,
% 0.60/0.78 (~(neq(nil, V!46) & ssList(tl(V!46)) & (~(U!45 = tl(V!46))))),
% 0.60/0.78 inference(or_elim,[status(thm)],[30])).
% 0.60/0.78 tff(133,plain,
% 0.60/0.78 ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (U!45 = tl(V!46))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.60/0.78 tff(134,plain,
% 0.60/0.78 (U!45 = tl(V!46)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[133, 127, 110])).
% 0.60/0.78 tff(135,plain,
% 0.60/0.78 ((~(~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46)))))) <=> ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(136,plain,
% 0.60/0.78 ((neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46))) <=> (~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46)))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(137,plain,
% 0.60/0.78 ((~(neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46)))) <=> (~(~((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46))))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[136])).
% 0.60/0.78 tff(138,plain,
% 0.60/0.78 ((~(neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46)))) <=> ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[137, 135])).
% 0.60/0.78 tff(139,plain,
% 0.60/0.78 (~(neq(nil, V!46) & ssList(tl(V!46)) & (U!45 = tl(V!46)))),
% 0.60/0.78 inference(or_elim,[status(thm)],[30])).
% 0.60/0.78 tff(140,plain,
% 0.60/0.78 ((~neq(nil, V!46)) | (~ssList(tl(V!46))) | (~(U!45 = tl(V!46)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.60/0.78 tff(141,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[140, 134, 127, 110])).
% 0.60/0.78 % SZS output end Proof
% 0.60/0.78 % E exiting
%------------------------------------------------------------------------------