%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC204+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:30 AM UTC 2025
% Result : Theorem 17.67s 17.84s
% Output : Proof 17.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC204+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 08:42:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 17.67/17.84 % SZS status Theorem
% 17.67/17.84 % SZS output start Proof
% 17.67/17.84 tff(ssList_type, type, (
% 17.67/17.84 ssList: $i > $o)).
% 17.67/17.84 tff(tl_type, type, (
% 17.67/17.84 tl: $i > $i)).
% 17.67/17.84 tff(tptp_fun_V_46_type, type, (
% 17.67/17.84 tptp_fun_V_46: $i)).
% 17.67/17.84 tff(nil_type, type, (
% 17.67/17.84 nil: $i)).
% 17.67/17.84 tff(segmentP_type, type, (
% 17.67/17.84 segmentP: ( $i * $i ) > $o)).
% 17.67/17.84 tff(neq_type, type, (
% 17.67/17.84 neq: ( $i * $i ) > $o)).
% 17.67/17.84 tff(app_type, type, (
% 17.67/17.84 app: ( $i * $i ) > $i)).
% 17.67/17.84 tff(tptp_fun_U_45_type, type, (
% 17.67/17.84 tptp_fun_U_45: $i)).
% 17.67/17.84 tff(tptp_fun_V_43_type, type, (
% 17.67/17.84 tptp_fun_V_43: $i > $i)).
% 17.67/17.84 tff(cons_type, type, (
% 17.67/17.84 cons: ( $i * $i ) > $i)).
% 17.67/17.84 tff(tptp_fun_W_44_type, type, (
% 17.67/17.84 tptp_fun_W_44: $i > $i)).
% 17.67/17.84 tff(ssItem_type, type, (
% 17.67/17.84 ssItem: $i > $o)).
% 17.67/17.84 tff(1,plain,
% 17.67/17.84 ((ssList(U!45) & (~((~ssList(V!46)) | neq(U!45, nil) | (~ssList(U!45)) | (ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46))) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~(neq(U!45, nil) | (~ssList(U!45)) | (~ssList(V!46)) | (ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46))) | (~neq(V!46, nil)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(2,plain,
% 17.67/17.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(3,plain,
% 17.67/17.84 ((~![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) & (~(X = Y))) & ?[Z: $i] : (((ssList(Z) & (tl(X) = Z)) & (app(W, Z) = Y)) & neq(nil, X)))) | neq(U, nil)) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssList(Y) & (~(X = Y))) & ?[Z: $i] : (((ssList(Z) & (tl(X) = Z)) & (app(W, Z) = Y)) & neq(nil, X)))) | neq(U, nil)) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 17.67/17.84 tff(5,plain,
% 17.67/17.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 17.67/17.84 tff(6,plain,
% 17.67/17.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[5, 2])).
% 17.67/17.84 tff(7,plain,
% 17.67/17.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 17.67/17.84 tff(8,plain,
% 17.67/17.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | neq(U, nil) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[7, 2])).
% 17.67/17.84 tff(9,plain,
% 17.67/17.84 (ssList(U!45) & (~(neq(U!45, nil) | (~ssList(U!45)) | (~ssList(V!46)) | (ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46))) | (~neq(V!46, nil))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[8, 1])).
% 17.67/17.84 tff(10,plain,
% 17.67/17.84 (~(neq(U!45, nil) | (~ssList(U!45)) | (~ssList(V!46)) | (ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46))) | (~neq(V!46, nil)))),
% 17.67/17.84 inference(and_elim,[status(thm)],[9])).
% 17.67/17.84 tff(11,plain,
% 17.67/17.84 (ssList(V!46)),
% 17.67/17.84 inference(or_elim,[status(thm)],[10])).
% 17.67/17.84 tff(12,plain,
% 17.67/17.84 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(13,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[12])).
% 17.67/17.84 tff(14,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(15,plain,
% 17.67/17.84 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(16,plain,
% 17.67/17.84 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[15])).
% 17.67/17.84 tff(17,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 17.67/17.84 tff(18,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[17, 16])).
% 17.67/17.84 tff(19,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[18, 14])).
% 17.67/17.84 tff(20,plain,(
% 17.67/17.84 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(skolemize,[status(sab)],[19])).
% 17.67/17.84 tff(21,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[20, 13])).
% 17.67/17.84 tff(22,plain,
% 17.67/17.84 (((~![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)))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(23,plain,
% 17.67/17.84 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 17.67/17.84 inference(quant_inst,[status(thm)],[])).
% 17.67/17.84 tff(24,plain,
% 17.67/17.84 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[23, 22])).
% 17.67/17.84 tff(25,plain,
% 17.67/17.84 (segmentP(nil, V!46) <=> (nil = V!46)),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 17.67/17.84 tff(26,plain,
% 17.67/17.84 (^[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))))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(27,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[26])).
% 17.67/17.84 tff(28,plain,
% 17.67/17.84 (^[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))))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(29,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[28])).
% 17.67/17.84 tff(30,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(transitivity,[status(thm)],[29, 27])).
% 17.67/17.84 tff(31,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(32,plain,
% 17.67/17.84 (^[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)))))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(33,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[32])).
% 17.67/17.84 tff(34,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 17.67/17.84 tff(35,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[34, 33])).
% 17.67/17.84 tff(36,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[35, 31])).
% 17.67/17.84 tff(37,plain,(
% 17.67/17.84 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 17.67/17.84 inference(skolemize,[status(sab)],[36])).
% 17.67/17.84 tff(38,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[37, 30])).
% 17.67/17.84 tff(39,plain,
% 17.67/17.84 (((~![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)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(40,plain,
% 17.67/17.84 ((~![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)))))),
% 17.67/17.84 inference(quant_inst,[status(thm)],[])).
% 17.67/17.84 tff(41,plain,
% 17.67/17.84 ((~![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))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[40, 39])).
% 17.67/17.84 tff(42,plain,
% 17.67/17.84 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[41, 38, 11])).
% 17.67/17.84 tff(43,plain,
% 17.67/17.84 (ssList(nil) <=> ssList(nil)),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(44,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 17.67/17.84 tff(45,plain,
% 17.67/17.84 (ssList(nil)),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[44, 43])).
% 17.67/17.84 tff(46,plain,
% 17.67/17.84 (((~![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))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(47,plain,
% 17.67/17.84 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 17.67/17.84 inference(quant_inst,[status(thm)],[])).
% 17.67/17.84 tff(48,plain,
% 17.67/17.84 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[47, 46])).
% 17.67/17.84 tff(49,plain,
% 17.67/17.84 (~((V!46 = nil) <=> neq(V!46, nil))),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 17.67/17.84 tff(50,plain,
% 17.67/17.84 (neq(V!46, nil)),
% 17.67/17.84 inference(or_elim,[status(thm)],[10])).
% 17.67/17.84 tff(51,plain,
% 17.67/17.84 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 17.67/17.84 inference(tautology,[status(thm)],[])).
% 17.67/17.84 tff(52,plain,
% 17.67/17.84 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[51, 50])).
% 17.67/17.84 tff(53,plain,
% 17.67/17.84 (~(V!46 = nil)),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[52, 49])).
% 17.67/17.84 tff(54,plain,
% 17.67/17.84 (^[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)))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(55,plain,
% 17.67/17.84 (![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))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[54])).
% 17.67/17.84 tff(56,plain,
% 17.67/17.84 (^[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)))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(57,plain,
% 17.67/17.84 (![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))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[56])).
% 17.67/17.84 tff(58,plain,
% 17.67/17.84 (![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))))),
% 17.67/17.84 inference(transitivity,[status(thm)],[57, 55])).
% 17.67/17.84 tff(59,plain,
% 17.67/17.84 (^[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)))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(60,plain,
% 17.67/17.84 (![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))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[59])).
% 17.67/17.84 tff(61,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(62,plain,
% 17.67/17.84 (^[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)))))))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(63,plain,
% 17.67/17.84 (![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)))))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[62])).
% 17.67/17.84 tff(64,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')).
% 17.67/17.84 tff(65,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[64, 63])).
% 17.67/17.84 tff(66,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[65, 61])).
% 17.67/17.84 tff(67,plain,(
% 17.67/17.84 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 17.67/17.84 inference(skolemize,[status(sab)],[66])).
% 17.67/17.84 tff(68,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[67, 60])).
% 17.67/17.84 tff(69,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[68, 58])).
% 17.67/17.84 tff(70,plain,
% 17.67/17.84 (((~![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))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(71,plain,
% 17.67/17.84 (((~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))))),
% 17.67/17.84 inference(rewrite,[status(thm)],[])).
% 17.67/17.84 tff(72,plain,
% 17.67/17.84 (((~![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)))))),
% 17.67/17.84 inference(monotonicity,[status(thm)],[71])).
% 17.67/17.84 tff(73,plain,
% 17.67/17.84 (((~![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))))),
% 17.67/17.84 inference(transitivity,[status(thm)],[72, 70])).
% 17.67/17.84 tff(74,plain,
% 17.67/17.84 ((~![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))))),
% 17.67/17.84 inference(quant_inst,[status(thm)],[])).
% 17.67/17.84 tff(75,plain,
% 17.67/17.84 ((~![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)))),
% 17.67/17.84 inference(modus_ponens,[status(thm)],[74, 73])).
% 17.67/17.84 tff(76,plain,
% 17.67/17.84 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 17.67/17.84 inference(unit_resolution,[status(thm)],[75, 69, 11])).
% 17.67/17.84 tff(77,plain,
% 17.67/17.84 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 17.67/17.84 inference(bind,[status(th)],[])).
% 17.67/17.84 tff(78,plain,
% 17.67/17.84 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.84 inference(quant_intro,[status(thm)],[77])).
% 17.67/17.85 tff(79,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(80,plain,
% 17.67/17.85 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(81,plain,
% 17.67/17.85 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[80])).
% 17.67/17.85 tff(82,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 17.67/17.85 tff(83,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[82, 81])).
% 17.67/17.85 tff(84,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[83, 79])).
% 17.67/17.85 tff(85,plain,(
% 17.67/17.85 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(skolemize,[status(sab)],[84])).
% 17.67/17.85 tff(86,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[85, 78])).
% 17.67/17.85 tff(87,plain,
% 17.67/17.85 (((~![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))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(88,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(89,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[88, 87])).
% 17.67/17.85 tff(90,plain,
% 17.67/17.85 (segmentP(V!46, nil)),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[89, 86, 11])).
% 17.67/17.85 tff(91,plain,
% 17.67/17.85 (((~![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)))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(92,plain,
% 17.67/17.85 (((~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)))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(93,plain,
% 17.67/17.85 (((~![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))))),
% 17.67/17.85 inference(monotonicity,[status(thm)],[92])).
% 17.67/17.85 tff(94,plain,
% 17.67/17.85 (((~![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)))),
% 17.67/17.85 inference(transitivity,[status(thm)],[93, 91])).
% 17.67/17.85 tff(95,plain,
% 17.67/17.85 ((~![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)))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(96,plain,
% 17.67/17.85 ((~![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))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[95, 94])).
% 17.67/17.85 tff(97,plain,
% 17.67/17.85 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[96, 45, 90, 76])).
% 17.67/17.85 tff(98,plain,
% 17.67/17.85 (~segmentP(nil, V!46)),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[97, 53])).
% 17.67/17.85 tff(99,plain,
% 17.67/17.85 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 17.67/17.85 inference(tautology,[status(thm)],[])).
% 17.67/17.85 tff(100,plain,
% 17.67/17.85 (~(nil = V!46)),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[99, 98, 25])).
% 17.67/17.85 tff(101,plain,
% 17.67/17.85 (^[U: $i] : refl(((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U))))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(102,plain,
% 17.67/17.85 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[101])).
% 17.67/17.85 tff(103,plain,
% 17.67/17.85 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(104,plain,
% 17.67/17.85 (^[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)))))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(105,plain,
% 17.67/17.85 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[104])).
% 17.67/17.85 tff(106,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax24')).
% 17.67/17.85 tff(107,plain,
% 17.67/17.85 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[106, 105])).
% 17.67/17.85 tff(108,plain,
% 17.67/17.85 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[107, 103])).
% 17.67/17.85 tff(109,plain,(
% 17.67/17.85 ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(skolemize,[status(sab)],[108])).
% 17.67/17.85 tff(110,plain,
% 17.67/17.85 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[109, 102])).
% 17.67/17.85 tff(111,plain,
% 17.67/17.85 (((~![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))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(112,plain,
% 17.67/17.85 (((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(113,plain,
% 17.67/17.85 (((~![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)))),
% 17.67/17.85 inference(monotonicity,[status(thm)],[112])).
% 17.67/17.85 tff(114,plain,
% 17.67/17.85 (((~![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))),
% 17.67/17.85 inference(transitivity,[status(thm)],[113, 111])).
% 17.67/17.85 tff(115,plain,
% 17.67/17.85 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(116,plain,
% 17.67/17.85 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46)),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[115, 114])).
% 17.67/17.85 tff(117,plain,
% 17.67/17.85 (ssList(tl(V!46))),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[116, 110, 11, 100])).
% 17.67/17.85 tff(118,plain,
% 17.67/17.85 (((~![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)))))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(119,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(120,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[119, 118])).
% 17.67/17.85 tff(121,plain,
% 17.67/17.85 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[120, 38, 45])).
% 17.67/17.85 tff(122,plain,
% 17.67/17.85 (((~![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))))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(123,plain,
% 17.67/17.85 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(124,plain,
% 17.67/17.85 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[123, 122])).
% 17.67/17.85 tff(125,plain,
% 17.67/17.85 (~((nil = V!46) <=> neq(nil, V!46))),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[124, 11, 121])).
% 17.67/17.85 tff(126,plain,
% 17.67/17.85 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 17.67/17.85 inference(tautology,[status(thm)],[])).
% 17.67/17.85 tff(127,plain,
% 17.67/17.85 (neq(nil, V!46)),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[126, 100, 125])).
% 17.67/17.85 tff(128,plain,
% 17.67/17.85 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(129,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[128])).
% 17.67/17.85 tff(130,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(131,plain,
% 17.67/17.85 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(132,plain,
% 17.67/17.85 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[131])).
% 17.67/17.85 tff(133,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 17.67/17.85 tff(134,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[133, 132])).
% 17.67/17.85 tff(135,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[134, 130])).
% 17.67/17.85 tff(136,plain,(
% 17.67/17.85 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(skolemize,[status(sab)],[135])).
% 17.67/17.85 tff(137,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[136, 129])).
% 17.67/17.85 tff(138,plain,
% 17.67/17.85 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(139,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 17.67/17.85 inference(quant_inst,[status(thm)],[])).
% 17.67/17.85 tff(140,plain,
% 17.67/17.85 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[139, 138])).
% 17.67/17.85 tff(141,plain,
% 17.67/17.85 (app(V!46, nil) = V!46),
% 17.67/17.85 inference(unit_resolution,[status(thm)],[140, 137, 11])).
% 17.67/17.85 tff(142,plain,
% 17.67/17.85 (V!46 = app(V!46, nil)),
% 17.67/17.85 inference(symmetry,[status(thm)],[141])).
% 17.67/17.85 tff(143,plain,
% 17.67/17.85 (tl(V!46) = tl(app(V!46, nil))),
% 17.67/17.85 inference(monotonicity,[status(thm)],[142])).
% 17.67/17.85 tff(144,plain,
% 17.67/17.85 (tl(app(V!46, nil)) = tl(V!46)),
% 17.67/17.85 inference(symmetry,[status(thm)],[143])).
% 17.67/17.85 tff(145,plain,
% 17.67/17.85 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(146,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[145])).
% 17.67/17.85 tff(147,plain,
% 17.67/17.85 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(148,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[147])).
% 17.67/17.85 tff(149,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(transitivity,[status(thm)],[148, 146])).
% 17.67/17.85 tff(150,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(rewrite,[status(thm)],[])).
% 17.67/17.85 tff(151,plain,
% 17.67/17.85 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))), ((ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> (ssList(V) => ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))))), rewrite((ssList(V) => ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))), ((ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))), (![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> (ssList(U) => ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))), rewrite((ssList(U) => ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))))),
% 17.67/17.85 inference(bind,[status(th)],[])).
% 17.67/17.85 tff(152,plain,
% 17.67/17.85 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(quant_intro,[status(thm)],[151])).
% 17.67/17.85 tff(153,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax86')).
% 17.67/17.85 tff(154,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[153, 152])).
% 17.67/17.85 tff(155,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[154, 150])).
% 17.67/17.85 tff(156,plain,(
% 17.67/17.85 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(skolemize,[status(sab)],[155])).
% 17.67/17.85 tff(157,plain,
% 17.67/17.85 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 17.67/17.85 inference(modus_ponens,[status(thm)],[156, 149])).
% 17.67/17.85 tff(158,plain,
% 17.67/17.85 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(159,plain,
% 17.70/17.85 (((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(160,plain,
% 17.70/17.85 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))))),
% 17.70/17.85 inference(monotonicity,[status(thm)],[159])).
% 17.70/17.85 tff(161,plain,
% 17.70/17.85 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 17.70/17.85 inference(transitivity,[status(thm)],[160, 158])).
% 17.70/17.85 tff(162,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(163,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[162, 161])).
% 17.70/17.85 tff(164,plain,
% 17.70/17.85 (![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[163, 157, 11])).
% 17.70/17.85 tff(165,plain,
% 17.70/17.85 (((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | ((~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | (~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(166,plain,
% 17.70/17.85 ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | ((~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(167,plain,
% 17.70/17.85 ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | (~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[166, 165])).
% 17.70/17.85 tff(168,plain,
% 17.70/17.85 ((nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil))),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[167, 45, 164])).
% 17.70/17.85 tff(169,plain,
% 17.70/17.85 (tl(app(V!46, nil)) = app(tl(V!46), nil)),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[168, 100])).
% 17.70/17.85 tff(170,plain,
% 17.70/17.85 (app(tl(V!46), nil) = tl(app(V!46, nil))),
% 17.70/17.85 inference(symmetry,[status(thm)],[169])).
% 17.70/17.85 tff(171,plain,
% 17.70/17.85 (app(tl(V!46), nil) = tl(V!46)),
% 17.70/17.85 inference(transitivity,[status(thm)],[170, 144])).
% 17.70/17.85 tff(172,plain,
% 17.70/17.85 (ssList(app(tl(V!46), nil)) <=> ssList(tl(V!46))),
% 17.70/17.85 inference(monotonicity,[status(thm)],[171])).
% 17.70/17.85 tff(173,plain,
% 17.70/17.85 (ssList(tl(V!46)) <=> ssList(app(tl(V!46), nil))),
% 17.70/17.85 inference(symmetry,[status(thm)],[172])).
% 17.70/17.85 tff(174,plain,
% 17.70/17.85 (ssList(app(tl(V!46), nil))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[117, 173])).
% 17.70/17.85 tff(175,plain,
% 17.70/17.85 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 17.70/17.85 inference(bind,[status(th)],[])).
% 17.70/17.85 tff(176,plain,
% 17.70/17.85 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(quant_intro,[status(thm)],[175])).
% 17.70/17.85 tff(177,plain,
% 17.70/17.85 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(178,plain,
% 17.70/17.85 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 17.70/17.85 inference(bind,[status(th)],[])).
% 17.70/17.85 tff(179,plain,
% 17.70/17.85 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(quant_intro,[status(thm)],[178])).
% 17.70/17.85 tff(180,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 17.70/17.85 tff(181,plain,
% 17.70/17.85 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[180, 179])).
% 17.70/17.85 tff(182,plain,
% 17.70/17.85 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[181, 177])).
% 17.70/17.85 tff(183,plain,(
% 17.70/17.85 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(skolemize,[status(sab)],[182])).
% 17.70/17.85 tff(184,plain,
% 17.70/17.85 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[183, 176])).
% 17.70/17.85 tff(185,plain,
% 17.70/17.85 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(tl(V!46), nil))) | (app(nil, app(tl(V!46), nil)) = app(tl(V!46), nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(tl(V!46), nil))) | (app(nil, app(tl(V!46), nil)) = app(tl(V!46), nil)))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(186,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(tl(V!46), nil))) | (app(nil, app(tl(V!46), nil)) = app(tl(V!46), nil)))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(187,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(tl(V!46), nil))) | (app(nil, app(tl(V!46), nil)) = app(tl(V!46), nil))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[186, 185])).
% 17.70/17.85 tff(188,plain,
% 17.70/17.85 (app(nil, app(tl(V!46), nil)) = app(tl(V!46), nil)),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[187, 184, 174])).
% 17.70/17.85 tff(189,plain,
% 17.70/17.85 (tl(V!46) = app(tl(V!46), nil)),
% 17.70/17.85 inference(transitivity,[status(thm)],[143, 169])).
% 17.70/17.85 tff(190,plain,
% 17.70/17.85 (ssList(U!45)),
% 17.70/17.85 inference(and_elim,[status(thm)],[9])).
% 17.70/17.85 tff(191,plain,
% 17.70/17.85 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(192,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(193,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[192, 191])).
% 17.70/17.85 tff(194,plain,
% 17.70/17.85 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[193, 38, 190])).
% 17.70/17.85 tff(195,plain,
% 17.70/17.85 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(196,plain,
% 17.70/17.85 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(197,plain,
% 17.70/17.85 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[196, 195])).
% 17.70/17.85 tff(198,plain,
% 17.70/17.85 (~((U!45 = nil) <=> neq(U!45, nil))),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[197, 45, 194])).
% 17.70/17.85 tff(199,plain,
% 17.70/17.85 (~neq(U!45, nil)),
% 17.70/17.85 inference(or_elim,[status(thm)],[10])).
% 17.70/17.85 tff(200,plain,
% 17.70/17.85 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 17.70/17.85 inference(tautology,[status(thm)],[])).
% 17.70/17.85 tff(201,plain,
% 17.70/17.85 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[200, 199])).
% 17.70/17.85 tff(202,plain,
% 17.70/17.85 (U!45 = nil),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[201, 198])).
% 17.70/17.85 tff(203,plain,
% 17.70/17.85 (app(U!45, tl(V!46)) = app(nil, app(tl(V!46), nil))),
% 17.70/17.85 inference(monotonicity,[status(thm)],[202, 189])).
% 17.70/17.85 tff(204,plain,
% 17.70/17.85 (app(U!45, tl(V!46)) = tl(V!46)),
% 17.70/17.85 inference(transitivity,[status(thm)],[203, 188, 170, 144])).
% 17.70/17.85 tff(205,plain,
% 17.70/17.85 (ssList(app(U!45, tl(V!46))) <=> ssList(tl(V!46))),
% 17.70/17.85 inference(monotonicity,[status(thm)],[204])).
% 17.70/17.85 tff(206,plain,
% 17.70/17.85 (ssList(tl(V!46)) <=> ssList(app(U!45, tl(V!46)))),
% 17.70/17.85 inference(symmetry,[status(thm)],[205])).
% 17.70/17.85 tff(207,plain,
% 17.70/17.85 (ssList(app(U!45, tl(V!46)))),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[117, 206])).
% 17.70/17.85 tff(208,plain,
% 17.70/17.85 ((V!46 = app(tl(V!46), nil)) <=> (app(tl(V!46), nil) = V!46)),
% 17.70/17.85 inference(commutativity,[status(thm)],[])).
% 17.70/17.85 tff(209,plain,
% 17.70/17.85 (app(U!45, tl(V!46)) = app(tl(V!46), nil)),
% 17.70/17.85 inference(transitivity,[status(thm)],[203, 188])).
% 17.70/17.85 tff(210,plain,
% 17.70/17.85 ((V!46 = app(U!45, tl(V!46))) <=> (V!46 = app(tl(V!46), nil))),
% 17.70/17.85 inference(monotonicity,[status(thm)],[209])).
% 17.70/17.85 tff(211,plain,
% 17.70/17.85 ((V!46 = app(U!45, tl(V!46))) <=> (app(tl(V!46), nil) = V!46)),
% 17.70/17.85 inference(transitivity,[status(thm)],[210, 208])).
% 17.70/17.85 tff(212,plain,
% 17.70/17.85 ((app(tl(V!46), nil) = V!46) <=> (V!46 = app(U!45, tl(V!46)))),
% 17.70/17.85 inference(symmetry,[status(thm)],[211])).
% 17.70/17.85 tff(213,plain,
% 17.70/17.85 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(V!46)) | (app(nil, V!46) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(V!46)) | (app(nil, V!46) = V!46))),
% 17.70/17.85 inference(rewrite,[status(thm)],[])).
% 17.70/17.85 tff(214,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(V!46)) | (app(nil, V!46) = V!46))),
% 17.70/17.85 inference(quant_inst,[status(thm)],[])).
% 17.70/17.85 tff(215,plain,
% 17.70/17.85 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(V!46)) | (app(nil, V!46) = V!46)),
% 17.70/17.85 inference(modus_ponens,[status(thm)],[214, 213])).
% 17.70/17.85 tff(216,plain,
% 17.70/17.85 (app(nil, V!46) = V!46),
% 17.70/17.85 inference(unit_resolution,[status(thm)],[215, 184, 11])).
% 17.70/17.85 tff(217,plain,
% 17.70/17.85 (app(U!45, V!46) = app(nil, V!46)),
% 17.70/17.85 inference(monotonicity,[status(thm)],[202])).
% 17.70/17.85 tff(218,plain,
% 17.70/17.85 (app(U!45, V!46) = V!46),
% 17.70/17.85 inference(transitivity,[status(thm)],[217, 216])).
% 17.70/17.85 tff(219,plain,
% 17.70/17.85 (^[U: $i] : refl(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))),
% 17.70/17.85 inference(bind,[status(th)],[])).
% 17.70/17.85 tff(220,plain,
% 17.70/17.85 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 17.70/17.85 inference(quant_intro,[status(thm)],[219])).
% 17.70/17.85 tff(221,plain,
% 17.70/17.85 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) <=> (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))), rewrite(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(222,plain,
% 17.70/17.86 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[221])).
% 17.70/17.86 tff(223,plain,
% 17.70/17.86 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))))), rewrite(((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(224,plain,
% 17.70/17.86 (![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[223])).
% 17.70/17.86 tff(225,plain,
% 17.70/17.86 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(226,plain,
% 17.70/17.86 (^[U: $i] : trans(monotonicity(rewrite(((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))))), rewrite((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(227,plain,
% 17.70/17.86 (![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[226])).
% 17.70/17.86 tff(228,axiom,(![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax20')).
% 17.70/17.86 tff(229,plain,
% 17.70/17.86 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[228, 227])).
% 17.70/17.86 tff(230,plain,
% 17.70/17.86 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[229, 225])).
% 17.70/17.86 tff(231,plain,(
% 17.70/17.86 ![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U)))),
% 17.70/17.86 inference(skolemize,[status(sab)],[230])).
% 17.70/17.86 tff(232,plain,
% 17.70/17.86 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[231, 224])).
% 17.70/17.86 tff(233,plain,
% 17.70/17.86 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[232, 222])).
% 17.70/17.86 tff(234,plain,
% 17.70/17.86 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[233, 220])).
% 17.70/17.86 tff(235,plain,
% 17.70/17.86 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(236,plain,
% 17.70/17.86 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(237,plain,
% 17.70/17.86 ((~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))) <=> (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(238,plain,
% 17.70/17.86 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[237])).
% 17.70/17.86 tff(239,plain,
% 17.70/17.86 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(transitivity,[status(thm)],[238, 236])).
% 17.70/17.86 tff(240,plain,
% 17.70/17.86 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[239])).
% 17.70/17.86 tff(241,plain,
% 17.70/17.86 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(transitivity,[status(thm)],[240, 235])).
% 17.70/17.86 tff(242,plain,
% 17.70/17.86 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 17.70/17.86 inference(quant_inst,[status(thm)],[])).
% 17.70/17.86 tff(243,plain,
% 17.70/17.86 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[242, 241])).
% 17.70/17.86 tff(244,plain,
% 17.70/17.86 ((nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[243, 234, 11])).
% 17.70/17.86 tff(245,plain,
% 17.70/17.86 (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[244, 100])).
% 17.70/17.86 tff(246,plain,
% 17.70/17.86 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)),
% 17.70/17.86 inference(tautology,[status(thm)],[])).
% 17.70/17.86 tff(247,plain,
% 17.70/17.86 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[246, 245])).
% 17.70/17.86 tff(248,plain,
% 17.70/17.86 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tl(V!46)),
% 17.70/17.86 inference(monotonicity,[status(thm)],[247])).
% 17.70/17.86 tff(249,plain,
% 17.70/17.86 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | ssList(tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(tautology,[status(thm)],[])).
% 17.70/17.86 tff(250,plain,
% 17.70/17.86 (ssList(tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[249, 245])).
% 17.70/17.86 tff(251,plain,
% 17.70/17.86 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(252,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[251])).
% 17.70/17.86 tff(253,plain,
% 17.70/17.86 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(254,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[253])).
% 17.70/17.86 tff(255,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(transitivity,[status(thm)],[254, 252])).
% 17.70/17.86 tff(256,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(257,plain,
% 17.70/17.86 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (tl(cons(V, U)) = U)) <=> ((~ssItem(V)) | (tl(cons(V, U)) = U)))), (![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)) <=> ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(258,plain,
% 17.70/17.86 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[257])).
% 17.70/17.86 tff(259,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax25')).
% 17.70/17.86 tff(260,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[259, 258])).
% 17.70/17.86 tff(261,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[260, 256])).
% 17.70/17.86 tff(262,plain,(
% 17.70/17.86 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(skolemize,[status(sab)],[261])).
% 17.70/17.86 tff(263,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[262, 255])).
% 17.70/17.86 tff(264,plain,
% 17.70/17.86 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(265,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))),
% 17.70/17.86 inference(quant_inst,[status(thm)],[])).
% 17.70/17.86 tff(266,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[265, 264])).
% 17.70/17.86 tff(267,plain,
% 17.70/17.86 (![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[266, 263, 250])).
% 17.70/17.86 tff(268,plain,
% 17.70/17.86 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | ssItem(tptp_fun_W_44(V!46))),
% 17.70/17.86 inference(tautology,[status(thm)],[])).
% 17.70/17.86 tff(269,plain,
% 17.70/17.86 (ssItem(tptp_fun_W_44(V!46))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[268, 245])).
% 17.70/17.86 tff(270,plain,
% 17.70/17.86 (((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) <=> ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | (~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(271,plain,
% 17.70/17.86 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(quant_inst,[status(thm)],[])).
% 17.70/17.86 tff(272,plain,
% 17.70/17.86 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | (~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[271, 270])).
% 17.70/17.86 tff(273,plain,
% 17.70/17.86 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[272, 269, 267])).
% 17.70/17.86 tff(274,plain,
% 17.70/17.86 (tptp_fun_V_43(V!46) = tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(symmetry,[status(thm)],[273])).
% 17.70/17.86 tff(275,plain,
% 17.70/17.86 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(276,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(quant_inst,[status(thm)],[])).
% 17.70/17.86 tff(277,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[276, 275])).
% 17.70/17.86 tff(278,plain,
% 17.70/17.86 (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[277, 184, 250])).
% 17.70/17.86 tff(279,plain,
% 17.70/17.86 (app(U!45, tptp_fun_V_43(V!46)) = app(nil, tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[202])).
% 17.70/17.86 tff(280,plain,
% 17.70/17.86 (app(U!45, tptp_fun_V_43(V!46)) = app(tl(V!46), nil)),
% 17.70/17.86 inference(transitivity,[status(thm)],[279, 278, 274, 248, 143, 169])).
% 17.70/17.86 tff(281,plain,
% 17.70/17.86 ((app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46)) <=> (app(tl(V!46), nil) = V!46)),
% 17.70/17.86 inference(monotonicity,[status(thm)],[280, 218])).
% 17.70/17.86 tff(282,plain,
% 17.70/17.86 ((app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46)) <=> (V!46 = app(U!45, tl(V!46)))),
% 17.70/17.86 inference(transitivity,[status(thm)],[281, 212])).
% 17.70/17.86 tff(283,plain,
% 17.70/17.86 ((~(app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46))) <=> (~(V!46 = app(U!45, tl(V!46))))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[282])).
% 17.70/17.86 tff(284,plain,
% 17.70/17.86 ((app(U!45, V!46) = app(U!45, tptp_fun_V_43(V!46))) <=> (app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46))),
% 17.70/17.86 inference(commutativity,[status(thm)],[])).
% 17.70/17.86 tff(285,plain,
% 17.70/17.86 (app(nil, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(symmetry,[status(thm)],[279])).
% 17.70/17.86 tff(286,plain,
% 17.70/17.86 (tptp_fun_V_43(V!46) = app(nil, tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(symmetry,[status(thm)],[278])).
% 17.70/17.86 tff(287,plain,
% 17.70/17.86 (tptp_fun_V_43(V!46) = app(U!45, tptp_fun_V_43(V!46))),
% 17.70/17.86 inference(transitivity,[status(thm)],[286, 285])).
% 17.70/17.86 tff(288,plain,
% 17.70/17.86 (app(nil, V!46) = app(U!45, V!46)),
% 17.70/17.86 inference(symmetry,[status(thm)],[217])).
% 17.70/17.86 tff(289,plain,
% 17.70/17.86 (V!46 = app(nil, V!46)),
% 17.70/17.86 inference(symmetry,[status(thm)],[216])).
% 17.70/17.86 tff(290,plain,
% 17.70/17.86 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(U!45, V!46)),
% 17.70/17.86 inference(transitivity,[status(thm)],[247, 289, 288])).
% 17.70/17.86 tff(291,plain,
% 17.70/17.86 ((cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)) <=> (app(U!45, V!46) = app(U!45, tptp_fun_V_43(V!46)))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[290, 287])).
% 17.70/17.86 tff(292,plain,
% 17.70/17.86 ((cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)) <=> (app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46))),
% 17.70/17.86 inference(transitivity,[status(thm)],[291, 284])).
% 17.70/17.86 tff(293,plain,
% 17.70/17.86 ((~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))) <=> (~(app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46)))),
% 17.70/17.86 inference(monotonicity,[status(thm)],[292])).
% 17.70/17.86 tff(294,plain,
% 17.70/17.86 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(295,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[294])).
% 17.70/17.86 tff(296,plain,
% 17.70/17.86 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(297,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[296])).
% 17.70/17.86 tff(298,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(transitivity,[status(thm)],[297, 295])).
% 17.70/17.86 tff(299,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(300,plain,
% 17.70/17.86 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 17.70/17.86 inference(bind,[status(th)],[])).
% 17.70/17.86 tff(301,plain,
% 17.70/17.86 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(quant_intro,[status(thm)],[300])).
% 17.70/17.86 tff(302,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 17.70/17.86 tff(303,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[302, 301])).
% 17.70/17.86 tff(304,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[303, 299])).
% 17.70/17.86 tff(305,plain,(
% 17.70/17.86 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(skolemize,[status(sab)],[304])).
% 17.70/17.86 tff(306,plain,
% 17.70/17.86 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[305, 298])).
% 17.70/17.86 tff(307,plain,
% 17.70/17.86 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))))),
% 17.70/17.86 inference(rewrite,[status(thm)],[])).
% 17.70/17.86 tff(308,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))))),
% 17.70/17.86 inference(quant_inst,[status(thm)],[])).
% 17.70/17.86 tff(309,plain,
% 17.70/17.86 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))),
% 17.70/17.86 inference(modus_ponens,[status(thm)],[308, 307])).
% 17.70/17.86 tff(310,plain,
% 17.70/17.86 (![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))),
% 17.70/17.86 inference(unit_resolution,[status(thm)],[309, 306, 250])).
% 17.70/17.86 tff(311,plain,
% 17.70/17.86 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))),
% 17.70/17.92 inference(rewrite,[status(thm)],[])).
% 17.70/17.92 tff(312,plain,
% 17.70/17.92 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))),
% 17.70/17.92 inference(quant_inst,[status(thm)],[])).
% 17.70/17.92 tff(313,plain,
% 17.70/17.92 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))),
% 17.70/17.92 inference(modus_ponens,[status(thm)],[312, 311])).
% 17.70/17.92 tff(314,plain,
% 17.70/17.92 (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))),
% 17.70/17.92 inference(unit_resolution,[status(thm)],[313, 269, 310])).
% 17.70/17.92 tff(315,plain,
% 17.70/17.92 (~(app(U!45, tptp_fun_V_43(V!46)) = app(U!45, V!46))),
% 17.70/17.92 inference(modus_ponens,[status(thm)],[314, 293])).
% 17.70/17.92 tff(316,plain,
% 17.70/17.92 (~(V!46 = app(U!45, tl(V!46)))),
% 17.70/17.92 inference(modus_ponens,[status(thm)],[315, 283])).
% 17.70/17.92 tff(317,plain,
% 17.70/17.92 ((~(~((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))))) <=> ((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))),
% 17.70/17.92 inference(rewrite,[status(thm)],[])).
% 17.70/17.92 tff(318,plain,
% 17.70/17.92 ((ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46))) <=> (~((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))))),
% 17.70/17.92 inference(rewrite,[status(thm)],[])).
% 17.70/17.92 tff(319,plain,
% 17.70/17.92 ((~(ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46)))) <=> (~(~((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))))),
% 17.70/17.92 inference(monotonicity,[status(thm)],[318])).
% 17.70/17.92 tff(320,plain,
% 17.70/17.92 ((~(ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46)))) <=> ((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))),
% 17.70/17.92 inference(transitivity,[status(thm)],[319, 317])).
% 17.70/17.92 tff(321,plain,
% 17.70/17.92 (~(ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46)))),
% 17.70/17.92 inference(or_elim,[status(thm)],[10])).
% 17.70/17.92 tff(322,plain,
% 17.70/17.92 ((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))),
% 17.70/17.92 inference(modus_ponens,[status(thm)],[321, 320])).
% 17.70/17.92 tff(323,plain,
% 17.70/17.92 ($false),
% 17.70/17.92 inference(unit_resolution,[status(thm)],[322, 316, 207, 127, 117])).
% 17.70/17.92 % SZS output end Proof
% 17.70/17.92 % E exiting
%------------------------------------------------------------------------------