%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC253+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:30:41 AM UTC 2025
% Result : Theorem 81.13s 81.32s
% Output : Proof 81.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC253+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 08:45:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 81.13/81.32 % SZS status Theorem
% 81.13/81.32 % SZS output start Proof
% 81.13/81.32 tff(app_type, type, (
% 81.13/81.32 app: ( $i * $i ) > $i)).
% 81.13/81.32 tff(tl_type, type, (
% 81.13/81.32 tl: $i > $i)).
% 81.13/81.32 tff(tptp_fun_V_46_type, type, (
% 81.13/81.32 tptp_fun_V_46: $i)).
% 81.13/81.32 tff(tptp_fun_U_45_type, type, (
% 81.13/81.32 tptp_fun_U_45: $i)).
% 81.13/81.32 tff(tptp_fun_V_43_type, type, (
% 81.13/81.32 tptp_fun_V_43: $i > $i)).
% 81.13/81.32 tff(nil_type, type, (
% 81.13/81.32 nil: $i)).
% 81.13/81.32 tff(cons_type, type, (
% 81.13/81.32 cons: ( $i * $i ) > $i)).
% 81.13/81.32 tff(hd_type, type, (
% 81.13/81.32 hd: $i > $i)).
% 81.13/81.32 tff(ssList_type, type, (
% 81.13/81.32 ssList: $i > $o)).
% 81.13/81.32 tff(neq_type, type, (
% 81.13/81.32 neq: ( $i * $i ) > $o)).
% 81.13/81.32 tff(singletonP_type, type, (
% 81.13/81.32 singletonP: $i > $o)).
% 81.13/81.32 tff(tptp_fun_W_44_type, type, (
% 81.13/81.32 tptp_fun_W_44: $i > $i)).
% 81.13/81.32 tff(ssItem_type, type, (
% 81.13/81.32 ssItem: $i > $o)).
% 81.13/81.32 tff(segmentP_type, type, (
% 81.13/81.32 segmentP: ( $i * $i ) > $o)).
% 81.13/81.32 tff(tptp_fun_V_4_type, type, (
% 81.13/81.32 tptp_fun_V_4: $i > $i)).
% 81.13/81.32 tff(1,plain,
% 81.13/81.32 ((V!46 = app(nil, app(U!45, tptp_fun_V_43(V!46)))) <=> (app(nil, app(U!45, tptp_fun_V_43(V!46))) = V!46)),
% 81.13/81.32 inference(commutativity,[status(thm)],[])).
% 81.13/81.32 tff(2,plain,
% 81.13/81.32 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(3,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[2])).
% 81.13/81.32 tff(4,plain,
% 81.13/81.32 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(5,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[4])).
% 81.13/81.32 tff(6,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(transitivity,[status(thm)],[5, 3])).
% 81.13/81.32 tff(7,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(8,plain,
% 81.13/81.32 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(9,plain,
% 81.13/81.32 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[8])).
% 81.13/81.32 tff(10,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax82')).
% 81.13/81.32 tff(11,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[10, 9])).
% 81.13/81.32 tff(12,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[11, 7])).
% 81.13/81.32 tff(13,plain,(
% 81.13/81.32 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(skolemize,[status(sab)],[12])).
% 81.13/81.32 tff(14,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[13, 6])).
% 81.13/81.32 tff(15,plain,
% 81.13/81.32 (ssList(nil) <=> ssList(nil)),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(16,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 81.13/81.32 tff(17,plain,
% 81.13/81.32 (ssList(nil)),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[16, 15])).
% 81.13/81.32 tff(18,plain,
% 81.13/81.32 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W))))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(19,plain,
% 81.13/81.32 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W))))))),
% 81.13/81.32 inference(quant_inst,[status(thm)],[])).
% 81.13/81.32 tff(20,plain,
% 81.13/81.32 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[19, 18])).
% 81.13/81.32 tff(21,plain,
% 81.13/81.32 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[20, 17, 14])).
% 81.13/81.32 tff(22,plain,
% 81.13/81.32 ((ssList(U!45) & (~((~ssList(V!46)) | (~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))) | singletonP(U!45) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | singletonP(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)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(23,plain,
% 81.13/81.32 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(24,plain,
% 81.13/81.32 ((~![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)))) | singletonP(U)) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(25,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)))) | singletonP(U)) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 81.13/81.32 tff(26,plain,
% 81.13/81.32 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[25, 24])).
% 81.13/81.32 tff(27,plain,
% 81.13/81.32 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[26, 23])).
% 81.13/81.32 tff(28,plain,
% 81.13/81.32 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[27, 23])).
% 81.13/81.32 tff(29,plain,
% 81.13/81.32 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (~(V = app(U, tl(V)))) & neq(nil, V) & ssList(tl(V))) | singletonP(U) | (~neq(V, nil))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[28, 23])).
% 81.13/81.32 tff(30,plain,
% 81.13/81.32 (ssList(U!45) & (~((~ssList(U!45)) | singletonP(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))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[29, 22])).
% 81.13/81.32 tff(31,plain,
% 81.13/81.32 (ssList(U!45)),
% 81.13/81.32 inference(and_elim,[status(thm)],[30])).
% 81.13/81.32 tff(32,plain,
% 81.13/81.32 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(33,plain,
% 81.13/81.32 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W)))))),
% 81.13/81.32 inference(quant_inst,[status(thm)],[])).
% 81.13/81.32 tff(34,plain,
% 81.13/81.32 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, V), W) = app(nil, app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[33, 32])).
% 81.13/81.32 tff(35,plain,
% 81.13/81.32 (![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 81.13/81.32 tff(36,plain,
% 81.13/81.32 (~((~ssList(U!45)) | singletonP(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)))),
% 81.13/81.32 inference(and_elim,[status(thm)],[30])).
% 81.13/81.32 tff(37,plain,
% 81.13/81.32 (ssList(V!46)),
% 81.13/81.32 inference(or_elim,[status(thm)],[36])).
% 81.13/81.32 tff(38,plain,
% 81.13/81.32 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(39,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[38])).
% 81.13/81.32 tff(40,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(41,plain,
% 81.13/81.32 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(42,plain,
% 81.13/81.32 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[41])).
% 81.13/81.32 tff(43,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 81.13/81.32 tff(44,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[43, 42])).
% 81.13/81.32 tff(45,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[44, 40])).
% 81.13/81.32 tff(46,plain,(
% 81.13/81.32 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(skolemize,[status(sab)],[45])).
% 81.13/81.32 tff(47,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[46, 39])).
% 81.13/81.32 tff(48,plain,
% 81.13/81.32 (((~![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)))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(49,plain,
% 81.13/81.32 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 81.13/81.32 inference(quant_inst,[status(thm)],[])).
% 81.13/81.32 tff(50,plain,
% 81.13/81.32 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[49, 48])).
% 81.13/81.32 tff(51,plain,
% 81.13/81.32 (segmentP(nil, V!46) <=> (nil = V!46)),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 81.13/81.32 tff(52,plain,
% 81.13/81.32 (^[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))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(53,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[52])).
% 81.13/81.32 tff(54,plain,
% 81.13/81.32 (^[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))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(55,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[54])).
% 81.13/81.32 tff(56,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(transitivity,[status(thm)],[55, 53])).
% 81.13/81.32 tff(57,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(58,plain,
% 81.13/81.32 (^[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)))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(59,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[58])).
% 81.13/81.32 tff(60,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 81.13/81.32 tff(61,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[60, 59])).
% 81.13/81.32 tff(62,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[61, 57])).
% 81.13/81.32 tff(63,plain,(
% 81.13/81.32 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 81.13/81.32 inference(skolemize,[status(sab)],[62])).
% 81.13/81.32 tff(64,plain,
% 81.13/81.32 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[63, 56])).
% 81.13/81.32 tff(65,plain,
% 81.13/81.32 (((~![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)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(66,plain,
% 81.13/81.32 ((~![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)))))),
% 81.13/81.32 inference(quant_inst,[status(thm)],[])).
% 81.13/81.32 tff(67,plain,
% 81.13/81.32 ((~![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))))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[66, 65])).
% 81.13/81.32 tff(68,plain,
% 81.13/81.32 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[67, 64, 37])).
% 81.13/81.32 tff(69,plain,
% 81.13/81.32 (((~![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))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(70,plain,
% 81.13/81.32 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 81.13/81.32 inference(quant_inst,[status(thm)],[])).
% 81.13/81.32 tff(71,plain,
% 81.13/81.32 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 81.13/81.32 inference(modus_ponens,[status(thm)],[70, 69])).
% 81.13/81.32 tff(72,plain,
% 81.13/81.32 (~((V!46 = nil) <=> neq(V!46, nil))),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[71, 17, 68])).
% 81.13/81.32 tff(73,plain,
% 81.13/81.32 (neq(V!46, nil)),
% 81.13/81.32 inference(or_elim,[status(thm)],[36])).
% 81.13/81.32 tff(74,plain,
% 81.13/81.32 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 81.13/81.32 inference(tautology,[status(thm)],[])).
% 81.13/81.32 tff(75,plain,
% 81.13/81.32 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[74, 73])).
% 81.13/81.32 tff(76,plain,
% 81.13/81.32 (~(V!46 = nil)),
% 81.13/81.32 inference(unit_resolution,[status(thm)],[75, 72])).
% 81.13/81.32 tff(77,plain,
% 81.13/81.32 (^[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)))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(78,plain,
% 81.13/81.32 (![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))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[77])).
% 81.13/81.32 tff(79,plain,
% 81.13/81.32 (^[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)))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(80,plain,
% 81.13/81.32 (![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))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[79])).
% 81.13/81.32 tff(81,plain,
% 81.13/81.32 (![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))))),
% 81.13/81.32 inference(transitivity,[status(thm)],[80, 78])).
% 81.13/81.32 tff(82,plain,
% 81.13/81.32 (^[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)))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(83,plain,
% 81.13/81.32 (![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))))),
% 81.13/81.32 inference(quant_intro,[status(thm)],[82])).
% 81.13/81.32 tff(84,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.32 inference(rewrite,[status(thm)],[])).
% 81.13/81.32 tff(85,plain,
% 81.13/81.32 (^[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)))))))),
% 81.13/81.32 inference(bind,[status(th)],[])).
% 81.13/81.32 tff(86,plain,
% 81.13/81.32 (![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)))))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[85])).
% 81.13/81.33 tff(87,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')).
% 81.13/81.33 tff(88,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[87, 86])).
% 81.13/81.33 tff(89,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[88, 84])).
% 81.13/81.33 tff(90,plain,(
% 81.13/81.33 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 81.13/81.33 inference(skolemize,[status(sab)],[89])).
% 81.13/81.33 tff(91,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[90, 83])).
% 81.13/81.33 tff(92,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[91, 81])).
% 81.13/81.33 tff(93,plain,
% 81.13/81.33 (((~![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))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(94,plain,
% 81.13/81.33 (((~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))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(95,plain,
% 81.13/81.33 (((~![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)))))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[94])).
% 81.13/81.33 tff(96,plain,
% 81.13/81.33 (((~![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))))),
% 81.13/81.33 inference(transitivity,[status(thm)],[95, 93])).
% 81.13/81.33 tff(97,plain,
% 81.13/81.33 ((~![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))))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(98,plain,
% 81.13/81.33 ((~![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)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[97, 96])).
% 81.13/81.33 tff(99,plain,
% 81.13/81.33 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[98, 92, 37])).
% 81.13/81.33 tff(100,plain,
% 81.13/81.33 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(101,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[100])).
% 81.13/81.33 tff(102,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(103,plain,
% 81.13/81.33 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(104,plain,
% 81.13/81.33 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[103])).
% 81.13/81.33 tff(105,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 81.13/81.33 tff(106,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[105, 104])).
% 81.13/81.33 tff(107,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[106, 102])).
% 81.13/81.33 tff(108,plain,(
% 81.13/81.33 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(skolemize,[status(sab)],[107])).
% 81.13/81.33 tff(109,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[108, 101])).
% 81.13/81.33 tff(110,plain,
% 81.13/81.33 (((~![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))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(111,plain,
% 81.13/81.33 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(112,plain,
% 81.13/81.33 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[111, 110])).
% 81.13/81.33 tff(113,plain,
% 81.13/81.33 (segmentP(V!46, nil)),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[112, 109, 37])).
% 81.13/81.33 tff(114,plain,
% 81.13/81.33 (((~![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)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(115,plain,
% 81.13/81.33 (((~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)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(116,plain,
% 81.13/81.33 (((~![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))))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[115])).
% 81.13/81.33 tff(117,plain,
% 81.13/81.33 (((~![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)))),
% 81.13/81.33 inference(transitivity,[status(thm)],[116, 114])).
% 81.13/81.33 tff(118,plain,
% 81.13/81.33 ((~![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)))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(119,plain,
% 81.13/81.33 ((~![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))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[118, 117])).
% 81.13/81.33 tff(120,plain,
% 81.13/81.33 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[119, 17, 113, 99])).
% 81.13/81.33 tff(121,plain,
% 81.13/81.33 (~segmentP(nil, V!46)),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[120, 76])).
% 81.13/81.33 tff(122,plain,
% 81.13/81.33 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 81.13/81.33 inference(tautology,[status(thm)],[])).
% 81.13/81.33 tff(123,plain,
% 81.13/81.33 (~(nil = V!46)),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[122, 121, 51])).
% 81.13/81.33 tff(124,plain,
% 81.13/81.33 (^[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))))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(125,plain,
% 81.13/81.33 (![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)))))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[124])).
% 81.13/81.33 tff(126,plain,
% 81.13/81.33 (^[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)))))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(127,plain,
% 81.13/81.33 (![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)))))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[126])).
% 81.13/81.33 tff(128,plain,
% 81.13/81.33 (^[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)))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(129,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[128])).
% 81.13/81.33 tff(130,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(131,plain,
% 81.13/81.33 (^[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)))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(132,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[131])).
% 81.13/81.33 tff(133,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')).
% 81.13/81.33 tff(134,plain,
% 81.13/81.33 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[133, 132])).
% 81.13/81.33 tff(135,plain,
% 81.13/81.33 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[134, 130])).
% 81.13/81.33 tff(136,plain,(
% 81.13/81.33 ![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)))),
% 81.13/81.33 inference(skolemize,[status(sab)],[135])).
% 81.13/81.33 tff(137,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[136, 129])).
% 81.13/81.33 tff(138,plain,
% 81.13/81.33 (![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)))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[137, 127])).
% 81.13/81.33 tff(139,plain,
% 81.13/81.33 (![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)))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[138, 125])).
% 81.13/81.33 tff(140,plain,
% 81.13/81.33 (((~![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)))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(141,plain,
% 81.13/81.33 (((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)))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(142,plain,
% 81.13/81.33 ((~((~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))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(143,plain,
% 81.13/81.33 (((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)))))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[142])).
% 81.13/81.33 tff(144,plain,
% 81.13/81.33 (((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)))))),
% 81.13/81.33 inference(transitivity,[status(thm)],[143, 141])).
% 81.13/81.33 tff(145,plain,
% 81.13/81.33 (((~![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))))))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[144])).
% 81.13/81.33 tff(146,plain,
% 81.13/81.33 (((~![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)))))),
% 81.13/81.33 inference(transitivity,[status(thm)],[145, 140])).
% 81.13/81.33 tff(147,plain,
% 81.13/81.33 ((~![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)))))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(148,plain,
% 81.13/81.33 ((~![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))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[147, 146])).
% 81.13/81.33 tff(149,plain,
% 81.13/81.33 ((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))))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[148, 139, 37])).
% 81.13/81.33 tff(150,plain,
% 81.13/81.33 (~((~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)))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[149, 123])).
% 81.13/81.33 tff(151,plain,
% 81.13/81.33 (((~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))),
% 81.13/81.33 inference(tautology,[status(thm)],[])).
% 81.13/81.33 tff(152,plain,
% 81.13/81.33 (ssList(tptp_fun_V_43(V!46))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[151, 150])).
% 81.13/81.33 tff(153,plain,
% 81.13/81.33 (((~![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))) | (~ssList(tptp_fun_V_43(V!46))) | (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(154,plain,
% 81.13/81.33 ((~![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(155,plain,
% 81.13/81.33 ((~![W: $i] : ((~ssList(W)) | (app(app(nil, U!45), W) = app(nil, app(U!45, W))))) | (~ssList(tptp_fun_V_43(V!46))) | (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[154, 153])).
% 81.13/81.33 tff(156,plain,
% 81.13/81.33 (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[155, 152, 35])).
% 81.13/81.33 tff(157,plain,
% 81.13/81.33 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(158,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[157])).
% 81.13/81.33 tff(159,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(160,plain,
% 81.13/81.33 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(161,plain,
% 81.13/81.33 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[160])).
% 81.13/81.33 tff(162,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 81.13/81.33 tff(163,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[162, 161])).
% 81.13/81.33 tff(164,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[163, 159])).
% 81.13/81.33 tff(165,plain,(
% 81.13/81.33 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(skolemize,[status(sab)],[164])).
% 81.13/81.33 tff(166,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[165, 158])).
% 81.13/81.33 tff(167,plain,
% 81.13/81.33 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(168,plain,
% 81.13/81.33 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(169,plain,
% 81.13/81.33 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[168, 167])).
% 81.13/81.33 tff(170,plain,
% 81.13/81.33 (app(nil, U!45) = U!45),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[169, 166, 31])).
% 81.13/81.33 tff(171,plain,
% 81.13/81.33 (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[170])).
% 81.13/81.33 tff(172,plain,
% 81.13/81.33 (app(U!45, tptp_fun_V_43(V!46)) = app(app(nil, U!45), tptp_fun_V_43(V!46))),
% 81.13/81.33 inference(symmetry,[status(thm)],[171])).
% 81.13/81.33 tff(173,plain,
% 81.13/81.33 (((~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)),
% 81.13/81.33 inference(tautology,[status(thm)],[])).
% 81.13/81.33 tff(174,plain,
% 81.13/81.33 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[173, 150])).
% 81.13/81.33 tff(175,plain,
% 81.13/81.33 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tl(V!46)),
% 81.13/81.33 inference(monotonicity,[status(thm)],[174])).
% 81.13/81.33 tff(176,plain,
% 81.13/81.33 (^[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))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(177,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[176])).
% 81.13/81.33 tff(178,plain,
% 81.13/81.33 (^[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))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(179,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[178])).
% 81.13/81.33 tff(180,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(transitivity,[status(thm)],[179, 177])).
% 81.13/81.33 tff(181,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(182,plain,
% 81.13/81.33 (^[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)))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(183,plain,
% 81.13/81.33 (![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)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[182])).
% 81.13/81.33 tff(184,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax25')).
% 81.13/81.33 tff(185,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[184, 183])).
% 81.13/81.33 tff(186,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[185, 181])).
% 81.13/81.33 tff(187,plain,(
% 81.13/81.33 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 81.13/81.33 inference(skolemize,[status(sab)],[186])).
% 81.13/81.33 tff(188,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[187, 180])).
% 81.13/81.33 tff(189,plain,
% 81.13/81.33 (((~![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))))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(190,plain,
% 81.13/81.33 ((~![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))))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(191,plain,
% 81.13/81.33 ((~![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)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[190, 189])).
% 81.13/81.33 tff(192,plain,
% 81.13/81.33 (![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[191, 188, 152])).
% 81.13/81.33 tff(193,plain,
% 81.13/81.33 (((~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))),
% 81.13/81.33 inference(tautology,[status(thm)],[])).
% 81.13/81.33 tff(194,plain,
% 81.13/81.33 (ssItem(tptp_fun_W_44(V!46))),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[193, 150])).
% 81.13/81.33 tff(195,plain,
% 81.13/81.33 (((~![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)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(196,plain,
% 81.13/81.33 ((~![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)))),
% 81.13/81.33 inference(quant_inst,[status(thm)],[])).
% 81.13/81.33 tff(197,plain,
% 81.13/81.33 ((~![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))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[196, 195])).
% 81.13/81.33 tff(198,plain,
% 81.13/81.33 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)),
% 81.13/81.33 inference(unit_resolution,[status(thm)],[197, 194, 192])).
% 81.13/81.33 tff(199,plain,
% 81.13/81.33 (tptp_fun_V_43(V!46) = tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 81.13/81.33 inference(symmetry,[status(thm)],[198])).
% 81.13/81.33 tff(200,plain,
% 81.13/81.33 (tptp_fun_V_43(V!46) = tl(V!46)),
% 81.13/81.33 inference(transitivity,[status(thm)],[199, 175])).
% 81.13/81.33 tff(201,plain,
% 81.13/81.33 (app(U!45, tptp_fun_V_43(V!46)) = app(U!45, tl(V!46))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[200])).
% 81.13/81.33 tff(202,plain,
% 81.13/81.33 (app(U!45, tl(V!46)) = app(U!45, tptp_fun_V_43(V!46))),
% 81.13/81.33 inference(symmetry,[status(thm)],[201])).
% 81.13/81.33 tff(203,plain,
% 81.13/81.33 (app(U!45, tl(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))),
% 81.13/81.33 inference(transitivity,[status(thm)],[202, 172, 156])).
% 81.13/81.33 tff(204,plain,
% 81.13/81.33 ((V!46 = app(U!45, tl(V!46))) <=> (V!46 = app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.33 inference(monotonicity,[status(thm)],[203])).
% 81.13/81.33 tff(205,plain,
% 81.13/81.33 ((V!46 = app(U!45, tl(V!46))) <=> (app(nil, app(U!45, tptp_fun_V_43(V!46))) = V!46)),
% 81.13/81.33 inference(transitivity,[status(thm)],[204, 1])).
% 81.13/81.33 tff(206,plain,
% 81.13/81.33 ((app(nil, app(U!45, tptp_fun_V_43(V!46))) = V!46) <=> (V!46 = app(U!45, tl(V!46)))),
% 81.13/81.33 inference(symmetry,[status(thm)],[205])).
% 81.13/81.33 tff(207,plain,
% 81.13/81.33 (app(U!45, tptp_fun_V_43(V!46)) = app(nil, app(U!45, tptp_fun_V_43(V!46)))),
% 81.13/81.33 inference(transitivity,[status(thm)],[172, 156])).
% 81.13/81.33 tff(208,plain,
% 81.13/81.33 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(209,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[208])).
% 81.13/81.33 tff(210,plain,
% 81.13/81.33 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(211,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[210])).
% 81.13/81.33 tff(212,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(transitivity,[status(thm)],[211, 209])).
% 81.13/81.33 tff(213,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.33 tff(214,plain,
% 81.13/81.33 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (hd(cons(V, U)) = V)) <=> ((~ssItem(V)) | (hd(cons(V, U)) = V)))), (![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)) <=> ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))))),
% 81.13/81.33 inference(bind,[status(th)],[])).
% 81.13/81.33 tff(215,plain,
% 81.13/81.33 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(quant_intro,[status(thm)],[214])).
% 81.13/81.33 tff(216,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax23')).
% 81.13/81.33 tff(217,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[216, 215])).
% 81.13/81.33 tff(218,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[217, 213])).
% 81.13/81.33 tff(219,plain,(
% 81.13/81.33 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(skolemize,[status(sab)],[218])).
% 81.13/81.33 tff(220,plain,
% 81.13/81.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 81.13/81.33 inference(modus_ponens,[status(thm)],[219, 212])).
% 81.13/81.33 tff(221,plain,
% 81.13/81.33 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 81.13/81.33 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(222,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(223,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[222, 221])).
% 81.13/81.34 tff(224,plain,
% 81.13/81.34 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[223, 220, 152])).
% 81.13/81.34 tff(225,plain,
% 81.13/81.34 (((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(226,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(227,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[226, 225])).
% 81.13/81.34 tff(228,plain,
% 81.13/81.34 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[227, 194, 224])).
% 81.13/81.34 tff(229,plain,
% 81.13/81.34 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = hd(V!46)),
% 81.13/81.34 inference(monotonicity,[status(thm)],[174])).
% 81.13/81.34 tff(230,plain,
% 81.13/81.34 (hd(V!46) = hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 81.13/81.34 inference(symmetry,[status(thm)],[229])).
% 81.13/81.34 tff(231,plain,
% 81.13/81.34 (hd(V!46) = tptp_fun_W_44(V!46)),
% 81.13/81.34 inference(transitivity,[status(thm)],[230, 228])).
% 81.13/81.34 tff(232,plain,
% 81.13/81.34 (cons(hd(V!46), tptp_fun_V_43(V!46)) = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[231])).
% 81.13/81.34 tff(233,plain,
% 81.13/81.34 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(234,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[233])).
% 81.13/81.34 tff(235,plain,
% 81.13/81.34 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(236,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[235])).
% 81.13/81.34 tff(237,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(transitivity,[status(thm)],[236, 234])).
% 81.13/81.34 tff(238,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(239,plain,
% 81.13/81.34 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(240,plain,
% 81.13/81.34 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[239])).
% 81.13/81.34 tff(241,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 81.13/81.34 tff(242,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[241, 240])).
% 81.13/81.34 tff(243,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[242, 238])).
% 81.13/81.34 tff(244,plain,(
% 81.13/81.34 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(skolemize,[status(sab)],[243])).
% 81.13/81.34 tff(245,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[244, 237])).
% 81.13/81.34 tff(246,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(247,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(248,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[247, 246])).
% 81.13/81.34 tff(249,plain,
% 81.13/81.34 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[248, 245, 152])).
% 81.13/81.34 tff(250,plain,
% 81.13/81.34 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(251,plain,
% 81.13/81.34 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[250])).
% 81.13/81.34 tff(252,plain,
% 81.13/81.34 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(253,plain,
% 81.13/81.34 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssItem(hd(U))) <=> ((nil = U) | ssItem(hd(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> (ssList(U) => ((nil = U) | ssItem(hd(U)))))), rewrite((ssList(U) => ((nil = U) | ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(254,plain,
% 81.13/81.34 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[253])).
% 81.13/81.34 tff(255,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax22')).
% 81.13/81.34 tff(256,plain,
% 81.13/81.34 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[255, 254])).
% 81.13/81.34 tff(257,plain,
% 81.13/81.34 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[256, 252])).
% 81.13/81.34 tff(258,plain,(
% 81.13/81.34 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(skolemize,[status(sab)],[257])).
% 81.13/81.34 tff(259,plain,
% 81.13/81.34 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[258, 251])).
% 81.13/81.34 tff(260,plain,
% 81.13/81.34 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(261,plain,
% 81.13/81.34 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(262,plain,
% 81.13/81.34 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46))))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[261])).
% 81.13/81.34 tff(263,plain,
% 81.13/81.34 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46)))),
% 81.13/81.34 inference(transitivity,[status(thm)],[262, 260])).
% 81.13/81.34 tff(264,plain,
% 81.13/81.34 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(265,plain,
% 81.13/81.34 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | (nil = V!46) | ssItem(hd(V!46))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[264, 263])).
% 81.13/81.34 tff(266,plain,
% 81.13/81.34 ((nil = V!46) | ssItem(hd(V!46))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[265, 259, 37])).
% 81.13/81.34 tff(267,plain,
% 81.13/81.34 (ssItem(hd(V!46))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[266, 123])).
% 81.13/81.34 tff(268,plain,
% 81.13/81.34 (((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(269,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(270,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46)))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[269, 268])).
% 81.13/81.34 tff(271,plain,
% 81.13/81.34 (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[270, 267, 249])).
% 81.13/81.34 tff(272,plain,
% 81.13/81.34 (app(cons(hd(V!46), nil), tptp_fun_V_43(V!46)) = cons(hd(V!46), tptp_fun_V_43(V!46))),
% 81.13/81.34 inference(symmetry,[status(thm)],[271])).
% 81.13/81.34 tff(273,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(274,plain,
% 81.13/81.34 (((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(275,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[274])).
% 81.13/81.34 tff(276,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 81.13/81.34 inference(transitivity,[status(thm)],[275, 273])).
% 81.13/81.34 tff(277,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(278,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[277, 276])).
% 81.13/81.34 tff(279,plain,
% 81.13/81.34 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[278, 17, 245])).
% 81.13/81.34 tff(280,plain,
% 81.13/81.34 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(281,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(282,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[281, 280])).
% 81.13/81.34 tff(283,plain,
% 81.13/81.34 (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[282, 279, 267])).
% 81.13/81.34 tff(284,plain,
% 81.13/81.34 (app(cons(hd(V!46), nil), nil) = cons(hd(V!46), nil)),
% 81.13/81.34 inference(symmetry,[status(thm)],[283])).
% 81.13/81.34 tff(285,plain,
% 81.13/81.34 (app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[284])).
% 81.13/81.34 tff(286,plain,
% 81.13/81.34 (app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = V!46),
% 81.13/81.34 inference(transitivity,[status(thm)],[285, 272, 232, 174])).
% 81.13/81.34 tff(287,plain,
% 81.13/81.34 ((app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))) <=> (V!46 = app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[286, 207])).
% 81.13/81.34 tff(288,plain,
% 81.13/81.34 ((app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))) <=> (app(nil, app(U!45, tptp_fun_V_43(V!46))) = V!46)),
% 81.13/81.34 inference(transitivity,[status(thm)],[287, 1])).
% 81.13/81.34 tff(289,plain,
% 81.13/81.34 ((app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))) <=> (V!46 = app(U!45, tl(V!46)))),
% 81.13/81.34 inference(transitivity,[status(thm)],[288, 206])).
% 81.13/81.34 tff(290,plain,
% 81.13/81.34 ((~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))) <=> (~(V!46 = app(U!45, tl(V!46))))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[289])).
% 81.13/81.34 tff(291,plain,
% 81.13/81.34 ((app(cons(hd(V!46), nil), nil) = U!45) <=> (cons(hd(V!46), nil) = U!45)),
% 81.13/81.34 inference(monotonicity,[status(thm)],[284])).
% 81.13/81.34 tff(292,plain,
% 81.13/81.34 ((cons(hd(V!46), nil) = U!45) <=> (app(cons(hd(V!46), nil), nil) = U!45)),
% 81.13/81.34 inference(symmetry,[status(thm)],[291])).
% 81.13/81.34 tff(293,plain,
% 81.13/81.34 ((~(cons(hd(V!46), nil) = U!45)) <=> (~(app(cons(hd(V!46), nil), nil) = U!45))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[292])).
% 81.13/81.34 tff(294,plain,
% 81.13/81.34 (^[U: $i] : refl(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(295,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[294])).
% 81.13/81.34 tff(296,plain,
% 81.13/81.34 (^[U: $i] : rewrite(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(297,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[296])).
% 81.13/81.34 tff(298,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(transitivity,[status(thm)],[297, 295])).
% 81.13/81.34 tff(299,plain,
% 81.13/81.34 (^[U: $i] : rewrite(((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(300,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[299])).
% 81.13/81.34 tff(301,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(302,plain,
% 81.13/81.34 (^[U: $i] : trans(monotonicity(rewrite((singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))) <=> (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))))), rewrite((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(303,plain,
% 81.13/81.34 (![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[302])).
% 81.13/81.34 tff(304,axiom,(![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax4')).
% 81.13/81.34 tff(305,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[304, 303])).
% 81.13/81.34 tff(306,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[305, 301])).
% 81.13/81.34 tff(307,plain,(
% 81.13/81.34 ![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U))))))),
% 81.13/81.34 inference(skolemize,[status(sab)],[306])).
% 81.13/81.34 tff(308,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[307, 300])).
% 81.13/81.34 tff(309,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[308, 298])).
% 81.13/81.34 tff(310,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(311,plain,
% 81.13/81.34 (((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))))))) <=> ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(312,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[311])).
% 81.13/81.34 tff(313,plain,
% 81.13/81.34 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 81.13/81.34 inference(transitivity,[status(thm)],[312, 310])).
% 81.13/81.34 tff(314,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(315,plain,
% 81.13/81.34 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[314, 313])).
% 81.13/81.34 tff(316,plain,
% 81.13/81.34 (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[315, 309, 31])).
% 81.13/81.34 tff(317,plain,
% 81.13/81.34 (((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))) | (singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))),
% 81.13/81.34 inference(tautology,[status(thm)],[])).
% 81.13/81.34 tff(318,plain,
% 81.13/81.34 (singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[317, 316])).
% 81.13/81.34 tff(319,plain,
% 81.13/81.34 (~singletonP(U!45)),
% 81.13/81.34 inference(or_elim,[status(thm)],[36])).
% 81.13/81.34 tff(320,plain,
% 81.13/81.34 ((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 81.13/81.34 inference(tautology,[status(thm)],[])).
% 81.13/81.34 tff(321,plain,
% 81.13/81.34 ((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[320, 319])).
% 81.13/81.34 tff(322,plain,
% 81.13/81.34 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[321, 318])).
% 81.13/81.34 tff(323,plain,
% 81.13/81.34 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | ((~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | (~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = U!45)))),
% 81.13/81.34 inference(rewrite,[status(thm)],[])).
% 81.13/81.34 tff(324,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | ((~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = U!45)))),
% 81.13/81.34 inference(quant_inst,[status(thm)],[])).
% 81.13/81.34 tff(325,plain,
% 81.13/81.34 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | (~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = U!45))),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[324, 323])).
% 81.13/81.34 tff(326,plain,
% 81.13/81.34 (~(cons(hd(V!46), nil) = U!45)),
% 81.13/81.34 inference(unit_resolution,[status(thm)],[325, 322, 267])).
% 81.13/81.34 tff(327,plain,
% 81.13/81.34 (~(app(cons(hd(V!46), nil), nil) = U!45)),
% 81.13/81.34 inference(modus_ponens,[status(thm)],[326, 293])).
% 81.13/81.34 tff(328,plain,
% 81.13/81.34 (ssList(app(cons(hd(V!46), nil), nil)) <=> ssList(cons(hd(V!46), nil))),
% 81.13/81.34 inference(monotonicity,[status(thm)],[284])).
% 81.13/81.34 tff(329,plain,
% 81.13/81.34 (ssList(cons(hd(V!46), nil)) <=> ssList(app(cons(hd(V!46), nil), nil))),
% 81.13/81.34 inference(symmetry,[status(thm)],[328])).
% 81.13/81.34 tff(330,plain,
% 81.13/81.34 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(331,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[330])).
% 81.13/81.34 tff(332,plain,
% 81.13/81.34 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 81.13/81.34 inference(bind,[status(th)],[])).
% 81.13/81.34 tff(333,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.34 inference(quant_intro,[status(thm)],[332])).
% 81.13/81.34 tff(334,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.34 inference(transitivity,[status(thm)],[333, 331])).
% 81.13/81.34 tff(335,plain,
% 81.13/81.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(336,plain,
% 81.13/81.35 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(337,plain,
% 81.13/81.35 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[336])).
% 81.13/81.35 tff(338,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 81.13/81.35 tff(339,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[338, 337])).
% 81.13/81.35 tff(340,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[339, 335])).
% 81.13/81.35 tff(341,plain,(
% 81.13/81.35 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(skolemize,[status(sab)],[340])).
% 81.13/81.35 tff(342,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[341, 334])).
% 81.13/81.35 tff(343,plain,
% 81.13/81.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(344,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(345,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[344, 343])).
% 81.13/81.35 tff(346,plain,
% 81.13/81.35 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[345, 342, 17])).
% 81.13/81.35 tff(347,plain,
% 81.13/81.35 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(348,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(349,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[348, 347])).
% 81.13/81.35 tff(350,plain,
% 81.13/81.35 (ssList(cons(hd(V!46), nil))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[349, 346, 267])).
% 81.13/81.35 tff(351,plain,
% 81.13/81.35 (ssList(app(cons(hd(V!46), nil), nil))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[350, 329])).
% 81.13/81.35 tff(352,plain,
% 81.13/81.35 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(353,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[352])).
% 81.13/81.35 tff(354,plain,
% 81.13/81.35 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(355,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[354])).
% 81.13/81.35 tff(356,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(transitivity,[status(thm)],[355, 353])).
% 81.13/81.35 tff(357,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(358,plain,
% 81.13/81.35 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(W, V) = app(U, V)) => (W = U)) <=> ((~(app(W, V) = app(U, V))) | (W = U))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> (ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))))), rewrite((ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), (![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(359,plain,
% 81.13/81.35 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[358])).
% 81.13/81.35 tff(360,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax79')).
% 81.13/81.35 tff(361,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[360, 359])).
% 81.13/81.35 tff(362,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[361, 357])).
% 81.13/81.35 tff(363,plain,(
% 81.13/81.35 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(skolemize,[status(sab)],[362])).
% 81.13/81.35 tff(364,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[363, 356])).
% 81.13/81.35 tff(365,plain,
% 81.13/81.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V))))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(366,plain,
% 81.13/81.35 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(W, V) = app(U!45, V)))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V))))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(367,plain,
% 81.13/81.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(W, V) = app(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))))),
% 81.13/81.35 inference(monotonicity,[status(thm)],[366])).
% 81.13/81.35 tff(368,plain,
% 81.13/81.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(W, V) = app(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V))))))),
% 81.13/81.35 inference(transitivity,[status(thm)],[367, 365])).
% 81.13/81.35 tff(369,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(W, V) = app(U!45, V))))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(370,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[369, 368])).
% 81.13/81.35 tff(371,plain,
% 81.13/81.35 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[370, 364, 31])).
% 81.13/81.35 tff(372,plain,
% 81.13/81.35 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))) | (~ssList(tptp_fun_V_43(V!46))) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(373,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(374,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, V) = app(U!45, V)))))) | (~ssList(tptp_fun_V_43(V!46))) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[373, 372])).
% 81.13/81.35 tff(375,plain,
% 81.13/81.35 (![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[374, 371, 152])).
% 81.13/81.35 tff(376,plain,
% 81.13/81.35 (((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))) | ((~ssList(app(cons(hd(V!46), nil), nil))) | (app(cons(hd(V!46), nil), nil) = U!45) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))) | (~ssList(app(cons(hd(V!46), nil), nil))) | (app(cons(hd(V!46), nil), nil) = U!45) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(377,plain,
% 81.13/81.35 ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))) | ((~ssList(app(cons(hd(V!46), nil), nil))) | (app(cons(hd(V!46), nil), nil) = U!45) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(378,plain,
% 81.13/81.35 ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(W, tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))))) | (~ssList(app(cons(hd(V!46), nil), nil))) | (app(cons(hd(V!46), nil), nil) = U!45) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[377, 376])).
% 81.13/81.35 tff(379,plain,
% 81.13/81.35 (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46)))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[378, 375, 351, 327])).
% 81.13/81.35 tff(380,plain,
% 81.13/81.35 (~(V!46 = app(U!45, tl(V!46)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[379, 290])).
% 81.13/81.35 tff(381,plain,
% 81.13/81.35 (^[U: $i] : refl(((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(382,plain,
% 81.13/81.35 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[381])).
% 81.13/81.35 tff(383,plain,
% 81.13/81.35 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(384,plain,
% 81.13/81.35 (^[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)))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(385,plain,
% 81.13/81.35 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[384])).
% 81.13/81.35 tff(386,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax24')).
% 81.13/81.35 tff(387,plain,
% 81.13/81.35 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[386, 385])).
% 81.13/81.35 tff(388,plain,
% 81.13/81.35 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[387, 383])).
% 81.13/81.35 tff(389,plain,(
% 81.13/81.35 ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(skolemize,[status(sab)],[388])).
% 81.13/81.35 tff(390,plain,
% 81.13/81.35 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[389, 382])).
% 81.13/81.35 tff(391,plain,
% 81.13/81.35 (((~![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))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(392,plain,
% 81.13/81.35 (((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(393,plain,
% 81.13/81.35 (((~![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)))),
% 81.13/81.35 inference(monotonicity,[status(thm)],[392])).
% 81.13/81.35 tff(394,plain,
% 81.13/81.35 (((~![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))),
% 81.13/81.35 inference(transitivity,[status(thm)],[393, 391])).
% 81.13/81.35 tff(395,plain,
% 81.13/81.35 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(396,plain,
% 81.13/81.35 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssList(tl(V!46)) | (nil = V!46)),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[395, 394])).
% 81.13/81.35 tff(397,plain,
% 81.13/81.35 (ssList(tl(V!46))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[396, 390, 37, 123])).
% 81.13/81.35 tff(398,plain,
% 81.13/81.35 (((~![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)))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(399,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(400,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[399, 398])).
% 81.13/81.35 tff(401,plain,
% 81.13/81.35 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[400, 64, 17])).
% 81.13/81.35 tff(402,plain,
% 81.13/81.35 (((~![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))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(403,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(404,plain,
% 81.13/81.35 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[403, 402])).
% 81.13/81.35 tff(405,plain,
% 81.13/81.35 (~((nil = V!46) <=> neq(nil, V!46))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[404, 37, 401])).
% 81.13/81.35 tff(406,plain,
% 81.13/81.35 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 81.13/81.35 inference(tautology,[status(thm)],[])).
% 81.13/81.35 tff(407,plain,
% 81.13/81.35 (neq(nil, V!46)),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[406, 123, 405])).
% 81.13/81.35 tff(408,plain,
% 81.13/81.35 (ssList(app(U!45, tl(V!46))) <=> ssList(app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.35 inference(monotonicity,[status(thm)],[203])).
% 81.13/81.35 tff(409,plain,
% 81.13/81.35 (ssList(app(nil, app(U!45, tptp_fun_V_43(V!46)))) <=> ssList(app(U!45, tl(V!46)))),
% 81.13/81.35 inference(symmetry,[status(thm)],[408])).
% 81.13/81.35 tff(410,plain,
% 81.13/81.35 (ssList(app(U!45, tptp_fun_V_43(V!46))) <=> ssList(app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.13/81.35 inference(monotonicity,[status(thm)],[207])).
% 81.13/81.35 tff(411,plain,
% 81.13/81.35 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(412,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[411])).
% 81.13/81.35 tff(413,plain,
% 81.13/81.35 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(414,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[413])).
% 81.13/81.35 tff(415,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(transitivity,[status(thm)],[414, 412])).
% 81.13/81.35 tff(416,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(417,plain,
% 81.13/81.35 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ssList(app(U, V))) <=> ((~ssList(V)) | ssList(app(U, V))))), (![V: $i] : (ssList(V) => ssList(app(U, V))) <=> ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))))),
% 81.13/81.35 inference(bind,[status(th)],[])).
% 81.13/81.35 tff(418,plain,
% 81.13/81.35 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(quant_intro,[status(thm)],[417])).
% 81.13/81.35 tff(419,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax26')).
% 81.13/81.35 tff(420,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[419, 418])).
% 81.13/81.35 tff(421,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[420, 416])).
% 81.13/81.35 tff(422,plain,(
% 81.13/81.35 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(skolemize,[status(sab)],[421])).
% 81.13/81.35 tff(423,plain,
% 81.13/81.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[422, 415])).
% 81.13/81.35 tff(424,plain,
% 81.13/81.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ssList(app(U!45, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ssList(app(U!45, V))))),
% 81.13/81.35 inference(rewrite,[status(thm)],[])).
% 81.13/81.35 tff(425,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ssList(app(U!45, V))))),
% 81.13/81.35 inference(quant_inst,[status(thm)],[])).
% 81.13/81.35 tff(426,plain,
% 81.13/81.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))),
% 81.13/81.35 inference(modus_ponens,[status(thm)],[425, 424])).
% 81.13/81.35 tff(427,plain,
% 81.13/81.35 (![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))),
% 81.13/81.35 inference(unit_resolution,[status(thm)],[426, 423, 31])).
% 81.35/81.57 tff(428,plain,
% 81.35/81.57 (((~![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ssList(app(U!45, tptp_fun_V_43(V!46))))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))) | (~ssList(tptp_fun_V_43(V!46))) | ssList(app(U!45, tptp_fun_V_43(V!46))))),
% 81.35/81.57 inference(rewrite,[status(thm)],[])).
% 81.35/81.57 tff(429,plain,
% 81.35/81.57 ((~![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ssList(app(U!45, tptp_fun_V_43(V!46))))),
% 81.35/81.57 inference(quant_inst,[status(thm)],[])).
% 81.35/81.57 tff(430,plain,
% 81.35/81.57 ((~![V: $i] : ((~ssList(V)) | ssList(app(U!45, V)))) | (~ssList(tptp_fun_V_43(V!46))) | ssList(app(U!45, tptp_fun_V_43(V!46)))),
% 81.35/81.57 inference(modus_ponens,[status(thm)],[429, 428])).
% 81.35/81.57 tff(431,plain,
% 81.35/81.57 (ssList(app(U!45, tptp_fun_V_43(V!46)))),
% 81.35/81.57 inference(unit_resolution,[status(thm)],[430, 427, 152])).
% 81.35/81.57 tff(432,plain,
% 81.35/81.57 (ssList(app(nil, app(U!45, tptp_fun_V_43(V!46))))),
% 81.35/81.57 inference(modus_ponens,[status(thm)],[431, 410])).
% 81.35/81.57 tff(433,plain,
% 81.35/81.57 (ssList(app(U!45, tl(V!46)))),
% 81.35/81.57 inference(modus_ponens,[status(thm)],[432, 409])).
% 81.35/81.57 tff(434,plain,
% 81.35/81.57 ((~(~((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))))),
% 81.35/81.57 inference(rewrite,[status(thm)],[])).
% 81.35/81.57 tff(435,plain,
% 81.35/81.57 ((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)))))),
% 81.35/81.57 inference(rewrite,[status(thm)],[])).
% 81.35/81.57 tff(436,plain,
% 81.35/81.57 ((~(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))))))),
% 81.35/81.57 inference(monotonicity,[status(thm)],[435])).
% 81.35/81.57 tff(437,plain,
% 81.35/81.57 ((~(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))))),
% 81.35/81.57 inference(transitivity,[status(thm)],[436, 434])).
% 81.35/81.57 tff(438,plain,
% 81.35/81.57 (~(ssList(app(U!45, tl(V!46))) & (~(V!46 = app(U!45, tl(V!46)))) & neq(nil, V!46) & ssList(tl(V!46)))),
% 81.35/81.57 inference(or_elim,[status(thm)],[36])).
% 81.35/81.57 tff(439,plain,
% 81.35/81.57 ((V!46 = app(U!45, tl(V!46))) | (~ssList(app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))),
% 81.35/81.57 inference(modus_ponens,[status(thm)],[438, 437])).
% 81.35/81.57 tff(440,plain,
% 81.35/81.57 (V!46 = app(U!45, tl(V!46))),
% 81.35/81.57 inference(unit_resolution,[status(thm)],[439, 433, 407, 397])).
% 81.35/81.57 tff(441,plain,
% 81.35/81.57 ($false),
% 81.35/81.57 inference(unit_resolution,[status(thm)],[440, 380])).
% 81.35/81.57 % SZS output end Proof
% 81.35/81.57 % E exiting
%------------------------------------------------------------------------------