%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC355+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:59 AM UTC 2025
% Result : Theorem 3.96s 4.14s
% Output : Proof 4.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWC355+1 : TPTP v9.0.0. Released v2.4.0.
% 0.05/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n007.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 20 09:08:50 EDT 2025
% 0.10/0.30 % CPUTime :
% 3.96/4.14 % SZS status Theorem
% 3.96/4.14 % SZS output start Proof
% 3.96/4.14 tff(tptp_fun_V_46_type, type, (
% 3.96/4.14 tptp_fun_V_46: $i)).
% 3.96/4.14 tff(app_type, type, (
% 3.96/4.14 app: ( $i * $i ) > $i)).
% 3.96/4.14 tff(nil_type, type, (
% 3.96/4.14 nil: $i)).
% 3.96/4.14 tff(cons_type, type, (
% 3.96/4.14 cons: ( $i * $i ) > $i)).
% 3.96/4.14 tff(tptp_fun_Y_47_type, type, (
% 3.96/4.14 tptp_fun_Y_47: $i)).
% 3.96/4.14 tff(tptp_fun_U_45_type, type, (
% 3.96/4.14 tptp_fun_U_45: $i)).
% 3.96/4.14 tff(ssItem_type, type, (
% 3.96/4.14 ssItem: $i > $o)).
% 3.96/4.14 tff(neq_type, type, (
% 3.96/4.14 neq: ( $i * $i ) > $o)).
% 3.96/4.14 tff(ssList_type, type, (
% 3.96/4.14 ssList: $i > $o)).
% 3.96/4.14 tff(segmentP_type, type, (
% 3.96/4.14 segmentP: ( $i * $i ) > $o)).
% 3.96/4.14 tff(tptp_fun_X_8_type, type, (
% 3.96/4.14 tptp_fun_X_8: ( $i * $i ) > $i)).
% 3.96/4.14 tff(tptp_fun_W_7_type, type, (
% 3.96/4.14 tptp_fun_W_7: ( $i * $i ) > $i)).
% 3.96/4.14 tff(1,plain,
% 3.96/4.14 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & ssList(V!46) & (~((~ssItem(Y!47)) | (~(app(U!45, cons(Y!47, nil)) = V!46)))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & (~segmentP(V!46, U!45)) & ssList(V!46) & (~((~ssItem(Y!47)) | (~(app(U!45, cons(Y!47, nil)) = V!46)))) & neq(V!46, nil))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(2,plain,
% 3.96/4.14 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil)))))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(3,plain,
% 3.96/4.14 ((~![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] : (ssItem(Y) => (~(app(W, cons(Y, nil)) = X)))) | segmentP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil)))))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ![Y: $i] : (ssItem(Y) => (~(app(W, cons(Y, nil)) = X)))) | segmentP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 3.96/4.14 tff(5,plain,
% 3.96/4.14 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.96/4.14 tff(6,plain,
% 3.96/4.14 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[5, 2])).
% 3.96/4.14 tff(7,plain,
% 3.96/4.14 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.96/4.14 tff(8,plain,
% 3.96/4.14 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | ![Y: $i] : ((~ssItem(Y)) | (~(app(U, cons(Y, nil)) = V))) | (~ssList(U)) | (~neq(V, nil))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[7, 2])).
% 3.96/4.14 tff(9,plain,
% 3.96/4.14 (ssList(U!45) & (~segmentP(V!46, U!45)) & ssList(V!46) & (~((~ssItem(Y!47)) | (~(app(U!45, cons(Y!47, nil)) = V!46)))) & neq(V!46, nil)),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[8, 1])).
% 3.96/4.14 tff(10,plain,
% 3.96/4.14 (~((~ssItem(Y!47)) | (~(app(U!45, cons(Y!47, nil)) = V!46)))),
% 3.96/4.14 inference(and_elim,[status(thm)],[9])).
% 3.96/4.14 tff(11,plain,
% 3.96/4.14 (app(U!45, cons(Y!47, nil)) = V!46),
% 3.96/4.14 inference(or_elim,[status(thm)],[10])).
% 3.96/4.14 tff(12,plain,
% 3.96/4.14 (^[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)))))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(13,plain,
% 3.96/4.14 (![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))))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[12])).
% 3.96/4.14 tff(14,plain,
% 3.96/4.14 (^[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)))))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(15,plain,
% 3.96/4.14 (![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))))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[14])).
% 3.96/4.14 tff(16,plain,
% 3.96/4.14 (![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))))),
% 3.96/4.14 inference(transitivity,[status(thm)],[15, 13])).
% 3.96/4.14 tff(17,plain,
% 3.96/4.14 (![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))))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(18,plain,
% 3.96/4.14 (^[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))))))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(19,plain,
% 3.96/4.14 (![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))))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[18])).
% 3.96/4.14 tff(20,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')).
% 3.96/4.14 tff(21,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[20, 19])).
% 3.96/4.14 tff(22,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[21, 17])).
% 3.96/4.14 tff(23,plain,(
% 3.96/4.14 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.96/4.14 inference(skolemize,[status(sab)],[22])).
% 3.96/4.14 tff(24,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[23, 16])).
% 3.96/4.14 tff(25,plain,
% 3.96/4.14 (ssList(nil) <=> ssList(nil)),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(26,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.96/4.14 tff(27,plain,
% 3.96/4.14 (ssList(nil)),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.96/4.14 tff(28,plain,
% 3.96/4.14 (((~![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))))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(29,plain,
% 3.96/4.14 (((~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))))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(30,plain,
% 3.96/4.14 (((~![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)))))),
% 3.96/4.14 inference(monotonicity,[status(thm)],[29])).
% 3.96/4.14 tff(31,plain,
% 3.96/4.14 (((~![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))))),
% 3.96/4.14 inference(transitivity,[status(thm)],[30, 28])).
% 3.96/4.14 tff(32,plain,
% 3.96/4.14 ((~![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))))),
% 3.96/4.14 inference(quant_inst,[status(thm)],[])).
% 3.96/4.14 tff(33,plain,
% 3.96/4.14 ((~![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)))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.96/4.14 tff(34,plain,
% 3.96/4.14 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 3.96/4.14 inference(unit_resolution,[status(thm)],[33, 27, 24])).
% 3.96/4.14 tff(35,plain,
% 3.96/4.14 (ssItem(Y!47)),
% 3.96/4.14 inference(or_elim,[status(thm)],[10])).
% 3.96/4.14 tff(36,plain,
% 3.96/4.14 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(Y!47)) | (cons(Y!47, nil) = app(cons(Y!47, nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(Y!47)) | (cons(Y!47, nil) = app(cons(Y!47, nil), nil)))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(37,plain,
% 3.96/4.14 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(Y!47)) | (cons(Y!47, nil) = app(cons(Y!47, nil), nil)))),
% 3.96/4.14 inference(quant_inst,[status(thm)],[])).
% 3.96/4.14 tff(38,plain,
% 3.96/4.14 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(Y!47)) | (cons(Y!47, nil) = app(cons(Y!47, nil), nil))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.96/4.14 tff(39,plain,
% 3.96/4.14 (cons(Y!47, nil) = app(cons(Y!47, nil), nil)),
% 3.96/4.14 inference(unit_resolution,[status(thm)],[38, 35, 34])).
% 3.96/4.14 tff(40,plain,
% 3.96/4.14 (app(cons(Y!47, nil), nil) = cons(Y!47, nil)),
% 3.96/4.14 inference(symmetry,[status(thm)],[39])).
% 3.96/4.14 tff(41,plain,
% 3.96/4.14 (ssList(U!45)),
% 3.96/4.14 inference(and_elim,[status(thm)],[9])).
% 3.96/4.14 tff(42,plain,
% 3.96/4.14 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(43,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[42])).
% 3.96/4.14 tff(44,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(45,plain,
% 3.96/4.14 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(46,plain,
% 3.96/4.14 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[45])).
% 3.96/4.14 tff(47,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 3.96/4.14 tff(48,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[47, 46])).
% 3.96/4.14 tff(49,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[48, 44])).
% 3.96/4.14 tff(50,plain,(
% 3.96/4.14 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(skolemize,[status(sab)],[49])).
% 3.96/4.14 tff(51,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[50, 43])).
% 3.96/4.14 tff(52,plain,
% 3.96/4.14 (((~![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))),
% 3.96/4.14 inference(rewrite,[status(thm)],[])).
% 3.96/4.14 tff(53,plain,
% 3.96/4.14 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 3.96/4.14 inference(quant_inst,[status(thm)],[])).
% 3.96/4.14 tff(54,plain,
% 3.96/4.14 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 3.96/4.14 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.96/4.14 tff(55,plain,
% 3.96/4.14 (app(nil, U!45) = U!45),
% 3.96/4.14 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 3.96/4.14 tff(56,plain,
% 3.96/4.14 (app(app(nil, U!45), app(cons(Y!47, nil), nil)) = app(U!45, cons(Y!47, nil))),
% 3.96/4.14 inference(monotonicity,[status(thm)],[55, 40])).
% 3.96/4.14 tff(57,plain,
% 3.96/4.14 (app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46),
% 3.96/4.14 inference(transitivity,[status(thm)],[56, 11])).
% 3.96/4.14 tff(58,plain,
% 3.96/4.14 (ssList(V!46)),
% 3.96/4.14 inference(and_elim,[status(thm)],[9])).
% 3.96/4.14 tff(59,plain,
% 3.96/4.14 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(60,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[59])).
% 3.96/4.14 tff(61,plain,
% 3.96/4.14 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.96/4.14 inference(bind,[status(th)],[])).
% 3.96/4.14 tff(62,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.14 inference(quant_intro,[status(thm)],[61])).
% 3.96/4.14 tff(63,plain,
% 3.96/4.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.15 inference(transitivity,[status(thm)],[62, 60])).
% 3.96/4.15 tff(64,plain,
% 3.96/4.15 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(65,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[64])).
% 3.96/4.15 tff(66,plain,
% 3.96/4.15 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(67,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[66])).
% 3.96/4.15 tff(68,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.96/4.15 inference(rewrite,[status(thm)],[])).
% 3.96/4.15 tff(69,plain,
% 3.96/4.15 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(70,plain,
% 3.96/4.15 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[69])).
% 3.96/4.15 tff(71,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 3.96/4.15 tff(72,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.96/4.15 tff(73,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[72, 68])).
% 3.96/4.15 tff(74,plain,(
% 3.96/4.15 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.96/4.15 inference(skolemize,[status(sab)],[73])).
% 3.96/4.15 tff(75,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[74, 67])).
% 3.96/4.15 tff(76,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[75, 65])).
% 3.96/4.15 tff(77,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[76, 63])).
% 3.96/4.15 tff(78,plain,
% 3.96/4.15 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 3.96/4.15 inference(rewrite,[status(thm)],[])).
% 3.96/4.15 tff(79,plain,
% 3.96/4.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 3.96/4.15 inference(quant_inst,[status(thm)],[])).
% 3.96/4.15 tff(80,plain,
% 3.96/4.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[79, 78])).
% 3.96/4.15 tff(81,plain,
% 3.96/4.15 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[80, 77, 58])).
% 3.96/4.15 tff(82,plain,
% 3.96/4.15 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 3.96/4.15 inference(rewrite,[status(thm)],[])).
% 3.96/4.15 tff(83,plain,
% 3.96/4.15 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 3.96/4.15 inference(quant_inst,[status(thm)],[])).
% 3.96/4.15 tff(84,plain,
% 3.96/4.15 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[83, 82])).
% 3.96/4.15 tff(85,plain,
% 3.96/4.15 (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[84, 41, 81])).
% 3.96/4.15 tff(86,plain,
% 3.96/4.15 (((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))) | (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))),
% 3.96/4.15 inference(tautology,[status(thm)],[])).
% 3.96/4.15 tff(87,plain,
% 3.96/4.15 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[86, 85])).
% 3.96/4.15 tff(88,plain,
% 3.96/4.15 (~segmentP(V!46, U!45)),
% 3.96/4.15 inference(and_elim,[status(thm)],[9])).
% 3.96/4.15 tff(89,plain,
% 3.96/4.15 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.96/4.15 inference(tautology,[status(thm)],[])).
% 3.96/4.15 tff(90,plain,
% 3.96/4.15 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[89, 88])).
% 3.96/4.15 tff(91,plain,
% 3.96/4.15 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[90, 87])).
% 3.96/4.15 tff(92,plain,
% 3.96/4.15 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 3.96/4.15 inference(rewrite,[status(thm)],[])).
% 3.96/4.15 tff(93,plain,
% 3.96/4.15 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 3.96/4.15 inference(quant_inst,[status(thm)],[])).
% 3.96/4.15 tff(94,plain,
% 3.96/4.15 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[93, 92])).
% 3.96/4.15 tff(95,plain,
% 3.96/4.15 (![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 3.96/4.15 inference(unit_resolution,[status(thm)],[94, 27, 91])).
% 3.96/4.15 tff(96,plain,
% 3.96/4.15 (ssList(app(cons(Y!47, nil), nil)) <=> ssList(cons(Y!47, nil))),
% 3.96/4.15 inference(monotonicity,[status(thm)],[40])).
% 3.96/4.15 tff(97,plain,
% 3.96/4.15 (ssList(cons(Y!47, nil)) <=> ssList(app(cons(Y!47, nil), nil))),
% 3.96/4.15 inference(symmetry,[status(thm)],[96])).
% 3.96/4.15 tff(98,plain,
% 3.96/4.15 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(99,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[98])).
% 3.96/4.15 tff(100,plain,
% 3.96/4.15 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(101,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[100])).
% 3.96/4.15 tff(102,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(transitivity,[status(thm)],[101, 99])).
% 3.96/4.15 tff(103,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(rewrite,[status(thm)],[])).
% 3.96/4.15 tff(104,plain,
% 3.96/4.15 (^[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))))))),
% 3.96/4.15 inference(bind,[status(th)],[])).
% 3.96/4.15 tff(105,plain,
% 3.96/4.15 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(quant_intro,[status(thm)],[104])).
% 3.96/4.15 tff(106,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 3.96/4.15 tff(107,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[106, 105])).
% 3.96/4.15 tff(108,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(modus_ponens,[status(thm)],[107, 103])).
% 3.96/4.15 tff(109,plain,(
% 3.96/4.15 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.96/4.15 inference(skolemize,[status(sab)],[108])).
% 3.96/4.15 tff(110,plain,
% 3.96/4.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 4.00/4.17 inference(modus_ponens,[status(thm)],[109, 102])).
% 4.00/4.17 tff(111,plain,
% 4.00/4.17 (((~![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))))),
% 4.00/4.17 inference(rewrite,[status(thm)],[])).
% 4.00/4.17 tff(112,plain,
% 4.00/4.17 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 4.00/4.17 inference(quant_inst,[status(thm)],[])).
% 4.00/4.17 tff(113,plain,
% 4.00/4.17 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 4.00/4.17 inference(modus_ponens,[status(thm)],[112, 111])).
% 4.00/4.17 tff(114,plain,
% 4.00/4.17 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 4.00/4.17 inference(unit_resolution,[status(thm)],[113, 110, 27])).
% 4.00/4.17 tff(115,plain,
% 4.00/4.17 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(Y!47)) | ssList(cons(Y!47, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(Y!47)) | ssList(cons(Y!47, nil)))),
% 4.00/4.17 inference(rewrite,[status(thm)],[])).
% 4.00/4.17 tff(116,plain,
% 4.00/4.17 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(Y!47)) | ssList(cons(Y!47, nil)))),
% 4.00/4.17 inference(quant_inst,[status(thm)],[])).
% 4.00/4.17 tff(117,plain,
% 4.00/4.17 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(Y!47)) | ssList(cons(Y!47, nil))),
% 4.00/4.17 inference(modus_ponens,[status(thm)],[116, 115])).
% 4.00/4.17 tff(118,plain,
% 4.00/4.17 (ssList(cons(Y!47, nil))),
% 4.00/4.17 inference(unit_resolution,[status(thm)],[117, 35, 114])).
% 4.00/4.17 tff(119,plain,
% 4.00/4.17 (ssList(app(cons(Y!47, nil), nil))),
% 4.00/4.17 inference(modus_ponens,[status(thm)],[118, 97])).
% 4.00/4.17 tff(120,plain,
% 4.00/4.17 (((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(app(cons(Y!47, nil), nil))) | (~(app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(app(cons(Y!47, nil), nil))) | (~(app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46)))),
% 4.00/4.17 inference(rewrite,[status(thm)],[])).
% 4.00/4.17 tff(121,plain,
% 4.00/4.17 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(app(cons(Y!47, nil), nil))) | (~(app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46)))),
% 4.00/4.17 inference(quant_inst,[status(thm)],[])).
% 4.00/4.17 tff(122,plain,
% 4.00/4.17 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(app(cons(Y!47, nil), nil))) | (~(app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46))),
% 4.00/4.17 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.00/4.17 tff(123,plain,
% 4.00/4.17 (~(app(app(nil, U!45), app(cons(Y!47, nil), nil)) = V!46)),
% 4.00/4.17 inference(unit_resolution,[status(thm)],[122, 119, 95])).
% 4.00/4.17 tff(124,plain,
% 4.00/4.17 ($false),
% 4.00/4.17 inference(unit_resolution,[status(thm)],[123, 57])).
% 4.00/4.17 % SZS output end Proof
% 4.00/4.17 % E exiting
%------------------------------------------------------------------------------