%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC182+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 05:30:26 AM UTC 2025
% Result : Theorem 7.84s 8.01s
% Output : Proof 7.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC182+1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.12 % 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 08:34:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 7.84/8.01 % SZS status Theorem
% 7.84/8.01 % SZS output start Proof
% 7.84/8.01 tff(nil_type, type, (
% 7.84/8.01 nil: $i)).
% 7.84/8.01 tff(app_type, type, (
% 7.84/8.01 app: ( $i * $i ) > $i)).
% 7.84/8.01 tff(tptp_fun_X1_49_type, type, (
% 7.84/8.01 tptp_fun_X1_49: $i)).
% 7.84/8.01 tff(cons_type, type, (
% 7.84/8.01 cons: ( $i * $i ) > $i)).
% 7.84/8.01 tff(tptp_fun_Y_47_type, type, (
% 7.84/8.01 tptp_fun_Y_47: $i)).
% 7.84/8.01 tff(tptp_fun_Z_48_type, type, (
% 7.84/8.01 tptp_fun_Z_48: $i)).
% 7.84/8.01 tff(tptp_fun_U_45_type, type, (
% 7.84/8.01 tptp_fun_U_45: $i)).
% 7.84/8.01 tff(ssList_type, type, (
% 7.84/8.01 ssList: $i > $o)).
% 7.84/8.01 tff(memberP_type, type, (
% 7.84/8.01 memberP: ( $i * $i ) > $o)).
% 7.84/8.01 tff(ssItem_type, type, (
% 7.84/8.01 ssItem: $i > $o)).
% 7.84/8.01 tff(tptp_fun_V_46_type, type, (
% 7.84/8.01 tptp_fun_V_46: $i)).
% 7.84/8.01 tff(frontsegP_type, type, (
% 7.84/8.01 frontsegP: ( $i * $i ) > $o)).
% 7.84/8.01 tff(tptp_fun_W_5_type, type, (
% 7.84/8.01 tptp_fun_W_5: ( $i * $i ) > $i)).
% 7.84/8.01 tff(1,plain,
% 7.84/8.01 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))) <=> (ssList(U!45) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.01 inference(rewrite,[status(thm)],[])).
% 7.84/8.01 tff(2,plain,
% 7.84/8.01 ((ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))) <=> (ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.01 inference(rewrite,[status(thm)],[])).
% 7.84/8.01 tff(3,plain,
% 7.84/8.01 ((ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))) <=> (ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.01 inference(rewrite,[status(thm)],[])).
% 7.84/8.01 tff(4,plain,
% 7.84/8.01 ((~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))) <=> (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))),
% 7.84/8.01 inference(rewrite,[status(thm)],[])).
% 7.84/8.01 tff(5,plain,
% 7.84/8.01 ((ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))) <=> (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.01 inference(monotonicity,[status(thm)],[4])).
% 7.84/8.01 tff(6,plain,
% 7.84/8.01 ((ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))) <=> (ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))))),
% 7.84/8.01 inference(monotonicity,[status(thm)],[5])).
% 7.84/8.01 tff(7,plain,
% 7.84/8.01 ((ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))) <=> (ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.01 inference(transitivity,[status(thm)],[6, 3])).
% 7.84/8.01 tff(8,plain,
% 7.84/8.01 ((ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))))) <=> (ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))))),
% 7.84/8.01 inference(monotonicity,[status(thm)],[7])).
% 7.84/8.01 tff(9,plain,
% 7.84/8.01 ((ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))))) <=> (ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[8, 2])).
% 7.84/8.02 tff(10,plain,
% 7.84/8.02 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))))),
% 7.84/8.02 inference(monotonicity,[status(thm)],[9])).
% 7.84/8.02 tff(11,plain,
% 7.84/8.02 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & (ssItem(Y!47) & (ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))))) <=> (ssList(U!45) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[10, 1])).
% 7.84/8.02 tff(12,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U))))))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(13,plain,
% 7.84/8.02 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(nil = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ![X1: $i] : (ssList(X1) => ((~(app(app(Z, cons(Y, nil)), X1) = U)) | ((~memberP(Z, Y)) & (~memberP(X1, Y))))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U))))))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(14,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(nil = W)) | (~(V = X))) | (~(U = W))) | ![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ![X1: $i] : (ssList(X1) => ((~(app(app(Z, cons(Y, nil)), X1) = U)) | ((~memberP(Z, Y)) & (~memberP(X1, Y))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 7.84/8.02 tff(15,plain,
% 7.84/8.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U)))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[14, 13])).
% 7.84/8.02 tff(16,plain,
% 7.84/8.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U)))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[15, 12])).
% 7.84/8.02 tff(17,plain,
% 7.84/8.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U)))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[16, 12])).
% 7.84/8.02 tff(18,plain,
% 7.84/8.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (((~memberP(Z, Y)) & (~memberP(X1, Y))) | (~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = U)))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[17, 12])).
% 7.84/8.02 tff(19,plain,
% 7.84/8.02 (ssList(U!45) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ssItem(Y!47) & ssList(Z!48) & (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[18, 11])).
% 7.84/8.02 tff(20,plain,
% 7.84/8.02 (U!45 = nil),
% 7.84/8.02 inference(and_elim,[status(thm)],[19])).
% 7.84/8.02 tff(21,plain,
% 7.84/8.02 (~(((~memberP(Z!48, Y!47)) & (~memberP(X1!49, Y!47))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45)))),
% 7.84/8.02 inference(and_elim,[status(thm)],[19])).
% 7.84/8.02 tff(22,plain,
% 7.84/8.02 (app(app(Z!48, cons(Y!47, nil)), X1!49) = U!45),
% 7.84/8.02 inference(or_elim,[status(thm)],[21])).
% 7.84/8.02 tff(23,plain,
% 7.84/8.02 (app(app(Z!48, cons(Y!47, nil)), X1!49) = nil),
% 7.84/8.02 inference(transitivity,[status(thm)],[22, 20])).
% 7.84/8.02 tff(24,plain,
% 7.84/8.02 (ssList(nil) <=> ssList(nil)),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(25,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 7.84/8.02 tff(26,plain,
% 7.84/8.02 (ssList(nil)),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[25, 24])).
% 7.84/8.02 tff(27,plain,
% 7.84/8.02 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(28,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[27])).
% 7.84/8.02 tff(29,plain,
% 7.84/8.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(30,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[29])).
% 7.84/8.02 tff(31,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[30, 28])).
% 7.84/8.02 tff(32,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(33,plain,
% 7.84/8.02 (^[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))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(34,plain,
% 7.84/8.02 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[33])).
% 7.84/8.02 tff(35,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 7.84/8.02 tff(36,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[35, 34])).
% 7.84/8.02 tff(37,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[36, 32])).
% 7.84/8.02 tff(38,plain,(
% 7.84/8.02 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(skolemize,[status(sab)],[37])).
% 7.84/8.02 tff(39,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[38, 31])).
% 7.84/8.02 tff(40,plain,
% 7.84/8.02 (((~![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))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(41,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(42,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[41, 40])).
% 7.84/8.02 tff(43,plain,
% 7.84/8.02 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[42, 39, 26])).
% 7.84/8.02 tff(44,plain,
% 7.84/8.02 (ssItem(Y!47)),
% 7.84/8.02 inference(and_elim,[status(thm)],[19])).
% 7.84/8.02 tff(45,plain,
% 7.84/8.02 (((~![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)))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(46,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(Y!47)) | ssList(cons(Y!47, nil)))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(47,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(Y!47)) | ssList(cons(Y!47, nil))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[46, 45])).
% 7.84/8.02 tff(48,plain,
% 7.84/8.02 (ssList(cons(Y!47, nil))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[47, 44, 43])).
% 7.84/8.02 tff(49,plain,
% 7.84/8.02 (ssList(Z!48)),
% 7.84/8.02 inference(and_elim,[status(thm)],[19])).
% 7.84/8.02 tff(50,plain,
% 7.84/8.02 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(51,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[50])).
% 7.84/8.02 tff(52,plain,
% 7.84/8.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(53,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[52])).
% 7.84/8.02 tff(54,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[53, 51])).
% 7.84/8.02 tff(55,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(56,plain,
% 7.84/8.02 (^[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))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(57,plain,
% 7.84/8.02 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[56])).
% 7.84/8.02 tff(58,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax26')).
% 7.84/8.02 tff(59,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[58, 57])).
% 7.84/8.02 tff(60,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[59, 55])).
% 7.84/8.02 tff(61,plain,(
% 7.84/8.02 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(skolemize,[status(sab)],[60])).
% 7.84/8.02 tff(62,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[61, 54])).
% 7.84/8.02 tff(63,plain,
% 7.84/8.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(64,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V))))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(65,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[64, 63])).
% 7.84/8.02 tff(66,plain,
% 7.84/8.02 (![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 7.84/8.02 tff(67,plain,
% 7.84/8.02 (((~![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))) | ((~ssList(cons(Y!47, nil))) | ssList(app(Z!48, cons(Y!47, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))) | (~ssList(cons(Y!47, nil))) | ssList(app(Z!48, cons(Y!47, nil))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(68,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))) | ((~ssList(cons(Y!47, nil))) | ssList(app(Z!48, cons(Y!47, nil))))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(69,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssList(V)) | ssList(app(Z!48, V)))) | (~ssList(cons(Y!47, nil))) | ssList(app(Z!48, cons(Y!47, nil)))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[68, 67])).
% 7.84/8.02 tff(70,plain,
% 7.84/8.02 (ssList(app(Z!48, cons(Y!47, nil)))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[69, 66, 48])).
% 7.84/8.02 tff(71,plain,
% 7.84/8.02 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(72,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[71])).
% 7.84/8.02 tff(73,plain,
% 7.84/8.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(74,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[73])).
% 7.84/8.02 tff(75,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[74, 72])).
% 7.84/8.02 tff(76,plain,
% 7.84/8.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(77,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[76])).
% 7.84/8.02 tff(78,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(79,plain,
% 7.84/8.02 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))) <=> (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), rewrite((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), (![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(80,plain,
% 7.84/8.02 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[79])).
% 7.84/8.02 tff(81,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax5')).
% 7.84/8.02 tff(82,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[81, 80])).
% 7.84/8.02 tff(83,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[82, 78])).
% 7.84/8.02 tff(84,plain,(
% 7.84/8.02 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U)))))))),
% 7.84/8.02 inference(skolemize,[status(sab)],[83])).
% 7.84/8.02 tff(85,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[84, 77])).
% 7.84/8.02 tff(86,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[85, 75])).
% 7.84/8.02 tff(87,plain,
% 7.84/8.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil))))))))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(88,plain,
% 7.84/8.02 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))) | (~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil))))))))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(89,plain,
% 7.84/8.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))) | (~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))))),
% 7.84/8.02 inference(monotonicity,[status(thm)],[88])).
% 7.84/8.02 tff(90,plain,
% 7.84/8.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))) | (~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil))))))))))),
% 7.84/8.02 inference(transitivity,[status(thm)],[89, 87])).
% 7.84/8.02 tff(91,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))) | (~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil)))))))))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(92,plain,
% 7.84/8.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[91, 90])).
% 7.84/8.02 tff(93,plain,
% 7.84/8.02 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[92, 86, 26])).
% 7.84/8.02 tff(94,plain,
% 7.84/8.02 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))) | ((~ssList(app(Z!48, cons(Y!47, nil)))) | (~((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil)))))))))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(95,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))) | ((~ssList(app(Z!48, cons(Y!47, nil)))) | (~((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil)))))))))),
% 7.84/8.02 inference(quant_inst,[status(thm)],[])).
% 7.84/8.02 tff(96,plain,
% 7.84/8.02 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = nil))))) | (~((~frontsegP(nil, V)) | (~((~ssList(tptp_fun_W_5(V, nil))) | (~(app(V, tptp_fun_W_5(V, nil)) = nil)))))))))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil))))))))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[95, 94])).
% 7.84/8.02 tff(97,plain,
% 7.84/8.02 (~((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil)))))))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[96, 93, 70])).
% 7.84/8.02 tff(98,plain,
% 7.84/8.02 (((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | (~((~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~((~ssList(tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil))) | (~(app(app(Z!48, cons(Y!47, nil)), tptp_fun_W_5(app(Z!48, cons(Y!47, nil)), nil)) = nil))))))) | (frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))),
% 7.84/8.02 inference(tautology,[status(thm)],[])).
% 7.84/8.02 tff(99,plain,
% 7.84/8.02 (frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))),
% 7.84/8.02 inference(unit_resolution,[status(thm)],[98, 97])).
% 7.84/8.02 tff(100,plain,
% 7.84/8.02 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(101,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[100])).
% 7.84/8.02 tff(102,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(rewrite,[status(thm)],[])).
% 7.84/8.02 tff(103,plain,
% 7.84/8.02 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 7.84/8.02 inference(bind,[status(th)],[])).
% 7.84/8.02 tff(104,plain,
% 7.84/8.02 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(quant_intro,[status(thm)],[103])).
% 7.84/8.02 tff(105,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax45')).
% 7.84/8.02 tff(106,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[105, 104])).
% 7.84/8.02 tff(107,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[106, 102])).
% 7.84/8.02 tff(108,plain,(
% 7.84/8.02 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(skolemize,[status(sab)],[107])).
% 7.84/8.02 tff(109,plain,
% 7.84/8.02 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 7.84/8.02 inference(modus_ponens,[status(thm)],[108, 101])).
% 7.84/8.02 tff(110,plain,
% 7.84/8.02 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(app(Z!48, cons(Y!47, nil)))) | frontsegP(app(Z!48, cons(Y!47, nil)), nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | frontsegP(app(Z!48, cons(Y!47, nil)), nil))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(111,plain,
% 7.84/8.03 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(app(Z!48, cons(Y!47, nil)))) | frontsegP(app(Z!48, cons(Y!47, nil)), nil))),
% 7.84/8.03 inference(quant_inst,[status(thm)],[])).
% 7.84/8.03 tff(112,plain,
% 7.84/8.03 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | frontsegP(app(Z!48, cons(Y!47, nil)), nil)),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[111, 110])).
% 7.84/8.03 tff(113,plain,
% 7.84/8.03 (frontsegP(app(Z!48, cons(Y!47, nil)), nil)),
% 7.84/8.03 inference(unit_resolution,[status(thm)],[112, 109, 70])).
% 7.84/8.03 tff(114,plain,
% 7.84/8.03 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(115,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[114])).
% 7.84/8.03 tff(116,plain,
% 7.84/8.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(117,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[116])).
% 7.84/8.03 tff(118,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 7.84/8.03 inference(transitivity,[status(thm)],[117, 115])).
% 7.84/8.03 tff(119,plain,
% 7.84/8.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(120,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[119])).
% 7.84/8.03 tff(121,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(122,plain,
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% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(123,plain,
% 7.84/8.03 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[122])).
% 7.84/8.03 tff(124,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 7.84/8.03 tff(125,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[124, 123])).
% 7.84/8.03 tff(126,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[125, 121])).
% 7.84/8.03 tff(127,plain,(
% 7.84/8.03 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 7.84/8.03 inference(skolemize,[status(sab)],[126])).
% 7.84/8.03 tff(128,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[127, 120])).
% 7.84/8.03 tff(129,plain,
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% 7.84/8.03 inference(modus_ponens,[status(thm)],[128, 118])).
% 7.84/8.03 tff(130,plain,
% 7.84/8.03 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V))))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(131,plain,
% 7.84/8.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V))))))),
% 7.84/8.03 inference(quant_inst,[status(thm)],[])).
% 7.84/8.03 tff(132,plain,
% 7.84/8.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[131, 130])).
% 7.84/8.03 tff(133,plain,
% 7.84/8.03 (![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))),
% 7.84/8.03 inference(unit_resolution,[status(thm)],[132, 129, 49])).
% 7.84/8.03 tff(134,plain,
% 7.84/8.03 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | ((~ssList(cons(Y!47, nil))) | (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | (~ssList(cons(Y!47, nil))) | (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil))))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(135,plain,
% 7.84/8.03 (((~ssList(cons(Y!47, nil))) | (~(((~(nil = cons(Y!47, nil))) | (~(nil = Z!48))) <=> (nil = app(Z!48, cons(Y!47, nil)))))) <=> ((~ssList(cons(Y!47, nil))) | (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil))))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(136,plain,
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% 7.84/8.03 inference(monotonicity,[status(thm)],[135])).
% 7.84/8.03 tff(137,plain,
% 7.84/8.03 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | ((~ssList(cons(Y!47, nil))) | (~(((~(nil = cons(Y!47, nil))) | (~(nil = Z!48))) <=> (nil = app(Z!48, cons(Y!47, nil))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | (~ssList(cons(Y!47, nil))) | (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil))))))),
% 7.84/8.03 inference(transitivity,[status(thm)],[136, 134])).
% 7.84/8.03 tff(138,plain,
% 7.84/8.03 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | ((~ssList(cons(Y!47, nil))) | (~(((~(nil = cons(Y!47, nil))) | (~(nil = Z!48))) <=> (nil = app(Z!48, cons(Y!47, nil))))))),
% 7.84/8.03 inference(quant_inst,[status(thm)],[])).
% 7.84/8.03 tff(139,plain,
% 7.84/8.03 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Z!48))) <=> (nil = app(Z!48, V)))))) | (~ssList(cons(Y!47, nil))) | (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[138, 137])).
% 7.84/8.03 tff(140,plain,
% 7.84/8.03 (~(((~(nil = Z!48)) | (~(nil = cons(Y!47, nil)))) <=> (nil = app(Z!48, cons(Y!47, nil))))),
% 7.84/8.03 inference(unit_resolution,[status(thm)],[139, 133, 48])).
% 7.84/8.03 tff(141,plain,
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% 7.84/8.03 inference(commutativity,[status(thm)],[])).
% 7.84/8.03 tff(142,plain,
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% 7.84/8.03 inference(symmetry,[status(thm)],[141])).
% 7.84/8.03 tff(143,plain,
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% 7.84/8.03 inference(monotonicity,[status(thm)],[142])).
% 7.84/8.03 tff(144,plain,
% 7.84/8.03 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
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% 7.84/8.03 inference(quant_intro,[status(thm)],[144])).
% 7.84/8.03 tff(146,plain,
% 7.84/8.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(147,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[146])).
% 7.84/8.03 tff(148,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 7.84/8.03 inference(transitivity,[status(thm)],[147, 145])).
% 7.84/8.03 tff(149,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
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% 7.84/8.03 inference(bind,[status(th)],[])).
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% 7.84/8.03 inference(quant_intro,[status(thm)],[150])).
% 7.84/8.03 tff(152,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
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% 7.84/8.03 inference(modus_ponens,[status(thm)],[153, 149])).
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% 7.84/8.03 inference(rewrite,[status(thm)],[])).
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% 7.84/8.03 inference(quant_inst,[status(thm)],[])).
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% 7.84/8.03 inference(modus_ponens,[status(thm)],[158, 157])).
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% 7.84/8.03 inference(rewrite,[status(thm)],[])).
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% 7.84/8.03 inference(quant_inst,[status(thm)],[])).
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% 7.84/8.03 inference(quant_intro,[status(thm)],[175])).
% 7.84/8.03 tff(177,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 7.84/8.03 inference(rewrite,[status(thm)],[])).
% 7.84/8.03 tff(178,plain,
% 7.84/8.03 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((frontsegP(U, V) & frontsegP(V, U)) => (U = V)) <=> ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))), ((ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> (ssList(V) => ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))), ((ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))))), (![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))))),
% 7.84/8.03 inference(bind,[status(th)],[])).
% 7.84/8.03 tff(179,plain,
% 7.84/8.03 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 7.84/8.03 inference(quant_intro,[status(thm)],[178])).
% 7.84/8.03 tff(180,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax41')).
% 7.84/8.03 tff(181,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[180, 179])).
% 7.84/8.03 tff(182,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[181, 177])).
% 7.84/8.03 tff(183,plain,(
% 7.84/8.03 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 7.84/8.03 inference(skolemize,[status(sab)],[182])).
% 7.84/8.03 tff(184,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[183, 176])).
% 7.84/8.03 tff(185,plain,
% 7.84/8.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 7.84/8.03 inference(modus_ponens,[status(thm)],[184, 174])).
% 7.84/8.03 tff(186,plain,
% 7.84/8.03 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | (~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))),
% 7.84/8.06 inference(rewrite,[status(thm)],[])).
% 7.84/8.06 tff(187,plain,
% 7.84/8.06 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))),
% 7.84/8.06 inference(quant_inst,[status(thm)],[])).
% 7.84/8.06 tff(188,plain,
% 7.84/8.06 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | (~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))),
% 7.84/8.06 inference(modus_ponens,[status(thm)],[187, 186])).
% 7.84/8.06 tff(189,plain,
% 7.84/8.06 (![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))),
% 7.84/8.06 inference(unit_resolution,[status(thm)],[188, 26, 185])).
% 7.84/8.06 tff(190,plain,
% 7.84/8.06 (((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | ((nil = app(Z!48, cons(Y!47, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~frontsegP(app(Z!48, cons(Y!47, nil)), nil)))) <=> ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | (nil = app(Z!48, cons(Y!47, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~frontsegP(app(Z!48, cons(Y!47, nil)), nil)))),
% 7.84/8.06 inference(rewrite,[status(thm)],[])).
% 7.84/8.06 tff(191,plain,
% 7.84/8.06 ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | ((nil = app(Z!48, cons(Y!47, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~frontsegP(app(Z!48, cons(Y!47, nil)), nil)))),
% 7.84/8.06 inference(quant_inst,[status(thm)],[])).
% 7.84/8.06 tff(192,plain,
% 7.84/8.06 ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | (nil = app(Z!48, cons(Y!47, nil))) | (~ssList(app(Z!48, cons(Y!47, nil)))) | (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~frontsegP(app(Z!48, cons(Y!47, nil)), nil))),
% 7.84/8.06 inference(modus_ponens,[status(thm)],[191, 190])).
% 7.84/8.06 tff(193,plain,
% 7.84/8.06 ((nil = app(Z!48, cons(Y!47, nil))) | (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))) | (~frontsegP(app(Z!48, cons(Y!47, nil)), nil))),
% 7.84/8.06 inference(unit_resolution,[status(thm)],[192, 189, 70])).
% 7.84/8.06 tff(194,plain,
% 7.84/8.06 (~frontsegP(nil, app(Z!48, cons(Y!47, nil)))),
% 7.84/8.06 inference(unit_resolution,[status(thm)],[193, 169, 113])).
% 7.84/8.06 tff(195,plain,
% 7.84/8.06 ((~(frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil))))) | frontsegP(nil, app(Z!48, cons(Y!47, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))),
% 7.84/8.06 inference(tautology,[status(thm)],[])).
% 7.84/8.06 tff(196,plain,
% 7.84/8.06 (![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))),
% 7.84/8.06 inference(unit_resolution,[status(thm)],[195, 194, 99])).
% 7.84/8.06 tff(197,plain,
% 7.84/8.06 (ssList(X1!49)),
% 7.84/8.06 inference(or_elim,[status(thm)],[21])).
% 7.84/8.06 tff(198,plain,
% 7.84/8.06 (((~![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))) | ((~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = nil)))) <=> ((~![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = nil)))),
% 7.84/8.06 inference(rewrite,[status(thm)],[])).
% 7.84/8.06 tff(199,plain,
% 7.84/8.06 ((~![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))) | ((~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = nil)))),
% 7.84/8.06 inference(quant_inst,[status(thm)],[])).
% 7.84/8.06 tff(200,plain,
% 7.84/8.06 ((~![W: $i] : ((~ssList(W)) | (~(app(app(Z!48, cons(Y!47, nil)), W) = nil)))) | (~ssList(X1!49)) | (~(app(app(Z!48, cons(Y!47, nil)), X1!49) = nil))),
% 7.84/8.06 inference(modus_ponens,[status(thm)],[199, 198])).
% 7.84/8.06 tff(201,plain,
% 7.84/8.06 ($false),
% 7.84/8.06 inference(unit_resolution,[status(thm)],[200, 197, 196, 23])).
% 7.84/8.06 % SZS output end Proof
% 7.84/8.06 % E exiting
%------------------------------------------------------------------------------