%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC008+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:29:54 AM UTC 2025
% Result : Theorem 2.75s 2.94s
% Output : Proof 2.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC008+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:59:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.75/2.94 % SZS status Theorem
% 2.75/2.94 % SZS output start Proof
% 2.75/2.94 tff(tptp_fun_V_46_type, type, (
% 2.75/2.94 tptp_fun_V_46: $i)).
% 2.75/2.94 tff(app_type, type, (
% 2.75/2.94 app: ( $i * $i ) > $i)).
% 2.75/2.94 tff(nil_type, type, (
% 2.75/2.94 nil: $i)).
% 2.75/2.94 tff(tptp_fun_W_5_type, type, (
% 2.75/2.94 tptp_fun_W_5: ( $i * $i ) > $i)).
% 2.75/2.94 tff(tptp_fun_U_45_type, type, (
% 2.75/2.94 tptp_fun_U_45: $i)).
% 2.75/2.94 tff(ssList_type, type, (
% 2.75/2.94 ssList: $i > $o)).
% 2.75/2.94 tff(equalelemsP_type, type, (
% 2.75/2.94 equalelemsP: $i > $o)).
% 2.75/2.94 tff(segmentP_type, type, (
% 2.75/2.94 segmentP: ( $i * $i ) > $o)).
% 2.75/2.94 tff(frontsegP_type, type, (
% 2.75/2.94 frontsegP: ( $i * $i ) > $o)).
% 2.75/2.94 tff(neq_type, type, (
% 2.75/2.94 neq: ( $i * $i ) > $o)).
% 2.75/2.94 tff(1,plain,
% 2.75/2.94 ((ssList(U!45) & (equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))) <=> (ssList(U!45) & equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(2,plain,
% 2.75/2.94 ((equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))) <=> (equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(3,plain,
% 2.75/2.94 ((ssList(U!45) & (equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))) <=> (ssList(U!45) & (equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[2])).
% 2.75/2.94 tff(4,plain,
% 2.75/2.94 ((ssList(U!45) & (equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))) <=> (ssList(U!45) & equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[3, 1])).
% 2.75/2.94 tff(5,plain,
% 2.75/2.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(6,plain,
% 2.75/2.94 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~frontsegP(X, W))) | (~equalelemsP(W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ?[X2: $i] : ((((ssList(X2) & neq(W, X2)) & frontsegP(X, X2)) & segmentP(X2, W)) & equalelemsP(X2)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~frontsegP(X, W))) | (~equalelemsP(W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ?[X2: $i] : ((((ssList(X2) & neq(W, X2)) & frontsegP(X, X2)) & segmentP(X2, W)) & equalelemsP(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 2.75/2.94 tff(8,plain,
% 2.75/2.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.75/2.94 tff(9,plain,
% 2.75/2.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[8, 5])).
% 2.75/2.94 tff(10,plain,
% 2.75/2.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.75/2.94 tff(11,plain,
% 2.75/2.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~equalelemsP(U)) | (~frontsegP(V, U)) | (~ssList(V)) | ?[X2: $i] : (ssList(X2) & neq(U, X2) & frontsegP(V, X2) & segmentP(X2, U) & equalelemsP(X2)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[10, 5])).
% 2.75/2.94 tff(12,plain,
% 2.75/2.94 (ssList(U!45) & equalelemsP(U!45) & frontsegP(V!46, U!45) & ssList(V!46) & ![X2: $i] : (~(ssList(X2) & neq(U!45, X2) & frontsegP(V!46, X2) & segmentP(X2, U!45) & equalelemsP(X2))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11, 4])).
% 2.75/2.94 tff(13,plain,
% 2.75/2.94 (ssList(V!46)),
% 2.75/2.94 inference(and_elim,[status(thm)],[12])).
% 2.75/2.94 tff(14,plain,
% 2.75/2.94 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(15,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[14])).
% 2.75/2.94 tff(16,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(17,plain,
% 2.75/2.94 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(18,plain,
% 2.75/2.94 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[17])).
% 2.75/2.94 tff(19,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 2.75/2.94 tff(20,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.75/2.94 tff(21,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.75/2.94 tff(22,plain,(
% 2.75/2.94 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(skolemize,[status(sab)],[21])).
% 2.75/2.94 tff(23,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.75/2.94 tff(24,plain,
% 2.75/2.94 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(25,plain,
% 2.75/2.94 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(26,plain,
% 2.75/2.94 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.75/2.94 tff(27,plain,
% 2.75/2.94 (app(V!46, nil) = V!46),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 2.75/2.94 tff(28,plain,
% 2.75/2.94 (^[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))))))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(29,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[28])).
% 2.75/2.94 tff(30,plain,
% 2.75/2.94 (^[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))))))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(31,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[30])).
% 2.75/2.94 tff(32,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[31, 29])).
% 2.75/2.94 tff(33,plain,
% 2.75/2.94 (^[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))))))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(34,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[33])).
% 2.75/2.94 tff(35,plain,
% 2.75/2.94 (![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)))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(36,plain,
% 2.75/2.94 (^[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)))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(37,plain,
% 2.75/2.94 (![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)))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[36])).
% 2.75/2.94 tff(38,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax5')).
% 2.75/2.94 tff(39,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[38, 37])).
% 2.75/2.94 tff(40,plain,
% 2.75/2.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[39, 35])).
% 2.75/2.94 tff(41,plain,(
% 2.75/2.94 ![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)))))))),
% 2.75/2.94 inference(skolemize,[status(sab)],[40])).
% 2.75/2.94 tff(42,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[41, 34])).
% 2.75/2.94 tff(43,plain,
% 2.75/2.94 (![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)))))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[42, 32])).
% 2.75/2.94 tff(44,plain,
% 2.75/2.94 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(45,plain,
% 2.75/2.94 (((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))))))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(46,plain,
% 2.75/2.94 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[45])).
% 2.75/2.94 tff(47,plain,
% 2.75/2.94 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46))))))))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[46, 44])).
% 2.75/2.94 tff(48,plain,
% 2.75/2.94 ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))) | (~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46)))))))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(49,plain,
% 2.75/2.94 ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[48, 47])).
% 2.75/2.94 tff(50,plain,
% 2.75/2.94 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[49, 43, 13])).
% 2.75/2.94 tff(51,plain,
% 2.75/2.94 (ssList(U!45)),
% 2.75/2.94 inference(and_elim,[status(thm)],[12])).
% 2.75/2.94 tff(52,plain,
% 2.75/2.94 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | (~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(53,plain,
% 2.75/2.94 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(54,plain,
% 2.75/2.94 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = V!46))))) | (~((~frontsegP(V!46, V)) | (~((~ssList(tptp_fun_W_5(V, V!46))) | (~(app(V, tptp_fun_W_5(V, V!46)) = V!46)))))))))) | (~ssList(U!45)) | (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.75/2.94 tff(55,plain,
% 2.75/2.94 (~((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[54, 51, 50])).
% 2.75/2.94 tff(56,plain,
% 2.75/2.94 (((~(frontsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(U!45, W) = V!46))))) | (~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))))) | ((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))),
% 2.75/2.94 inference(tautology,[status(thm)],[])).
% 2.75/2.94 tff(57,plain,
% 2.75/2.94 ((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[56, 55])).
% 2.75/2.94 tff(58,plain,
% 2.75/2.94 (frontsegP(V!46, U!45)),
% 2.75/2.94 inference(and_elim,[status(thm)],[12])).
% 2.75/2.94 tff(59,plain,
% 2.75/2.94 ((~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))) | (~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))),
% 2.75/2.94 inference(tautology,[status(thm)],[])).
% 2.75/2.94 tff(60,plain,
% 2.75/2.94 ((~((~frontsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))))) | (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[59, 58])).
% 2.75/2.94 tff(61,plain,
% 2.75/2.94 (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[60, 57])).
% 2.75/2.94 tff(62,plain,
% 2.75/2.94 (((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))) | (app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)),
% 2.75/2.94 inference(tautology,[status(thm)],[])).
% 2.75/2.94 tff(63,plain,
% 2.75/2.94 (app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[62, 61])).
% 2.75/2.94 tff(64,plain,
% 2.75/2.94 (app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = app(V!46, nil)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[63])).
% 2.75/2.94 tff(65,plain,
% 2.75/2.94 (app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46),
% 2.75/2.94 inference(transitivity,[status(thm)],[64, 27])).
% 2.75/2.94 tff(66,plain,
% 2.75/2.94 (((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46))) | ssList(tptp_fun_W_5(U!45, V!46))),
% 2.75/2.94 inference(tautology,[status(thm)],[])).
% 2.75/2.94 tff(67,plain,
% 2.75/2.94 (ssList(tptp_fun_W_5(U!45, V!46))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[66, 61])).
% 2.75/2.94 tff(68,plain,
% 2.75/2.94 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(69,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[68])).
% 2.75/2.94 tff(70,plain,
% 2.75/2.94 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(71,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[70])).
% 2.75/2.94 tff(72,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[71, 69])).
% 2.75/2.94 tff(73,plain,
% 2.75/2.94 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45))))))),
% 2.75/2.94 inference(bind,[status(th)],[])).
% 2.75/2.94 tff(74,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(quant_intro,[status(thm)],[73])).
% 2.75/2.94 tff(75,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(and_elim,[status(thm)],[12])).
% 2.75/2.94 tff(76,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.75/2.94 tff(77,plain,
% 2.75/2.94 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[76, 72])).
% 2.75/2.94 tff(78,plain,
% 2.75/2.94 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))) | ((~ssList(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))) | (~ssList(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45)))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(79,plain,
% 2.75/2.94 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))) | ((~ssList(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45)))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(80,plain,
% 2.75/2.94 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))) | (~ssList(U!45)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.75/2.94 tff(81,plain,
% 2.75/2.94 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[80, 51, 77])).
% 2.75/2.94 tff(82,plain,
% 2.75/2.94 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(83,plain,
% 2.75/2.94 (((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)) | (~(app(U!45, X1) = U!45)))) <=> ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(84,plain,
% 2.75/2.94 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[83])).
% 2.75/2.95 tff(85,plain,
% 2.75/2.95 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46))))),
% 2.75/2.95 inference(transitivity,[status(thm)],[84, 82])).
% 2.75/2.95 tff(86,plain,
% 2.75/2.95 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)) | (~(app(U!45, X1) = U!45))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(87,plain,
% 2.75/2.95 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(U!45, Z), X1) = V!46)) | (~(app(U!45, X1) = U!45))))) | (~ssList(tptp_fun_W_5(U!45, V!46))) | ![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[86, 85])).
% 2.75/2.95 tff(88,plain,
% 2.75/2.95 (![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[87, 81, 67])).
% 2.75/2.95 tff(89,plain,
% 2.75/2.95 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(90,plain,
% 2.75/2.95 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(U!45)) | (app(U!45, nil) = U!45))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(91,plain,
% 2.75/2.95 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(U!45)) | (app(U!45, nil) = U!45)),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.75/2.95 tff(92,plain,
% 2.75/2.95 (app(U!45, nil) = U!45),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[91, 23, 51])).
% 2.75/2.95 tff(93,plain,
% 2.75/2.95 (ssList(nil) <=> ssList(nil)),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(94,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 2.75/2.95 tff(95,plain,
% 2.75/2.95 (ssList(nil)),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.75/2.95 tff(96,plain,
% 2.75/2.95 (((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46)))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(97,plain,
% 2.75/2.95 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))) | ((~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46)))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(98,plain,
% 2.75/2.95 ((~![X1: $i] : ((~ssList(X1)) | (~(app(U!45, X1) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), X1) = V!46)))) | (~ssList(nil)) | (~(app(U!45, nil) = U!45)) | (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.75/2.95 tff(99,plain,
% 2.75/2.95 (~(app(app(U!45, tptp_fun_W_5(U!45, V!46)), nil) = V!46)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[98, 95, 92, 88])).
% 2.75/2.96 tff(100,plain,
% 2.75/2.96 ($false),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[99, 65])).
% 2.75/2.96 % SZS output end Proof
% 2.75/2.96 % E exiting
%------------------------------------------------------------------------------