%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC007+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 05:29:54 AM UTC 2025
% Result : Theorem 0.41s 0.59s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC007+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:01:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 % SZS output start Proof
% 0.41/0.59 tff(tptp_fun_V_46_type, type, (
% 0.41/0.59 tptp_fun_V_46: $i)).
% 0.41/0.59 tff(app_type, type, (
% 0.41/0.59 app: ( $i * $i ) > $i)).
% 0.41/0.59 tff(tptp_fun_W_5_type, type, (
% 0.41/0.59 tptp_fun_W_5: ( $i * $i ) > $i)).
% 0.41/0.59 tff(nil_type, type, (
% 0.41/0.59 nil: $i)).
% 0.41/0.59 tff(ssList_type, type, (
% 0.41/0.59 ssList: $i > $o)).
% 0.41/0.59 tff(tptp_fun_U_45_type, type, (
% 0.41/0.59 tptp_fun_U_45: $i)).
% 0.41/0.59 tff(frontsegP_type, type, (
% 0.41/0.59 frontsegP: ( $i * $i ) > $o)).
% 0.41/0.59 tff(1,plain,
% 0.41/0.59 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ![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) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(2,plain,
% 0.41/0.59 ((ssList(V!46) & ssList(nil) & (U!45 = nil) & ![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(V!46) & ssList(nil) & (U!45 = nil) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(3,plain,
% 0.41/0.59 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ![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) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[2])).
% 0.41/0.59 tff(4,plain,
% 0.41/0.59 ((ssList(U!45) & (ssList(V!46) & ssList(nil) & (U!45 = nil) & ![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) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[3, 1])).
% 0.41/0.59 tff(5,plain,
% 0.41/0.59 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[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] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(6,plain,
% 0.41/0.59 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(nil = W)) | (~(V = X))) | (~(U = W))) | ?[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] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(7,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] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.41/0.59 tff(8,plain,
% 0.41/0.59 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.41/0.59 tff(9,plain,
% 0.41/0.59 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.41/0.59 tff(10,plain,
% 0.41/0.59 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.41/0.59 tff(11,plain,
% 0.41/0.59 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(nil)) | (~(U = nil)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.41/0.59 tff(12,plain,
% 0.41/0.59 (ssList(U!45) & ssList(V!46) & ssList(nil) & (U!45 = nil) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.41/0.59 tff(13,plain,
% 0.41/0.59 (ssList(V!46)),
% 0.41/0.59 inference(and_elim,[status(thm)],[12])).
% 0.41/0.59 tff(14,plain,
% 0.41/0.59 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(15,plain,
% 0.41/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[14])).
% 0.41/0.59 tff(16,plain,
% 0.41/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(17,plain,
% 0.41/0.59 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(18,plain,
% 0.41/0.59 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[17])).
% 0.41/0.59 tff(19,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.41/0.59 tff(20,plain,
% 0.41/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.41/0.59 tff(21,plain,
% 0.41/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.41/0.59 tff(22,plain,(
% 0.41/0.59 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(skolemize,[status(sab)],[21])).
% 0.41/0.59 tff(23,plain,
% 0.41/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.41/0.59 tff(24,plain,
% 0.41/0.59 (((~![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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(25,plain,
% 0.41/0.59 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(26,plain,
% 0.41/0.59 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.41/0.59 tff(27,plain,
% 0.41/0.59 (app(V!46, nil) = V!46),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.41/0.59 tff(28,plain,
% 0.41/0.59 (ssList(nil) <=> ssList(nil)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(29,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.41/0.59 tff(30,plain,
% 0.41/0.59 (ssList(nil)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.41/0.59 tff(31,plain,
% 0.41/0.59 (^[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))))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(32,plain,
% 0.41/0.59 (![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)))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[31])).
% 0.41/0.59 tff(33,plain,
% 0.41/0.59 (^[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))))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(34,plain,
% 0.41/0.59 (![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)))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[33])).
% 0.41/0.59 tff(35,plain,
% 0.41/0.59 (![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)))))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[34, 32])).
% 0.41/0.59 tff(36,plain,
% 0.41/0.59 (^[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))))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(37,plain,
% 0.41/0.59 (![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)))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[36])).
% 0.41/0.59 tff(38,plain,
% 0.41/0.59 (![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)))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(39,plain,
% 0.41/0.59 (^[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)))))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(40,plain,
% 0.41/0.60 (![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)))))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[39])).
% 0.41/0.60 tff(41,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')).
% 0.41/0.60 tff(42,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.41/0.60 tff(43,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.41/0.60 tff(44,plain,(
% 0.41/0.60 ![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)))))))),
% 0.41/0.60 inference(skolemize,[status(sab)],[43])).
% 0.41/0.60 tff(45,plain,
% 0.41/0.60 (![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)))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.41/0.60 tff(46,plain,
% 0.41/0.60 (![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)))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.41/0.60 tff(47,plain,
% 0.41/0.60 (((~![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))))))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(48,plain,
% 0.41/0.60 (((~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))))))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(49,plain,
% 0.41/0.60 (((~![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)))))))))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[48])).
% 0.41/0.60 tff(50,plain,
% 0.41/0.60 (((~![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))))))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[49, 47])).
% 0.41/0.60 tff(51,plain,
% 0.41/0.60 ((~![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)))))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(52,plain,
% 0.41/0.60 ((~![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)))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.41/0.60 tff(53,plain,
% 0.41/0.60 (![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)))))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[52, 46, 30])).
% 0.41/0.60 tff(54,plain,
% 0.41/0.60 (((~![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(nil)) | (~((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(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(nil)) | (~((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(55,plain,
% 0.41/0.60 ((~![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(nil)) | (~((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(56,plain,
% 0.41/0.60 ((~![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(nil)) | (~((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.41/0.60 tff(57,plain,
% 0.41/0.60 (~((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[56, 30, 53])).
% 0.41/0.60 tff(58,plain,
% 0.41/0.60 (((~(frontsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = nil))))) | (~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))))))) | ((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(59,plain,
% 0.41/0.60 ((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.41/0.60 tff(60,plain,
% 0.41/0.60 (^[U: $i] : refl(((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(61,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[60])).
% 0.41/0.60 tff(62,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(63,plain,
% 0.41/0.60 (^[U: $i] : rewrite((ssList(U) => (frontsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(64,plain,
% 0.41/0.60 (![U: $i] : (ssList(U) => (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[63])).
% 0.41/0.60 tff(65,axiom,(![U: $i] : (ssList(U) => (frontsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax46')).
% 0.41/0.60 tff(66,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.41/0.60 tff(67,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.41/0.60 tff(68,plain,(
% 0.41/0.60 ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(skolemize,[status(sab)],[67])).
% 0.41/0.60 tff(69,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.41/0.60 tff(70,plain,
% 0.41/0.60 (((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | frontsegP(nil, nil))) <=> ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | frontsegP(nil, nil))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(71,plain,
% 0.41/0.60 (((~ssList(nil)) | (frontsegP(nil, nil) <=> (nil = nil))) <=> ((~ssList(nil)) | frontsegP(nil, nil))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(72,plain,
% 0.41/0.60 (((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (frontsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | frontsegP(nil, nil)))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[71])).
% 0.41/0.60 tff(73,plain,
% 0.41/0.60 (((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (frontsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | frontsegP(nil, nil))),
% 0.41/0.60 inference(transitivity,[status(thm)],[72, 70])).
% 0.41/0.60 tff(74,plain,
% 0.41/0.60 ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (frontsegP(nil, nil) <=> (nil = nil)))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(75,plain,
% 0.41/0.60 ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | frontsegP(nil, nil)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.41/0.60 tff(76,plain,
% 0.41/0.60 (frontsegP(nil, nil)),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[75, 30, 69])).
% 0.41/0.60 tff(77,plain,
% 0.41/0.60 ((~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))) | (~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(78,plain,
% 0.41/0.60 ((~((~frontsegP(nil, nil)) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))))) | (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.41/0.60 tff(79,plain,
% 0.41/0.60 (~((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil)))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[78, 59])).
% 0.41/0.60 tff(80,plain,
% 0.41/0.60 (((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))) | (app(nil, tptp_fun_W_5(nil, nil)) = nil)),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(81,plain,
% 0.41/0.60 (app(nil, tptp_fun_W_5(nil, nil)) = nil),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.41/0.60 tff(82,plain,
% 0.41/0.60 (app(V!46, app(nil, tptp_fun_W_5(nil, nil))) = app(V!46, nil)),
% 0.41/0.60 inference(monotonicity,[status(thm)],[81])).
% 0.41/0.60 tff(83,plain,
% 0.41/0.60 (((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = nil))) | ssList(tptp_fun_W_5(nil, nil))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(84,plain,
% 0.41/0.60 (ssList(tptp_fun_W_5(nil, nil))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[83, 79])).
% 0.41/0.60 tff(85,plain,
% 0.41/0.60 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(86,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[85])).
% 0.41/0.60 tff(87,plain,
% 0.41/0.60 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(88,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[87])).
% 0.41/0.60 tff(89,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[88, 86])).
% 0.41/0.60 tff(90,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(91,plain,
% 0.41/0.60 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(92,plain,
% 0.41/0.60 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[91])).
% 0.41/0.60 tff(93,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax82')).
% 0.41/0.60 tff(94,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.41/0.60 tff(95,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.41/0.60 tff(96,plain,(
% 0.41/0.60 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(skolemize,[status(sab)],[95])).
% 0.41/0.60 tff(97,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.41/0.60 tff(98,plain,
% 0.41/0.60 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(99,plain,
% 0.41/0.60 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(100,plain,
% 0.41/0.60 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.41/0.60 tff(101,plain,
% 0.41/0.60 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[100, 97, 13])).
% 0.41/0.60 tff(102,plain,
% 0.41/0.60 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W)))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(103,plain,
% 0.41/0.60 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W)))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(104,plain,
% 0.41/0.60 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, V), W) = app(V!46, app(V, W)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.41/0.60 tff(105,plain,
% 0.41/0.60 (![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[104, 30, 101])).
% 0.41/0.60 tff(106,plain,
% 0.41/0.60 (((~![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))) | ((~ssList(tptp_fun_W_5(nil, nil))) | (app(app(V!46, nil), tptp_fun_W_5(nil, nil)) = app(V!46, app(nil, tptp_fun_W_5(nil, nil)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))) | (~ssList(tptp_fun_W_5(nil, nil))) | (app(app(V!46, nil), tptp_fun_W_5(nil, nil)) = app(V!46, app(nil, tptp_fun_W_5(nil, nil)))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(107,plain,
% 0.41/0.60 ((~![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))) | ((~ssList(tptp_fun_W_5(nil, nil))) | (app(app(V!46, nil), tptp_fun_W_5(nil, nil)) = app(V!46, app(nil, tptp_fun_W_5(nil, nil)))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(108,plain,
% 0.41/0.60 ((~![W: $i] : ((~ssList(W)) | (app(app(V!46, nil), W) = app(V!46, app(nil, W))))) | (~ssList(tptp_fun_W_5(nil, nil))) | (app(app(V!46, nil), tptp_fun_W_5(nil, nil)) = app(V!46, app(nil, tptp_fun_W_5(nil, nil))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.41/0.60 tff(109,plain,
% 0.41/0.60 (app(app(V!46, nil), tptp_fun_W_5(nil, nil)) = app(V!46, app(nil, tptp_fun_W_5(nil, nil)))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[108, 105, 84])).
% 0.41/0.60 tff(110,plain,
% 0.41/0.60 (V!46 = app(V!46, nil)),
% 0.41/0.60 inference(symmetry,[status(thm)],[27])).
% 0.41/0.60 tff(111,plain,
% 0.41/0.60 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(112,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[111])).
% 0.41/0.60 tff(113,plain,
% 0.41/0.60 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(114,plain,
% 0.41/0.60 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(115,plain,
% 0.41/0.61 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[114])).
% 0.41/0.61 tff(116,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 0.41/0.61 tff(117,plain,
% 0.41/0.61 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.41/0.61 tff(118,plain,
% 0.41/0.61 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.41/0.61 tff(119,plain,(
% 0.41/0.61 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.61 inference(skolemize,[status(sab)],[118])).
% 0.41/0.61 tff(120,plain,
% 0.41/0.61 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.41/0.61 tff(121,plain,
% 0.41/0.61 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(V!46)) | (app(nil, V!46) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(V!46)) | (app(nil, V!46) = V!46))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(122,plain,
% 0.41/0.61 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(V!46)) | (app(nil, V!46) = V!46))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(123,plain,
% 0.41/0.61 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(V!46)) | (app(nil, V!46) = V!46)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.41/0.61 tff(124,plain,
% 0.41/0.61 (app(nil, V!46) = V!46),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[123, 120, 13])).
% 0.41/0.61 tff(125,plain,
% 0.41/0.61 (app(nil, V!46) = app(V!46, nil)),
% 0.41/0.61 inference(transitivity,[status(thm)],[124, 110])).
% 0.41/0.61 tff(126,plain,
% 0.41/0.61 (app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = app(app(V!46, nil), tptp_fun_W_5(nil, nil))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[125])).
% 0.41/0.61 tff(127,plain,
% 0.41/0.61 (app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46),
% 0.41/0.61 inference(transitivity,[status(thm)],[126, 109, 82, 27])).
% 0.41/0.61 tff(128,plain,
% 0.41/0.61 (U!45 = nil),
% 0.41/0.61 inference(and_elim,[status(thm)],[12])).
% 0.41/0.61 tff(129,plain,
% 0.41/0.61 (nil = U!45),
% 0.41/0.61 inference(symmetry,[status(thm)],[128])).
% 0.41/0.61 tff(130,plain,
% 0.41/0.61 (app(nil, tptp_fun_W_5(nil, nil)) = U!45),
% 0.41/0.61 inference(transitivity,[status(thm)],[81, 129])).
% 0.41/0.61 tff(131,plain,
% 0.41/0.61 (^[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))))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(132,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[131])).
% 0.41/0.61 tff(133,plain,
% 0.41/0.61 (^[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))))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(134,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[133])).
% 0.41/0.61 tff(135,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(transitivity,[status(thm)],[134, 132])).
% 0.41/0.61 tff(136,plain,
% 0.41/0.61 (^[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))))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(137,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[136])).
% 0.41/0.61 tff(138,plain,
% 0.41/0.61 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!46) & (app(Y, X1) = U!45)))))),
% 0.41/0.61 inference(and_elim,[status(thm)],[12])).
% 0.41/0.61 tff(139,plain,
% 0.41/0.61 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.41/0.61 tff(140,plain,
% 0.41/0.61 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!46)) | (~(app(Y, X1) = U!45)))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.41/0.61 tff(141,plain,
% 0.41/0.61 (((~![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(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, 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(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45)))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(142,plain,
% 0.41/0.61 ((~![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(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45)))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(143,plain,
% 0.41/0.61 ((~![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(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.41/0.61 tff(144,plain,
% 0.41/0.61 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[143, 30, 140])).
% 0.41/0.61 tff(145,plain,
% 0.41/0.61 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | (~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(146,plain,
% 0.41/0.61 (((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, V!46), X1) = V!46)) | (~(app(nil, X1) = U!45)))) <=> ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(147,plain,
% 0.41/0.61 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, V!46), X1) = V!46)) | (~(app(nil, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[146])).
% 0.41/0.61 tff(148,plain,
% 0.41/0.61 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, V!46), X1) = V!46)) | (~(app(nil, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | (~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46))))),
% 0.41/0.61 inference(transitivity,[status(thm)],[147, 145])).
% 0.41/0.61 tff(149,plain,
% 0.41/0.61 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | ((~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, V!46), X1) = V!46)) | (~(app(nil, X1) = U!45))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(150,plain,
% 0.41/0.61 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = V!46)) | (~(app(nil, X1) = U!45))))) | (~ssList(V!46)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.41/0.61 tff(151,plain,
% 0.41/0.61 (![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[150, 13, 144])).
% 0.41/0.61 tff(152,plain,
% 0.41/0.61 (((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))) | ((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = U!45)) | (~(app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))) | (~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = U!45)) | (~(app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(153,plain,
% 0.41/0.61 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))) | ((~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = U!45)) | (~(app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(154,plain,
% 0.41/0.61 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, V!46), X1) = V!46)))) | (~ssList(tptp_fun_W_5(nil, nil))) | (~(app(nil, tptp_fun_W_5(nil, nil)) = U!45)) | (~(app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.41/0.61 tff(155,plain,
% 0.41/0.61 (~(app(app(nil, V!46), tptp_fun_W_5(nil, nil)) = V!46)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[154, 151, 84, 130])).
% 0.41/0.61 tff(156,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[155, 127])).
% 0.41/0.61 % SZS output end Proof
% 0.41/0.62 % E exiting
%------------------------------------------------------------------------------