%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC094+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:09 AM UTC 2025
% Result : Theorem 0.43s 0.65s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWC094+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8042.1875MB
% 0.11/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Jun 20 08:18:40 EDT 2025
% 0.11/0.37 % CPUTime :
% 0.43/0.65 % SZS status Theorem
% 0.43/0.65 % SZS output start Proof
% 0.43/0.65 tff(tptp_fun_U_45_type, type, (
% 0.43/0.65 tptp_fun_U_45: $i)).
% 0.43/0.65 tff(app_type, type, (
% 0.43/0.65 app: ( $i * $i ) > $i)).
% 0.43/0.65 tff(tptp_fun_W_5_type, type, (
% 0.43/0.65 tptp_fun_W_5: ( $i * $i ) > $i)).
% 0.43/0.65 tff(nil_type, type, (
% 0.43/0.65 nil: $i)).
% 0.43/0.65 tff(ssList_type, type, (
% 0.43/0.65 ssList: $i > $o)).
% 0.43/0.65 tff(frontsegP_type, type, (
% 0.43/0.65 frontsegP: ( $i * $i ) > $o)).
% 0.43/0.65 tff(1,plain,
% 0.43/0.65 ((ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45)))))) <=> (ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(2,plain,
% 0.43/0.65 ((~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U)))))) <=> (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(3,plain,
% 0.43/0.65 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = U)) & (app(Y, X1) = V)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = U)) & (app(Y, X1) = V)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.43/0.65 tff(5,plain,
% 0.43/0.65 (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.43/0.65 tff(6,plain,
% 0.43/0.65 (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.43/0.65 tff(7,plain,
% 0.43/0.65 (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.43/0.65 tff(8,plain,
% 0.43/0.65 (~![U: $i] : ((~ssList(U)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.43/0.65 tff(9,plain,
% 0.43/0.65 (ssList(U!45) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.43/0.65 tff(10,plain,
% 0.43/0.65 (ssList(U!45)),
% 0.43/0.65 inference(and_elim,[status(thm)],[9])).
% 0.43/0.65 tff(11,plain,
% 0.43/0.65 (^[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))))))))))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(12,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[11])).
% 0.43/0.65 tff(13,plain,
% 0.43/0.65 (^[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))))))))))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(14,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[13])).
% 0.43/0.65 tff(15,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(transitivity,[status(thm)],[14, 12])).
% 0.43/0.65 tff(16,plain,
% 0.43/0.65 (^[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))))))))))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(17,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[16])).
% 0.43/0.65 tff(18,plain,
% 0.43/0.65 (![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)))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(19,plain,
% 0.43/0.65 (^[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)))))))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(20,plain,
% 0.43/0.65 (![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)))))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[19])).
% 0.43/0.65 tff(21,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')).
% 0.43/0.65 tff(22,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.43/0.65 tff(23,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.43/0.65 tff(24,plain,(
% 0.43/0.65 ![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)))))))),
% 0.43/0.65 inference(skolemize,[status(sab)],[23])).
% 0.43/0.65 tff(25,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.43/0.65 tff(26,plain,
% 0.43/0.65 (![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)))))))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.43/0.65 tff(27,plain,
% 0.43/0.65 (((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))) <=> ((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(28,plain,
% 0.43/0.65 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(29,plain,
% 0.43/0.65 (((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))))),
% 0.43/0.65 inference(monotonicity,[status(thm)],[28])).
% 0.43/0.65 tff(30,plain,
% 0.43/0.65 (((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 0.43/0.65 inference(transitivity,[status(thm)],[29, 27])).
% 0.43/0.65 tff(31,plain,
% 0.43/0.65 ((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))),
% 0.43/0.65 inference(quant_inst,[status(thm)],[])).
% 0.43/0.65 tff(32,plain,
% 0.43/0.65 ((~![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(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.43/0.65 tff(33,plain,
% 0.43/0.65 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[32, 26, 10])).
% 0.43/0.65 tff(34,plain,
% 0.43/0.65 (ssList(nil) <=> ssList(nil)),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(35,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.43/0.65 tff(36,plain,
% 0.43/0.65 (ssList(nil)),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.43/0.65 tff(37,plain,
% 0.43/0.65 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(38,plain,
% 0.43/0.65 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))),
% 0.43/0.65 inference(quant_inst,[status(thm)],[])).
% 0.43/0.65 tff(39,plain,
% 0.43/0.65 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))))))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.43/0.65 tff(40,plain,
% 0.43/0.65 (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[39, 36, 33])).
% 0.43/0.65 tff(41,plain,
% 0.43/0.65 (((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))))) | ((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))),
% 0.43/0.65 inference(tautology,[status(thm)],[])).
% 0.43/0.65 tff(42,plain,
% 0.43/0.65 ((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.43/0.65 tff(43,plain,
% 0.43/0.65 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(44,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[43])).
% 0.43/0.65 tff(45,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(46,plain,
% 0.43/0.65 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(47,plain,
% 0.43/0.65 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[46])).
% 0.43/0.65 tff(48,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax45')).
% 0.43/0.65 tff(49,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.43/0.65 tff(50,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.43/0.65 tff(51,plain,(
% 0.43/0.65 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(skolemize,[status(sab)],[50])).
% 0.43/0.65 tff(52,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.43/0.65 tff(53,plain,
% 0.43/0.65 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(U!45)) | frontsegP(U!45, nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(U!45)) | frontsegP(U!45, nil))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(54,plain,
% 0.43/0.65 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(U!45)) | frontsegP(U!45, nil))),
% 0.43/0.65 inference(quant_inst,[status(thm)],[])).
% 0.43/0.65 tff(55,plain,
% 0.43/0.65 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(U!45)) | frontsegP(U!45, nil)),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.43/0.65 tff(56,plain,
% 0.43/0.65 (frontsegP(U!45, nil)),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[55, 52, 10])).
% 0.43/0.65 tff(57,plain,
% 0.43/0.65 ((~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))) | (~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 0.43/0.65 inference(tautology,[status(thm)],[])).
% 0.43/0.65 tff(58,plain,
% 0.43/0.65 ((~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.43/0.65 tff(59,plain,
% 0.43/0.65 (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.43/0.65 tff(60,plain,
% 0.43/0.65 (((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))) | (app(nil, tptp_fun_W_5(nil, U!45)) = U!45)),
% 0.43/0.65 inference(tautology,[status(thm)],[])).
% 0.43/0.65 tff(61,plain,
% 0.43/0.65 (app(nil, tptp_fun_W_5(nil, U!45)) = U!45),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.43/0.65 tff(62,plain,
% 0.43/0.65 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(63,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[62])).
% 0.43/0.65 tff(64,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(65,plain,
% 0.43/0.65 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.43/0.65 inference(bind,[status(th)],[])).
% 0.43/0.65 tff(66,plain,
% 0.43/0.65 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(quant_intro,[status(thm)],[65])).
% 0.43/0.65 tff(67,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.43/0.65 tff(68,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.43/0.65 tff(69,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.43/0.65 tff(70,plain,(
% 0.43/0.65 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(skolemize,[status(sab)],[69])).
% 0.43/0.65 tff(71,plain,
% 0.43/0.65 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.43/0.65 tff(72,plain,
% 0.43/0.65 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil))),
% 0.43/0.65 inference(rewrite,[status(thm)],[])).
% 0.43/0.65 tff(73,plain,
% 0.43/0.65 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 0.43/0.65 inference(quant_inst,[status(thm)],[])).
% 0.43/0.65 tff(74,plain,
% 0.43/0.65 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 0.43/0.65 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.43/0.65 tff(75,plain,
% 0.43/0.65 (app(nil, nil) = nil),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[74, 36, 71])).
% 0.43/0.65 tff(76,plain,
% 0.43/0.65 (app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = app(nil, tptp_fun_W_5(nil, U!45))),
% 0.43/0.65 inference(monotonicity,[status(thm)],[75])).
% 0.43/0.65 tff(77,plain,
% 0.43/0.65 (app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45),
% 0.43/0.65 inference(transitivity,[status(thm)],[76, 61])).
% 0.43/0.65 tff(78,plain,
% 0.43/0.65 (((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))) | ssList(tptp_fun_W_5(nil, U!45))),
% 0.43/0.65 inference(tautology,[status(thm)],[])).
% 0.43/0.65 tff(79,plain,
% 0.43/0.65 (ssList(tptp_fun_W_5(nil, U!45))),
% 0.43/0.65 inference(unit_resolution,[status(thm)],[78, 59])).
% 0.43/0.65 tff(80,plain,
% 0.43/0.65 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))))),
% 0.43/0.66 inference(bind,[status(th)],[])).
% 0.43/0.66 tff(81,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(quant_intro,[status(thm)],[80])).
% 0.43/0.66 tff(82,plain,
% 0.43/0.66 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))))),
% 0.43/0.66 inference(bind,[status(th)],[])).
% 0.43/0.66 tff(83,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(quant_intro,[status(thm)],[82])).
% 0.43/0.66 tff(84,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(transitivity,[status(thm)],[83, 81])).
% 0.43/0.66 tff(85,plain,
% 0.43/0.66 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45))))))),
% 0.43/0.66 inference(bind,[status(th)],[])).
% 0.43/0.66 tff(86,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(quant_intro,[status(thm)],[85])).
% 0.43/0.66 tff(87,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!45) & (app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(and_elim,[status(thm)],[9])).
% 0.43/0.66 tff(88,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.43/0.66 tff(89,plain,
% 0.43/0.66 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))),
% 0.43/0.66 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.43/0.66 tff(90,plain,
% 0.43/0.66 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))) | ((~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))) | (~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45)))))),
% 0.43/0.66 inference(rewrite,[status(thm)],[])).
% 0.43/0.66 tff(91,plain,
% 0.43/0.66 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))) | ((~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45)))))),
% 0.43/0.66 inference(quant_inst,[status(thm)],[])).
% 0.43/0.66 tff(92,plain,
% 0.43/0.66 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!45)) | (~(app(Y, X1) = U!45)))))) | (~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))),
% 0.43/0.66 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.43/0.66 tff(93,plain,
% 0.43/0.66 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))),
% 0.43/0.66 inference(unit_resolution,[status(thm)],[92, 36, 89])).
% 0.43/0.66 tff(94,plain,
% 0.43/0.66 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45))))),
% 0.43/0.66 inference(rewrite,[status(thm)],[])).
% 0.43/0.66 tff(95,plain,
% 0.43/0.66 (((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!45)) | (~(app(nil, X1) = U!45)))) <=> ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45))))),
% 0.43/0.66 inference(rewrite,[status(thm)],[])).
% 0.43/0.66 tff(96,plain,
% 0.43/0.66 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!45)) | (~(app(nil, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))))),
% 0.43/0.66 inference(monotonicity,[status(thm)],[95])).
% 0.43/0.66 tff(97,plain,
% 0.43/0.66 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!45)) | (~(app(nil, X1) = U!45))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45))))),
% 0.43/0.66 inference(transitivity,[status(thm)],[96, 94])).
% 0.43/0.66 tff(98,plain,
% 0.43/0.66 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!45)) | (~(app(nil, X1) = U!45))))),
% 0.43/0.66 inference(quant_inst,[status(thm)],[])).
% 0.43/0.66 tff(99,plain,
% 0.43/0.66 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!45)) | (~(app(nil, X1) = U!45))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))),
% 0.43/0.66 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.43/0.66 tff(100,plain,
% 0.43/0.66 (![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))),
% 0.43/0.66 inference(unit_resolution,[status(thm)],[99, 36, 93])).
% 0.43/0.66 tff(101,plain,
% 0.43/0.66 (((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45)))),
% 0.43/0.66 inference(rewrite,[status(thm)],[])).
% 0.43/0.66 tff(102,plain,
% 0.43/0.66 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45)))),
% 0.43/0.66 inference(quant_inst,[status(thm)],[])).
% 0.43/0.66 tff(103,plain,
% 0.43/0.66 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = U!45)) | (~(app(app(nil, nil), X1) = U!45)))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45))),
% 0.43/0.66 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.43/0.66 tff(104,plain,
% 0.43/0.66 (~(app(app(nil, nil), tptp_fun_W_5(nil, U!45)) = U!45)),
% 0.43/0.66 inference(unit_resolution,[status(thm)],[103, 100, 79, 61])).
% 0.43/0.66 tff(105,plain,
% 0.43/0.66 ($false),
% 0.43/0.66 inference(unit_resolution,[status(thm)],[104, 77])).
% 0.43/0.66 % SZS output end Proof
% 0.43/0.67 % E exiting
%------------------------------------------------------------------------------