%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC357+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:59 AM UTC 2025
% Result : Theorem 4.31s 4.47s
% Output : Proof 4.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC357+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:09:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 4.31/4.47 % SZS status Theorem
% 4.31/4.47 % SZS output start Proof
% 4.31/4.47 tff(tptp_fun_V_46_type, type, (
% 4.31/4.47 tptp_fun_V_46: $i)).
% 4.31/4.47 tff(app_type, type, (
% 4.31/4.47 app: ( $i * $i ) > $i)).
% 4.31/4.47 tff(tptp_fun_W_5_type, type, (
% 4.31/4.47 tptp_fun_W_5: ( $i * $i ) > $i)).
% 4.31/4.47 tff(tptp_fun_U_45_type, type, (
% 4.31/4.47 tptp_fun_U_45: $i)).
% 4.31/4.47 tff(tptp_fun_W_6_type, type, (
% 4.31/4.47 tptp_fun_W_6: ( $i * $i ) > $i)).
% 4.31/4.47 tff(nil_type, type, (
% 4.31/4.47 nil: $i)).
% 4.31/4.47 tff(ssList_type, type, (
% 4.31/4.47 ssList: $i > $o)).
% 4.31/4.47 tff(frontsegP_type, type, (
% 4.31/4.47 frontsegP: ( $i * $i ) > $o)).
% 4.31/4.47 tff(neq_type, type, (
% 4.31/4.47 neq: ( $i * $i ) > $o)).
% 4.31/4.47 tff(segmentP_type, type, (
% 4.31/4.47 segmentP: ( $i * $i ) > $o)).
% 4.31/4.47 tff(rearsegP_type, type, (
% 4.31/4.47 rearsegP: ( $i * $i ) > $o)).
% 4.31/4.47 tff(tptp_fun_X_8_type, type, (
% 4.31/4.47 tptp_fun_X_8: ( $i * $i ) > $i)).
% 4.31/4.47 tff(tptp_fun_W_7_type, type, (
% 4.31/4.47 tptp_fun_W_7: ( $i * $i ) > $i)).
% 4.31/4.47 tff(1,plain,
% 4.31/4.47 ((ssList(U!45) & (~(segmentP(V!46, U!45) | (~ssList(V!46)) | (((~(nil = V!46)) | (~(nil = U!45))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))) | (~neq(V!46, nil)) | (~ssList(U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(2,plain,
% 4.31/4.47 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U)))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(3,plain,
% 4.31/4.47 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~frontsegP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U)))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~frontsegP(X, W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 4.31/4.47 tff(5,plain,
% 4.31/4.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.31/4.47 tff(6,plain,
% 4.31/4.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.31/4.47 tff(7,plain,
% 4.31/4.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.31/4.47 tff(8,plain,
% 4.31/4.47 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (((~(nil = V)) | (~(nil = U))) & ((~frontsegP(V, U)) | (~neq(U, nil)))) | (~neq(V, nil)) | (~ssList(U))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[7, 2])).
% 4.31/4.47 tff(9,plain,
% 4.31/4.47 (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[8, 1])).
% 4.31/4.47 tff(10,plain,
% 4.31/4.47 (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))))),
% 4.31/4.47 inference(and_elim,[status(thm)],[9])).
% 4.31/4.47 tff(11,plain,
% 4.31/4.47 (ssList(V!46)),
% 4.31/4.47 inference(or_elim,[status(thm)],[10])).
% 4.31/4.47 tff(12,plain,
% 4.31/4.47 (^[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))))))))))),
% 4.31/4.47 inference(bind,[status(th)],[])).
% 4.31/4.47 tff(13,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(quant_intro,[status(thm)],[12])).
% 4.31/4.47 tff(14,plain,
% 4.31/4.47 (^[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))))))))))),
% 4.31/4.47 inference(bind,[status(th)],[])).
% 4.31/4.47 tff(15,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(quant_intro,[status(thm)],[14])).
% 4.31/4.47 tff(16,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(transitivity,[status(thm)],[15, 13])).
% 4.31/4.47 tff(17,plain,
% 4.31/4.47 (^[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))))))))))),
% 4.31/4.47 inference(bind,[status(th)],[])).
% 4.31/4.47 tff(18,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(quant_intro,[status(thm)],[17])).
% 4.31/4.47 tff(19,plain,
% 4.31/4.47 (![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)))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(20,plain,
% 4.31/4.47 (^[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)))))))),
% 4.31/4.47 inference(bind,[status(th)],[])).
% 4.31/4.47 tff(21,plain,
% 4.31/4.47 (![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)))))),
% 4.31/4.47 inference(quant_intro,[status(thm)],[20])).
% 4.31/4.47 tff(22,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')).
% 4.31/4.47 tff(23,plain,
% 4.31/4.47 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 4.31/4.47 tff(24,plain,
% 4.31/4.47 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 4.31/4.47 tff(25,plain,(
% 4.31/4.47 ![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)))))))),
% 4.31/4.47 inference(skolemize,[status(sab)],[24])).
% 4.31/4.47 tff(26,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 4.31/4.47 tff(27,plain,
% 4.31/4.47 (![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)))))))))),
% 4.31/4.47 inference(modus_ponens,[status(thm)],[26, 16])).
% 4.31/4.47 tff(28,plain,
% 4.31/4.47 (((~![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))))))))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(29,plain,
% 4.31/4.47 (((~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))))))))))),
% 4.31/4.47 inference(rewrite,[status(thm)],[])).
% 4.31/4.47 tff(30,plain,
% 4.31/4.47 (((~![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)))))))))))),
% 4.31/4.47 inference(monotonicity,[status(thm)],[29])).
% 4.31/4.47 tff(31,plain,
% 4.31/4.47 (((~![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))))))))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[30, 28])).
% 4.31/4.48 tff(32,plain,
% 4.31/4.48 ((~![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)))))))))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(33,plain,
% 4.31/4.48 ((~![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)))))))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 4.31/4.48 tff(34,plain,
% 4.31/4.48 (![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)))))))))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[33, 27, 11])).
% 4.31/4.48 tff(35,plain,
% 4.31/4.48 (ssList(U!45)),
% 4.31/4.48 inference(and_elim,[status(thm)],[9])).
% 4.31/4.48 tff(36,plain,
% 4.31/4.48 (((~![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)))))))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(37,plain,
% 4.31/4.48 ((~![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)))))))))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(38,plain,
% 4.31/4.48 ((~![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))))))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.31/4.48 tff(39,plain,
% 4.31/4.48 (~((~(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)))))))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[38, 35, 34])).
% 4.31/4.48 tff(40,plain,
% 4.31/4.48 (((~(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)))))),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(41,plain,
% 4.31/4.48 ((~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))))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[40, 39])).
% 4.31/4.48 tff(42,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(43,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[42])).
% 4.31/4.48 tff(44,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(45,plain,
% 4.31/4.48 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(46,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[45])).
% 4.31/4.48 tff(47,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 4.31/4.48 tff(48,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.31/4.48 tff(49,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[48, 44])).
% 4.31/4.48 tff(50,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(skolemize,[status(sab)],[49])).
% 4.31/4.48 tff(51,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[50, 43])).
% 4.31/4.48 tff(52,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(53,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(54,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[53, 52])).
% 4.31/4.48 tff(55,plain,
% 4.31/4.48 (segmentP(nil, V!46) <=> (nil = V!46)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[54, 51, 11])).
% 4.31/4.48 tff(56,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(57,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[56])).
% 4.31/4.48 tff(58,plain,
% 4.31/4.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(59,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[58])).
% 4.31/4.48 tff(60,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[59, 57])).
% 4.31/4.48 tff(61,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(62,plain,
% 4.31/4.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(63,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[62])).
% 4.31/4.48 tff(64,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 4.31/4.48 tff(65,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 4.31/4.48 tff(66,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[65, 61])).
% 4.31/4.48 tff(67,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(skolemize,[status(sab)],[66])).
% 4.31/4.48 tff(68,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[67, 60])).
% 4.31/4.48 tff(69,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(70,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(71,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 4.31/4.48 tff(72,plain,
% 4.31/4.48 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[71, 68, 11])).
% 4.31/4.48 tff(73,plain,
% 4.31/4.48 (ssList(nil) <=> ssList(nil)),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(74,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 4.31/4.48 tff(75,plain,
% 4.31/4.48 (ssList(nil)),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 4.31/4.48 tff(76,plain,
% 4.31/4.48 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(77,plain,
% 4.31/4.48 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(78,plain,
% 4.31/4.48 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.31/4.48 tff(79,plain,
% 4.31/4.48 (~((V!46 = nil) <=> neq(V!46, nil))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[78, 75, 72])).
% 4.31/4.48 tff(80,plain,
% 4.31/4.48 (neq(V!46, nil)),
% 4.31/4.48 inference(or_elim,[status(thm)],[10])).
% 4.31/4.48 tff(81,plain,
% 4.31/4.48 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(82,plain,
% 4.31/4.48 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[81, 80])).
% 4.31/4.48 tff(83,plain,
% 4.31/4.48 (~(V!46 = nil)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[82, 79])).
% 4.31/4.48 tff(84,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(85,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[84])).
% 4.31/4.48 tff(86,plain,
% 4.31/4.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(87,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[86])).
% 4.31/4.48 tff(88,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[87, 85])).
% 4.31/4.48 tff(89,plain,
% 4.31/4.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(90,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[89])).
% 4.31/4.48 tff(91,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(92,plain,
% 4.31/4.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(93,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[92])).
% 4.31/4.48 tff(94,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 4.31/4.48 tff(95,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 4.31/4.48 tff(96,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[95, 91])).
% 4.31/4.48 tff(97,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 4.31/4.48 inference(skolemize,[status(sab)],[96])).
% 4.31/4.48 tff(98,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[97, 90])).
% 4.31/4.48 tff(99,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[98, 88])).
% 4.31/4.48 tff(100,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(101,plain,
% 4.31/4.48 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(102,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 4.31/4.48 inference(monotonicity,[status(thm)],[101])).
% 4.31/4.48 tff(103,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[102, 100])).
% 4.31/4.48 tff(104,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(105,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 4.31/4.48 tff(106,plain,
% 4.31/4.48 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[105, 99, 11])).
% 4.31/4.48 tff(107,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(108,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[107])).
% 4.31/4.48 tff(109,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(110,plain,
% 4.31/4.48 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(111,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[110])).
% 4.31/4.48 tff(112,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 4.31/4.48 tff(113,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 4.31/4.48 tff(114,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[113, 109])).
% 4.31/4.48 tff(115,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(skolemize,[status(sab)],[114])).
% 4.31/4.48 tff(116,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[115, 108])).
% 4.31/4.48 tff(117,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(118,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(119,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[118, 117])).
% 4.31/4.48 tff(120,plain,
% 4.31/4.48 (segmentP(V!46, nil)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[119, 116, 11])).
% 4.31/4.48 tff(121,plain,
% 4.31/4.48 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(122,plain,
% 4.31/4.48 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(123,plain,
% 4.31/4.48 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 4.31/4.48 inference(monotonicity,[status(thm)],[122])).
% 4.31/4.48 tff(124,plain,
% 4.31/4.48 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 4.31/4.48 inference(transitivity,[status(thm)],[123, 121])).
% 4.31/4.48 tff(125,plain,
% 4.31/4.48 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(126,plain,
% 4.31/4.48 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[125, 124])).
% 4.31/4.48 tff(127,plain,
% 4.31/4.48 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[126, 75, 120, 106])).
% 4.31/4.48 tff(128,plain,
% 4.31/4.48 (~segmentP(nil, V!46)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[127, 83])).
% 4.31/4.48 tff(129,plain,
% 4.31/4.48 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(130,plain,
% 4.31/4.48 (~(nil = V!46)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[129, 128, 55])).
% 4.31/4.48 tff(131,plain,
% 4.31/4.48 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(132,plain,
% 4.31/4.48 ((~(nil = U!45)) | (~(nil = V!46))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[131, 130])).
% 4.31/4.48 tff(133,plain,
% 4.31/4.48 ((~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(134,plain,
% 4.31/4.48 ((((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))) <=> (~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(135,plain,
% 4.31/4.48 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))) <=> (~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))))))),
% 4.31/4.48 inference(monotonicity,[status(thm)],[134])).
% 4.31/4.48 tff(136,plain,
% 4.31/4.48 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[135, 133])).
% 4.31/4.48 tff(137,plain,
% 4.31/4.48 (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))),
% 4.31/4.48 inference(or_elim,[status(thm)],[10])).
% 4.31/4.48 tff(138,plain,
% 4.31/4.48 ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 4.31/4.48 tff(139,plain,
% 4.31/4.48 (~((~frontsegP(V!46, U!45)) | (~neq(U!45, nil)))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[138, 132])).
% 4.31/4.48 tff(140,plain,
% 4.31/4.48 (((~frontsegP(V!46, U!45)) | (~neq(U!45, nil))) | frontsegP(V!46, U!45)),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(141,plain,
% 4.31/4.48 (frontsegP(V!46, U!45)),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[140, 139])).
% 4.31/4.48 tff(142,plain,
% 4.31/4.48 ((~((~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))))),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(143,plain,
% 4.31/4.48 (~((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46)))),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[142, 141, 41])).
% 4.31/4.48 tff(144,plain,
% 4.31/4.48 (((~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)),
% 4.31/4.48 inference(tautology,[status(thm)],[])).
% 4.31/4.48 tff(145,plain,
% 4.31/4.48 (app(U!45, tptp_fun_W_5(U!45, V!46)) = V!46),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[144, 143])).
% 4.31/4.48 tff(146,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(147,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[146])).
% 4.31/4.48 tff(148,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(149,plain,
% 4.31/4.48 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(150,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[149])).
% 4.31/4.48 tff(151,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 4.31/4.48 tff(152,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[151, 150])).
% 4.31/4.48 tff(153,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[152, 148])).
% 4.31/4.48 tff(154,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(skolemize,[status(sab)],[153])).
% 4.31/4.48 tff(155,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[154, 147])).
% 4.31/4.48 tff(156,plain,
% 4.31/4.48 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(157,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(158,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 4.31/4.48 tff(159,plain,
% 4.31/4.48 (app(nil, U!45) = U!45),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[158, 155, 35])).
% 4.31/4.48 tff(160,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(161,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[160])).
% 4.31/4.48 tff(162,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(163,plain,
% 4.31/4.48 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(164,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[163])).
% 4.31/4.48 tff(165,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 4.31/4.48 tff(166,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[165, 164])).
% 4.31/4.48 tff(167,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[166, 162])).
% 4.31/4.48 tff(168,plain,(
% 4.31/4.48 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(skolemize,[status(sab)],[167])).
% 4.31/4.48 tff(169,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[168, 161])).
% 4.31/4.48 tff(170,plain,
% 4.31/4.48 (((~![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))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(171,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 4.31/4.48 inference(quant_inst,[status(thm)],[])).
% 4.31/4.48 tff(172,plain,
% 4.31/4.48 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 4.31/4.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 4.31/4.48 tff(173,plain,
% 4.31/4.48 (app(nil, nil) = nil),
% 4.31/4.48 inference(unit_resolution,[status(thm)],[172, 75, 169])).
% 4.31/4.48 tff(174,plain,
% 4.31/4.48 (nil = app(nil, nil)),
% 4.31/4.48 inference(symmetry,[status(thm)],[173])).
% 4.31/4.48 tff(175,plain,
% 4.31/4.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(176,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[175])).
% 4.31/4.48 tff(177,plain,
% 4.31/4.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(178,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[177])).
% 4.31/4.48 tff(179,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.48 inference(transitivity,[status(thm)],[178, 176])).
% 4.31/4.48 tff(180,plain,
% 4.31/4.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(181,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[180])).
% 4.31/4.48 tff(182,plain,
% 4.31/4.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.31/4.48 inference(rewrite,[status(thm)],[])).
% 4.31/4.48 tff(183,plain,
% 4.31/4.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 4.31/4.48 inference(bind,[status(th)],[])).
% 4.31/4.48 tff(184,plain,
% 4.31/4.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.31/4.48 inference(quant_intro,[status(thm)],[183])).
% 4.31/4.48 tff(185,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax6')).
% 4.31/4.49 tff(186,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[185, 184])).
% 4.31/4.49 tff(187,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[186, 182])).
% 4.31/4.49 tff(188,plain,(
% 4.31/4.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 4.31/4.49 inference(skolemize,[status(sab)],[187])).
% 4.31/4.49 tff(189,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[188, 181])).
% 4.31/4.49 tff(190,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[189, 179])).
% 4.31/4.49 tff(191,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(192,plain,
% 4.31/4.49 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(193,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))))),
% 4.31/4.49 inference(monotonicity,[status(thm)],[192])).
% 4.31/4.49 tff(194,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 4.31/4.49 inference(transitivity,[status(thm)],[193, 191])).
% 4.31/4.49 tff(195,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(196,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[195, 194])).
% 4.31/4.49 tff(197,plain,
% 4.31/4.49 (![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[196, 190, 75])).
% 4.31/4.49 tff(198,plain,
% 4.31/4.49 (((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | ((~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | (~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(199,plain,
% 4.31/4.49 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | ((~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(200,plain,
% 4.31/4.49 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | (~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 4.31/4.49 tff(201,plain,
% 4.31/4.49 (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[200, 75, 197])).
% 4.31/4.49 tff(202,plain,
% 4.31/4.49 (((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))))) | ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))),
% 4.31/4.49 inference(tautology,[status(thm)],[])).
% 4.31/4.49 tff(203,plain,
% 4.31/4.49 ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[202, 201])).
% 4.31/4.49 tff(204,plain,
% 4.31/4.49 (^[U: $i] : refl(((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(205,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[204])).
% 4.31/4.49 tff(206,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(207,plain,
% 4.31/4.49 (^[U: $i] : rewrite((ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(208,plain,
% 4.31/4.49 (![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[207])).
% 4.31/4.49 tff(209,axiom,(![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax52')).
% 4.31/4.49 tff(210,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[209, 208])).
% 4.31/4.49 tff(211,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[210, 206])).
% 4.31/4.49 tff(212,plain,(
% 4.31/4.49 ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(skolemize,[status(sab)],[211])).
% 4.31/4.49 tff(213,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[212, 205])).
% 4.31/4.49 tff(214,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(215,plain,
% 4.31/4.49 (((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil))) <=> ((~ssList(nil)) | rearsegP(nil, nil))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(216,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil)))),
% 4.31/4.49 inference(monotonicity,[status(thm)],[215])).
% 4.31/4.49 tff(217,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 4.31/4.49 inference(transitivity,[status(thm)],[216, 214])).
% 4.31/4.49 tff(218,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(219,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil)),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[218, 217])).
% 4.31/4.49 tff(220,plain,
% 4.31/4.49 (rearsegP(nil, nil)),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[219, 75, 213])).
% 4.31/4.49 tff(221,plain,
% 4.31/4.49 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 4.31/4.49 inference(tautology,[status(thm)],[])).
% 4.31/4.49 tff(222,plain,
% 4.31/4.49 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[221, 220])).
% 4.31/4.49 tff(223,plain,
% 4.31/4.49 (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[222, 203])).
% 4.31/4.49 tff(224,plain,
% 4.31/4.49 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | (app(tptp_fun_W_6(nil, nil), nil) = nil)),
% 4.31/4.49 inference(tautology,[status(thm)],[])).
% 4.31/4.49 tff(225,plain,
% 4.31/4.49 (app(tptp_fun_W_6(nil, nil), nil) = nil),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[224, 223])).
% 4.31/4.49 tff(226,plain,
% 4.31/4.49 (app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)),
% 4.31/4.49 inference(transitivity,[status(thm)],[225, 174])).
% 4.31/4.49 tff(227,plain,
% 4.31/4.49 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | ssList(tptp_fun_W_6(nil, nil))),
% 4.31/4.49 inference(tautology,[status(thm)],[])).
% 4.31/4.49 tff(228,plain,
% 4.31/4.49 (ssList(tptp_fun_W_6(nil, nil))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[227, 223])).
% 4.31/4.49 tff(229,plain,
% 4.31/4.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(230,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[229])).
% 4.31/4.49 tff(231,plain,
% 4.31/4.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(232,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[231])).
% 4.31/4.49 tff(233,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(transitivity,[status(thm)],[232, 230])).
% 4.31/4.49 tff(234,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(235,plain,
% 4.31/4.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(W, V) = app(U, V)) => (W = U)) <=> ((~(app(W, V) = app(U, V))) | (W = U))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> (ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))))), rewrite((ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), (![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(236,plain,
% 4.31/4.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[235])).
% 4.31/4.49 tff(237,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax79')).
% 4.31/4.49 tff(238,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[237, 236])).
% 4.31/4.49 tff(239,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[238, 234])).
% 4.31/4.49 tff(240,plain,(
% 4.31/4.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(skolemize,[status(sab)],[239])).
% 4.31/4.49 tff(241,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[240, 233])).
% 4.31/4.49 tff(242,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(243,plain,
% 4.31/4.49 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V)))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(244,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))))),
% 4.31/4.49 inference(monotonicity,[status(thm)],[243])).
% 4.31/4.49 tff(245,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 4.31/4.49 inference(transitivity,[status(thm)],[244, 242])).
% 4.31/4.49 tff(246,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(247,plain,
% 4.31/4.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[246, 245])).
% 4.31/4.49 tff(248,plain,
% 4.31/4.49 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[247, 75, 241])).
% 4.31/4.49 tff(249,plain,
% 4.31/4.49 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(250,plain,
% 4.31/4.49 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(251,plain,
% 4.31/4.49 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[250, 249])).
% 4.31/4.49 tff(252,plain,
% 4.31/4.49 (![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[251, 75, 248])).
% 4.31/4.49 tff(253,plain,
% 4.31/4.49 (((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(254,plain,
% 4.31/4.49 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 4.31/4.49 inference(quant_inst,[status(thm)],[])).
% 4.31/4.49 tff(255,plain,
% 4.31/4.49 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[254, 253])).
% 4.31/4.49 tff(256,plain,
% 4.31/4.49 (tptp_fun_W_6(nil, nil) = nil),
% 4.31/4.49 inference(unit_resolution,[status(thm)],[255, 252, 228, 226])).
% 4.31/4.49 tff(257,plain,
% 4.31/4.49 (app(tptp_fun_W_6(nil, nil), U!45) = app(nil, U!45)),
% 4.31/4.49 inference(monotonicity,[status(thm)],[256])).
% 4.31/4.49 tff(258,plain,
% 4.31/4.49 (app(tptp_fun_W_6(nil, nil), U!45) = U!45),
% 4.31/4.49 inference(transitivity,[status(thm)],[257, 159])).
% 4.31/4.49 tff(259,plain,
% 4.31/4.49 (app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = app(U!45, tptp_fun_W_5(U!45, V!46))),
% 4.31/4.49 inference(monotonicity,[status(thm)],[258])).
% 4.31/4.49 tff(260,plain,
% 4.31/4.49 (app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46),
% 4.31/4.49 inference(transitivity,[status(thm)],[259, 145])).
% 4.31/4.49 tff(261,plain,
% 4.31/4.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(262,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[261])).
% 4.31/4.49 tff(263,plain,
% 4.31/4.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(264,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[263])).
% 4.31/4.49 tff(265,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(transitivity,[status(thm)],[264, 262])).
% 4.31/4.49 tff(266,plain,
% 4.31/4.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(267,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[266])).
% 4.31/4.49 tff(268,plain,
% 4.31/4.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(269,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[268])).
% 4.31/4.49 tff(270,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 4.31/4.49 inference(rewrite,[status(thm)],[])).
% 4.31/4.49 tff(271,plain,
% 4.31/4.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 4.31/4.49 inference(bind,[status(th)],[])).
% 4.31/4.49 tff(272,plain,
% 4.31/4.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 4.31/4.49 inference(quant_intro,[status(thm)],[271])).
% 4.31/4.49 tff(273,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax7')).
% 4.31/4.49 tff(274,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[273, 272])).
% 4.31/4.49 tff(275,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[274, 270])).
% 4.31/4.49 tff(276,plain,(
% 4.31/4.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 4.31/4.49 inference(skolemize,[status(sab)],[275])).
% 4.31/4.49 tff(277,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[276, 269])).
% 4.31/4.49 tff(278,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[277, 267])).
% 4.31/4.49 tff(279,plain,
% 4.31/4.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 4.31/4.49 inference(modus_ponens,[status(thm)],[278, 265])).
% 4.31/4.49 tff(280,plain,
% 4.31/4.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 4.31/4.50 inference(rewrite,[status(thm)],[])).
% 4.31/4.50 tff(281,plain,
% 4.31/4.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 4.31/4.50 inference(quant_inst,[status(thm)],[])).
% 4.31/4.50 tff(282,plain,
% 4.31/4.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 4.31/4.50 inference(modus_ponens,[status(thm)],[281, 280])).
% 4.31/4.50 tff(283,plain,
% 4.31/4.50 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 4.31/4.50 inference(unit_resolution,[status(thm)],[282, 279, 11])).
% 4.31/4.50 tff(284,plain,
% 4.31/4.50 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 4.31/4.50 inference(rewrite,[status(thm)],[])).
% 4.31/4.50 tff(285,plain,
% 4.31/4.50 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 4.31/4.50 inference(quant_inst,[status(thm)],[])).
% 4.31/4.50 tff(286,plain,
% 4.31/4.50 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))))),
% 4.31/4.50 inference(modus_ponens,[status(thm)],[285, 284])).
% 4.31/4.50 tff(287,plain,
% 4.31/4.50 (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))),
% 4.31/4.50 inference(unit_resolution,[status(thm)],[286, 35, 283])).
% 4.31/4.50 tff(288,plain,
% 4.31/4.50 (((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))) | (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))),
% 4.31/4.50 inference(tautology,[status(thm)],[])).
% 4.31/4.50 tff(289,plain,
% 4.31/4.50 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.31/4.50 inference(unit_resolution,[status(thm)],[288, 287])).
% 4.31/4.50 tff(290,plain,
% 4.31/4.50 (~segmentP(V!46, U!45)),
% 4.31/4.50 inference(or_elim,[status(thm)],[10])).
% 4.31/4.50 tff(291,plain,
% 4.31/4.50 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.31/4.50 inference(tautology,[status(thm)],[])).
% 4.31/4.50 tff(292,plain,
% 4.31/4.50 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.31/4.50 inference(unit_resolution,[status(thm)],[291, 290])).
% 4.31/4.50 tff(293,plain,
% 4.31/4.50 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.31/4.50 inference(unit_resolution,[status(thm)],[292, 289])).
% 4.31/4.50 tff(294,plain,
% 4.31/4.50 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))),
% 4.31/4.50 inference(rewrite,[status(thm)],[])).
% 4.31/4.50 tff(295,plain,
% 4.31/4.50 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))),
% 4.31/4.50 inference(quant_inst,[status(thm)],[])).
% 4.31/4.50 tff(296,plain,
% 4.31/4.50 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))),
% 4.31/4.52 inference(modus_ponens,[status(thm)],[295, 294])).
% 4.31/4.52 tff(297,plain,
% 4.31/4.52 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))),
% 4.31/4.52 inference(unit_resolution,[status(thm)],[296, 228, 293])).
% 4.31/4.52 tff(298,plain,
% 4.31/4.52 (((~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))),
% 4.31/4.52 inference(tautology,[status(thm)],[])).
% 4.31/4.52 tff(299,plain,
% 4.31/4.52 (ssList(tptp_fun_W_5(U!45, V!46))),
% 4.31/4.52 inference(unit_resolution,[status(thm)],[298, 143])).
% 4.31/4.52 tff(300,plain,
% 4.31/4.52 (((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | (~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46)))),
% 4.31/4.52 inference(rewrite,[status(thm)],[])).
% 4.31/4.52 tff(301,plain,
% 4.31/4.52 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | ((~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46)))),
% 4.31/4.52 inference(quant_inst,[status(thm)],[])).
% 4.31/4.52 tff(302,plain,
% 4.31/4.52 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | (~ssList(tptp_fun_W_5(U!45, V!46))) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46))),
% 4.31/4.52 inference(modus_ponens,[status(thm)],[301, 300])).
% 4.31/4.52 tff(303,plain,
% 4.31/4.52 (~(app(app(tptp_fun_W_6(nil, nil), U!45), tptp_fun_W_5(U!45, V!46)) = V!46)),
% 4.31/4.52 inference(unit_resolution,[status(thm)],[302, 299, 297])).
% 4.31/4.52 tff(304,plain,
% 4.31/4.52 ($false),
% 4.31/4.52 inference(unit_resolution,[status(thm)],[303, 260])).
% 4.31/4.52 % SZS output end Proof
% 4.31/4.52 % E exiting
%------------------------------------------------------------------------------