%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC122+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:30:13 AM UTC 2025
% Result : Theorem 4.86s 5.07s
% Output : Proof 4.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWC122+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 08:24:42 EDT 2025
% 0.14/0.37 % CPUTime :
% 4.86/5.07 % SZS status Theorem
% 4.86/5.07 % SZS output start Proof
% 4.86/5.07 tff(tptp_fun_V_46_type, type, (
% 4.86/5.07 tptp_fun_V_46: $i)).
% 4.86/5.07 tff(app_type, type, (
% 4.86/5.07 app: ( $i * $i ) > $i)).
% 4.86/5.07 tff(nil_type, type, (
% 4.86/5.07 nil: $i)).
% 4.86/5.07 tff(tptp_fun_U_45_type, type, (
% 4.86/5.07 tptp_fun_U_45: $i)).
% 4.86/5.07 tff(tptp_fun_W_6_type, type, (
% 4.86/5.07 tptp_fun_W_6: ( $i * $i ) > $i)).
% 4.86/5.07 tff(ssList_type, type, (
% 4.86/5.07 ssList: $i > $o)).
% 4.86/5.07 tff(segmentP_type, type, (
% 4.86/5.07 segmentP: ( $i * $i ) > $o)).
% 4.86/5.07 tff(neq_type, type, (
% 4.86/5.07 neq: ( $i * $i ) > $o)).
% 4.86/5.07 tff(rearsegP_type, type, (
% 4.86/5.07 rearsegP: ( $i * $i ) > $o)).
% 4.86/5.07 tff(tptp_fun_X_8_type, type, (
% 4.86/5.07 tptp_fun_X_8: ( $i * $i ) > $i)).
% 4.86/5.07 tff(tptp_fun_W_7_type, type, (
% 4.86/5.07 tptp_fun_W_7: ( $i * $i ) > $i)).
% 4.86/5.07 tff(1,plain,
% 4.86/5.07 ((ssList(U!45) & (~((neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)) | (~ssList(U!45)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45)))))),
% 4.86/5.07 inference(rewrite,[status(thm)],[])).
% 4.86/5.07 tff(2,plain,
% 4.86/5.07 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U)))))),
% 4.86/5.07 inference(rewrite,[status(thm)],[])).
% 4.86/5.07 tff(3,plain,
% 4.86/5.07 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ((~(nil = W)) & (nil = X))) | (neq(U, nil) & segmentP(V, U))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U)))))),
% 4.86/5.07 inference(rewrite,[status(thm)],[])).
% 4.86/5.07 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))) | ((~(nil = W)) & (nil = X))) | (neq(U, nil) & segmentP(V, U))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 4.86/5.07 tff(5,plain,
% 4.86/5.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.86/5.07 tff(6,plain,
% 4.86/5.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.86/5.07 tff(7,plain,
% 4.86/5.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.86/5.07 tff(8,plain,
% 4.86/5.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((neq(V, nil) & ((~neq(U, nil)) | (~rearsegP(V, U)))) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[7, 2])).
% 4.86/5.07 tff(9,plain,
% 4.86/5.07 (ssList(U!45) & (~((~ssList(U!45)) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45))))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[8, 1])).
% 4.86/5.07 tff(10,plain,
% 4.86/5.07 (~((~ssList(U!45)) | (neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))) | ((~(nil = U!45)) & (nil = V!46)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45)))),
% 4.86/5.07 inference(and_elim,[status(thm)],[9])).
% 4.86/5.07 tff(11,plain,
% 4.86/5.07 (ssList(V!46)),
% 4.86/5.07 inference(or_elim,[status(thm)],[10])).
% 4.86/5.07 tff(12,plain,
% 4.86/5.07 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 4.86/5.07 inference(bind,[status(th)],[])).
% 4.86/5.07 tff(13,plain,
% 4.86/5.07 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(quant_intro,[status(thm)],[12])).
% 4.86/5.07 tff(14,plain,
% 4.86/5.07 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(rewrite,[status(thm)],[])).
% 4.86/5.07 tff(15,plain,
% 4.86/5.07 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 4.86/5.07 inference(bind,[status(th)],[])).
% 4.86/5.07 tff(16,plain,
% 4.86/5.07 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(quant_intro,[status(thm)],[15])).
% 4.86/5.07 tff(17,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 4.86/5.07 tff(18,plain,
% 4.86/5.07 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[17, 16])).
% 4.86/5.07 tff(19,plain,
% 4.86/5.07 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[18, 14])).
% 4.86/5.07 tff(20,plain,(
% 4.86/5.07 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(skolemize,[status(sab)],[19])).
% 4.86/5.07 tff(21,plain,
% 4.86/5.07 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 4.86/5.07 inference(modus_ponens,[status(thm)],[20, 13])).
% 4.86/5.07 tff(22,plain,
% 4.86/5.07 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 4.86/5.07 inference(rewrite,[status(thm)],[])).
% 4.86/5.07 tff(23,plain,
% 4.86/5.07 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 4.86/5.07 inference(quant_inst,[status(thm)],[])).
% 4.86/5.07 tff(24,plain,
% 4.86/5.07 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[23, 22])).
% 4.86/5.08 tff(25,plain,
% 4.86/5.08 (app(V!46, nil) = V!46),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 4.86/5.08 tff(26,plain,
% 4.86/5.08 (^[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))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(27,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[26])).
% 4.86/5.08 tff(28,plain,
% 4.86/5.08 (^[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))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(29,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[28])).
% 4.86/5.08 tff(30,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(transitivity,[status(thm)],[29, 27])).
% 4.86/5.08 tff(31,plain,
% 4.86/5.08 (^[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))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(32,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[31])).
% 4.86/5.08 tff(33,plain,
% 4.86/5.08 (![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)))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(34,plain,
% 4.86/5.08 (^[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)))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(35,plain,
% 4.86/5.08 (![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)))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[34])).
% 4.86/5.08 tff(36,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax6')).
% 4.86/5.08 tff(37,plain,
% 4.86/5.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[36, 35])).
% 4.86/5.08 tff(38,plain,
% 4.86/5.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[37, 33])).
% 4.86/5.08 tff(39,plain,(
% 4.86/5.08 ![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)))))))),
% 4.86/5.08 inference(skolemize,[status(sab)],[38])).
% 4.86/5.08 tff(40,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[39, 32])).
% 4.86/5.08 tff(41,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[40, 30])).
% 4.86/5.08 tff(42,plain,
% 4.86/5.08 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(43,plain,
% 4.86/5.08 (((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))))))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(44,plain,
% 4.86/5.08 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))))),
% 4.86/5.08 inference(monotonicity,[status(thm)],[43])).
% 4.86/5.08 tff(45,plain,
% 4.86/5.08 (((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))) <=> ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 4.86/5.08 inference(transitivity,[status(thm)],[44, 42])).
% 4.86/5.08 tff(46,plain,
% 4.86/5.08 ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))),
% 4.86/5.08 inference(quant_inst,[status(thm)],[])).
% 4.86/5.08 tff(47,plain,
% 4.86/5.08 ((~![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(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[46, 45])).
% 4.86/5.08 tff(48,plain,
% 4.86/5.08 (![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[47, 41, 11])).
% 4.86/5.08 tff(49,plain,
% 4.86/5.08 (ssList(U!45)),
% 4.86/5.08 inference(and_elim,[status(thm)],[9])).
% 4.86/5.08 tff(50,plain,
% 4.86/5.08 (((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | (~ssList(U!45)) | (~((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(51,plain,
% 4.86/5.08 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | ((~ssList(U!45)) | (~((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))))))),
% 4.86/5.08 inference(quant_inst,[status(thm)],[])).
% 4.86/5.08 tff(52,plain,
% 4.86/5.08 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | (~ssList(U!45)) | (~((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[51, 50])).
% 4.86/5.08 tff(53,plain,
% 4.86/5.08 (~((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[52, 49, 48])).
% 4.86/5.08 tff(54,plain,
% 4.86/5.08 (((~(rearsegP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | (~(app(W, U!45) = V!46))))) | (~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))))))) | ((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))),
% 4.86/5.08 inference(tautology,[status(thm)],[])).
% 4.86/5.08 tff(55,plain,
% 4.86/5.08 ((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[54, 53])).
% 4.86/5.08 tff(56,plain,
% 4.86/5.08 (neq(V!46, nil)),
% 4.86/5.08 inference(or_elim,[status(thm)],[10])).
% 4.86/5.08 tff(57,plain,
% 4.86/5.08 ((~(~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))))) <=> ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(58,plain,
% 4.86/5.08 ((neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))) <=> (~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(59,plain,
% 4.86/5.08 ((~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))) <=> (~(~((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))))))),
% 4.86/5.08 inference(monotonicity,[status(thm)],[58])).
% 4.86/5.08 tff(60,plain,
% 4.86/5.08 ((~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))) <=> ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))))),
% 4.86/5.08 inference(transitivity,[status(thm)],[59, 57])).
% 4.86/5.08 tff(61,plain,
% 4.86/5.08 (~(neq(V!46, nil) & ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))),
% 4.86/5.08 inference(or_elim,[status(thm)],[10])).
% 4.86/5.08 tff(62,plain,
% 4.86/5.08 ((~neq(V!46, nil)) | (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[61, 60])).
% 4.86/5.08 tff(63,plain,
% 4.86/5.08 (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[62, 56])).
% 4.86/5.08 tff(64,plain,
% 4.86/5.08 (((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))) | rearsegP(V!46, U!45)),
% 4.86/5.08 inference(tautology,[status(thm)],[])).
% 4.86/5.08 tff(65,plain,
% 4.86/5.08 (rearsegP(V!46, U!45)),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[64, 63])).
% 4.86/5.08 tff(66,plain,
% 4.86/5.08 ((~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))) | (~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))))),
% 4.86/5.08 inference(tautology,[status(thm)],[])).
% 4.86/5.08 tff(67,plain,
% 4.86/5.08 ((~((~rearsegP(V!46, U!45)) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))))) | (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[66, 65])).
% 4.86/5.08 tff(68,plain,
% 4.86/5.08 (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[67, 55])).
% 4.86/5.08 tff(69,plain,
% 4.86/5.08 (((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))) | (app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)),
% 4.86/5.08 inference(tautology,[status(thm)],[])).
% 4.86/5.08 tff(70,plain,
% 4.86/5.08 (app(tptp_fun_W_6(U!45, V!46), U!45) = V!46),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[69, 68])).
% 4.86/5.08 tff(71,plain,
% 4.86/5.08 (app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = app(V!46, nil)),
% 4.86/5.08 inference(monotonicity,[status(thm)],[70])).
% 4.86/5.08 tff(72,plain,
% 4.86/5.08 (app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46),
% 4.86/5.08 inference(transitivity,[status(thm)],[71, 25])).
% 4.86/5.08 tff(73,plain,
% 4.86/5.08 (^[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)))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(74,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[73])).
% 4.86/5.08 tff(75,plain,
% 4.86/5.08 (^[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)))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(76,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[75])).
% 4.86/5.08 tff(77,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(transitivity,[status(thm)],[76, 74])).
% 4.86/5.08 tff(78,plain,
% 4.86/5.08 (^[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)))))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(79,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[78])).
% 4.86/5.08 tff(80,plain,
% 4.86/5.08 (^[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)))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(81,plain,
% 4.86/5.08 (![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))))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[80])).
% 4.86/5.08 tff(82,plain,
% 4.86/5.08 (![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))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(83,plain,
% 4.86/5.08 (^[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))))))))),
% 4.86/5.08 inference(bind,[status(th)],[])).
% 4.86/5.08 tff(84,plain,
% 4.86/5.08 (![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))))))),
% 4.86/5.08 inference(quant_intro,[status(thm)],[83])).
% 4.86/5.08 tff(85,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/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 4.86/5.08 tff(86,plain,
% 4.86/5.08 (![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))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[85, 84])).
% 4.86/5.08 tff(87,plain,
% 4.86/5.08 (![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))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[86, 82])).
% 4.86/5.08 tff(88,plain,(
% 4.86/5.08 ![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))))))))),
% 4.86/5.08 inference(skolemize,[status(sab)],[87])).
% 4.86/5.08 tff(89,plain,
% 4.86/5.08 (![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))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[88, 81])).
% 4.86/5.08 tff(90,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[89, 79])).
% 4.86/5.08 tff(91,plain,
% 4.86/5.08 (![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))))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[90, 77])).
% 4.86/5.08 tff(92,plain,
% 4.86/5.08 (((~![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))))))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(93,plain,
% 4.86/5.08 ((~![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))))))))))),
% 4.86/5.08 inference(quant_inst,[status(thm)],[])).
% 4.86/5.08 tff(94,plain,
% 4.86/5.08 ((~![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)))))))))),
% 4.86/5.08 inference(modus_ponens,[status(thm)],[93, 92])).
% 4.86/5.08 tff(95,plain,
% 4.86/5.08 (![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)))))))))),
% 4.86/5.08 inference(unit_resolution,[status(thm)],[94, 91, 11])).
% 4.86/5.08 tff(96,plain,
% 4.86/5.08 (((~![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)))))))))),
% 4.86/5.08 inference(rewrite,[status(thm)],[])).
% 4.86/5.08 tff(97,plain,
% 4.86/5.08 ((~![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)))))))))),
% 4.86/5.09 inference(quant_inst,[status(thm)],[])).
% 4.86/5.09 tff(98,plain,
% 4.86/5.09 ((~![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))))))))),
% 4.86/5.09 inference(modus_ponens,[status(thm)],[97, 96])).
% 4.86/5.09 tff(99,plain,
% 4.86/5.09 (~((~((~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)))))))),
% 4.86/5.09 inference(unit_resolution,[status(thm)],[98, 49, 95])).
% 4.86/5.09 tff(100,plain,
% 4.86/5.09 (((~((~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)))))),
% 4.86/5.09 inference(tautology,[status(thm)],[])).
% 4.86/5.09 tff(101,plain,
% 4.86/5.09 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.86/5.09 inference(unit_resolution,[status(thm)],[100, 99])).
% 4.86/5.09 tff(102,plain,
% 4.86/5.09 (((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))) | neq(U!45, nil)),
% 4.86/5.09 inference(tautology,[status(thm)],[])).
% 4.86/5.09 tff(103,plain,
% 4.86/5.09 (neq(U!45, nil)),
% 4.86/5.09 inference(unit_resolution,[status(thm)],[102, 63])).
% 4.86/5.09 tff(104,plain,
% 4.86/5.09 ((~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 4.86/5.09 inference(rewrite,[status(thm)],[])).
% 4.86/5.09 tff(105,plain,
% 4.86/5.09 ((neq(U!45, nil) & segmentP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 4.86/5.09 inference(rewrite,[status(thm)],[])).
% 4.86/5.09 tff(106,plain,
% 4.86/5.09 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 4.86/5.09 inference(monotonicity,[status(thm)],[105])).
% 4.86/5.09 tff(107,plain,
% 4.86/5.09 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 4.86/5.09 inference(transitivity,[status(thm)],[106, 104])).
% 4.86/5.09 tff(108,plain,
% 4.86/5.09 (~(neq(U!45, nil) & segmentP(V!46, U!45))),
% 4.86/5.09 inference(or_elim,[status(thm)],[10])).
% 4.86/5.09 tff(109,plain,
% 4.86/5.09 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 4.86/5.09 inference(modus_ponens,[status(thm)],[108, 107])).
% 4.86/5.09 tff(110,plain,
% 4.86/5.09 (~segmentP(V!46, U!45)),
% 4.86/5.09 inference(unit_resolution,[status(thm)],[109, 103])).
% 4.86/5.09 tff(111,plain,
% 4.86/5.09 ((~(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))))),
% 4.86/5.09 inference(tautology,[status(thm)],[])).
% 4.86/5.09 tff(112,plain,
% 4.86/5.09 ((~(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))))),
% 4.86/5.09 inference(unit_resolution,[status(thm)],[111, 110])).
% 4.86/5.09 tff(113,plain,
% 4.86/5.09 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 4.94/5.11 inference(unit_resolution,[status(thm)],[112, 101])).
% 4.94/5.11 tff(114,plain,
% 4.94/5.11 (((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46))) | ssList(tptp_fun_W_6(U!45, V!46))),
% 4.94/5.11 inference(tautology,[status(thm)],[])).
% 4.94/5.11 tff(115,plain,
% 4.94/5.11 (ssList(tptp_fun_W_6(U!45, V!46))),
% 4.94/5.11 inference(unit_resolution,[status(thm)],[114, 68])).
% 4.94/5.11 tff(116,plain,
% 4.94/5.11 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(U!45, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), 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(U!45, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46))))),
% 4.94/5.11 inference(rewrite,[status(thm)],[])).
% 4.94/5.11 tff(117,plain,
% 4.94/5.11 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(U!45, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46))))),
% 4.94/5.11 inference(quant_inst,[status(thm)],[])).
% 4.94/5.11 tff(118,plain,
% 4.94/5.11 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_6(U!45, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))),
% 4.94/5.11 inference(modus_ponens,[status(thm)],[117, 116])).
% 4.94/5.11 tff(119,plain,
% 4.94/5.11 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))),
% 4.94/5.11 inference(unit_resolution,[status(thm)],[118, 115, 113])).
% 4.94/5.11 tff(120,plain,
% 4.94/5.11 (ssList(nil) <=> ssList(nil)),
% 4.94/5.11 inference(rewrite,[status(thm)],[])).
% 4.94/5.11 tff(121,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 4.94/5.11 tff(122,plain,
% 4.94/5.11 (ssList(nil)),
% 4.94/5.11 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.94/5.11 tff(123,plain,
% 4.94/5.11 (((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))) | ((~ssList(nil)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))) | (~ssList(nil)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46)))),
% 4.94/5.11 inference(rewrite,[status(thm)],[])).
% 4.94/5.11 tff(124,plain,
% 4.94/5.11 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))) | ((~ssList(nil)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46)))),
% 4.94/5.11 inference(quant_inst,[status(thm)],[])).
% 4.94/5.11 tff(125,plain,
% 4.94/5.11 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))) | (~ssList(nil)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46))),
% 4.94/5.11 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.94/5.11 tff(126,plain,
% 4.94/5.11 (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46)),
% 4.94/5.11 inference(unit_resolution,[status(thm)],[125, 122, 119])).
% 4.94/5.11 tff(127,plain,
% 4.94/5.11 ($false),
% 4.94/5.11 inference(unit_resolution,[status(thm)],[126, 72])).
% 4.94/5.11 % SZS output end Proof
% 4.94/5.11 % E exiting
%------------------------------------------------------------------------------