%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC373+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:03 AM UTC 2025
% Result : Theorem 2.84s 3.05s
% Output : Proof 2.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC373+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:09:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.84/3.05 % SZS status Theorem
% 2.84/3.05 % SZS output start Proof
% 2.84/3.05 tff(tptp_fun_V_46_type, type, (
% 2.84/3.05 tptp_fun_V_46: $i)).
% 2.84/3.05 tff(app_type, type, (
% 2.84/3.05 app: ( $i * $i ) > $i)).
% 2.84/3.05 tff(nil_type, type, (
% 2.84/3.05 nil: $i)).
% 2.84/3.05 tff(tptp_fun_U_45_type, type, (
% 2.84/3.05 tptp_fun_U_45: $i)).
% 2.84/3.05 tff(tptp_fun_W_6_type, type, (
% 2.84/3.05 tptp_fun_W_6: ( $i * $i ) > $i)).
% 2.84/3.05 tff(ssList_type, type, (
% 2.84/3.05 ssList: $i > $o)).
% 2.84/3.05 tff(rearsegP_type, type, (
% 2.84/3.05 rearsegP: ( $i * $i ) > $o)).
% 2.84/3.05 tff(segmentP_type, type, (
% 2.84/3.05 segmentP: ( $i * $i ) > $o)).
% 2.84/3.05 tff(tptp_fun_X_8_type, type, (
% 2.84/3.05 tptp_fun_X_8: ( $i * $i ) > $i)).
% 2.84/3.05 tff(tptp_fun_W_7_type, type, (
% 2.84/3.05 tptp_fun_W_7: ( $i * $i ) > $i)).
% 2.84/3.05 tff(1,plain,
% 2.84/3.05 ((ssList(U!45) & (~(segmentP(V!46, U!45) | (~rearsegP(V!46, U!45)) | (~ssList(V!46)) | (~ssList(U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~rearsegP(V!46, U!45)) | (~ssList(V!46)))))),
% 2.84/3.05 inference(rewrite,[status(thm)],[])).
% 2.84/3.05 tff(2,plain,
% 2.84/3.05 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U)))))),
% 2.84/3.05 inference(rewrite,[status(thm)],[])).
% 2.84/3.05 tff(3,plain,
% 2.84/3.05 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~rearsegP(X, W))) | segmentP(V, U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U)))))),
% 2.84/3.05 inference(rewrite,[status(thm)],[])).
% 2.84/3.05 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~rearsegP(X, W))) | segmentP(V, U))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 2.84/3.05 tff(5,plain,
% 2.84/3.05 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U))))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.84/3.05 tff(6,plain,
% 2.84/3.05 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U))))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[5, 2])).
% 2.84/3.05 tff(7,plain,
% 2.84/3.05 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U))))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.84/3.05 tff(8,plain,
% 2.84/3.05 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~rearsegP(V, U)) | (~ssList(V)) | (~ssList(U))))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[7, 2])).
% 2.84/3.05 tff(9,plain,
% 2.84/3.05 (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~rearsegP(V!46, U!45)) | (~ssList(V!46))))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[8, 1])).
% 2.84/3.05 tff(10,plain,
% 2.84/3.05 (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~rearsegP(V!46, U!45)) | (~ssList(V!46)))),
% 2.84/3.05 inference(and_elim,[status(thm)],[9])).
% 2.84/3.05 tff(11,plain,
% 2.84/3.05 (ssList(V!46)),
% 2.84/3.05 inference(or_elim,[status(thm)],[10])).
% 2.84/3.05 tff(12,plain,
% 2.84/3.05 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.84/3.05 inference(bind,[status(th)],[])).
% 2.84/3.05 tff(13,plain,
% 2.84/3.05 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.05 inference(quant_intro,[status(thm)],[12])).
% 2.84/3.05 tff(14,plain,
% 2.84/3.05 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.05 inference(rewrite,[status(thm)],[])).
% 2.84/3.05 tff(15,plain,
% 2.84/3.05 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.84/3.05 inference(bind,[status(th)],[])).
% 2.84/3.05 tff(16,plain,
% 2.84/3.05 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.05 inference(quant_intro,[status(thm)],[15])).
% 2.84/3.05 tff(17,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 2.84/3.05 tff(18,plain,
% 2.84/3.05 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[17, 16])).
% 2.84/3.05 tff(19,plain,
% 2.84/3.05 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.05 inference(modus_ponens,[status(thm)],[18, 14])).
% 2.84/3.05 tff(20,plain,(
% 2.84/3.05 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.06 inference(skolemize,[status(sab)],[19])).
% 2.84/3.06 tff(21,plain,
% 2.84/3.06 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[20, 13])).
% 2.84/3.06 tff(22,plain,
% 2.84/3.06 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(23,plain,
% 2.84/3.06 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 2.84/3.06 inference(quant_inst,[status(thm)],[])).
% 2.84/3.06 tff(24,plain,
% 2.84/3.06 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[23, 22])).
% 2.84/3.06 tff(25,plain,
% 2.84/3.06 (app(V!46, nil) = V!46),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 2.84/3.06 tff(26,plain,
% 2.84/3.06 (^[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))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(27,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[26])).
% 2.84/3.06 tff(28,plain,
% 2.84/3.06 (^[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))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(29,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[28])).
% 2.84/3.06 tff(30,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(transitivity,[status(thm)],[29, 27])).
% 2.84/3.06 tff(31,plain,
% 2.84/3.06 (^[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))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(32,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[31])).
% 2.84/3.06 tff(33,plain,
% 2.84/3.06 (![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)))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(34,plain,
% 2.84/3.06 (^[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)))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(35,plain,
% 2.84/3.06 (![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)))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[34])).
% 2.84/3.06 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')).
% 2.84/3.06 tff(37,plain,
% 2.84/3.06 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.84/3.06 tff(38,plain,
% 2.84/3.06 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[37, 33])).
% 2.84/3.06 tff(39,plain,(
% 2.84/3.06 ![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)))))))),
% 2.84/3.06 inference(skolemize,[status(sab)],[38])).
% 2.84/3.06 tff(40,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[39, 32])).
% 2.84/3.06 tff(41,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[40, 30])).
% 2.84/3.06 tff(42,plain,
% 2.84/3.06 (((~![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))))))))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(43,plain,
% 2.84/3.06 (((~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))))))))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(44,plain,
% 2.84/3.06 (((~![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)))))))))))),
% 2.84/3.06 inference(monotonicity,[status(thm)],[43])).
% 2.84/3.06 tff(45,plain,
% 2.84/3.06 (((~![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))))))))))),
% 2.84/3.06 inference(transitivity,[status(thm)],[44, 42])).
% 2.84/3.06 tff(46,plain,
% 2.84/3.06 ((~![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)))))))))),
% 2.84/3.06 inference(quant_inst,[status(thm)],[])).
% 2.84/3.06 tff(47,plain,
% 2.84/3.06 ((~![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)))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.84/3.06 tff(48,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[47, 41, 11])).
% 2.84/3.06 tff(49,plain,
% 2.84/3.06 (ssList(U!45)),
% 2.84/3.06 inference(and_elim,[status(thm)],[9])).
% 2.84/3.06 tff(50,plain,
% 2.84/3.06 (((~![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)))))))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(51,plain,
% 2.84/3.06 ((~![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)))))))))),
% 2.84/3.06 inference(quant_inst,[status(thm)],[])).
% 2.84/3.06 tff(52,plain,
% 2.84/3.06 ((~![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))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.84/3.06 tff(53,plain,
% 2.84/3.06 (~((~(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)))))))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[52, 49, 48])).
% 2.84/3.06 tff(54,plain,
% 2.84/3.06 (((~(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)))))),
% 2.84/3.06 inference(tautology,[status(thm)],[])).
% 2.84/3.06 tff(55,plain,
% 2.84/3.06 ((~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))))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[54, 53])).
% 2.84/3.06 tff(56,plain,
% 2.84/3.06 (rearsegP(V!46, U!45)),
% 2.84/3.06 inference(or_elim,[status(thm)],[10])).
% 2.84/3.06 tff(57,plain,
% 2.84/3.06 ((~((~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))))),
% 2.84/3.06 inference(tautology,[status(thm)],[])).
% 2.84/3.06 tff(58,plain,
% 2.84/3.06 ((~((~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))))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[57, 56])).
% 2.84/3.06 tff(59,plain,
% 2.84/3.06 (~((~ssList(tptp_fun_W_6(U!45, V!46))) | (~(app(tptp_fun_W_6(U!45, V!46), U!45) = V!46)))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[58, 55])).
% 2.84/3.06 tff(60,plain,
% 2.84/3.06 (((~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)),
% 2.84/3.06 inference(tautology,[status(thm)],[])).
% 2.84/3.06 tff(61,plain,
% 2.84/3.06 (app(tptp_fun_W_6(U!45, V!46), U!45) = V!46),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[60, 59])).
% 2.84/3.06 tff(62,plain,
% 2.84/3.06 (app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = app(V!46, nil)),
% 2.84/3.06 inference(monotonicity,[status(thm)],[61])).
% 2.84/3.06 tff(63,plain,
% 2.84/3.06 (app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46),
% 2.84/3.06 inference(transitivity,[status(thm)],[62, 25])).
% 2.84/3.06 tff(64,plain,
% 2.84/3.06 (^[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)))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(65,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[64])).
% 2.84/3.06 tff(66,plain,
% 2.84/3.06 (^[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)))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(67,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[66])).
% 2.84/3.06 tff(68,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(transitivity,[status(thm)],[67, 65])).
% 2.84/3.06 tff(69,plain,
% 2.84/3.06 (^[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)))))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(70,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[69])).
% 2.84/3.06 tff(71,plain,
% 2.84/3.06 (^[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)))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(72,plain,
% 2.84/3.06 (![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))))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[71])).
% 2.84/3.06 tff(73,plain,
% 2.84/3.06 (![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))))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(74,plain,
% 2.84/3.06 (^[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))))))))),
% 2.84/3.06 inference(bind,[status(th)],[])).
% 2.84/3.06 tff(75,plain,
% 2.84/3.06 (![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))))))),
% 2.84/3.06 inference(quant_intro,[status(thm)],[74])).
% 2.84/3.06 tff(76,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')).
% 2.84/3.06 tff(77,plain,
% 2.84/3.06 (![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))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[76, 75])).
% 2.84/3.06 tff(78,plain,
% 2.84/3.06 (![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))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[77, 73])).
% 2.84/3.06 tff(79,plain,(
% 2.84/3.06 ![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))))))))),
% 2.84/3.06 inference(skolemize,[status(sab)],[78])).
% 2.84/3.06 tff(80,plain,
% 2.84/3.06 (![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))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[79, 72])).
% 2.84/3.06 tff(81,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[80, 70])).
% 2.84/3.06 tff(82,plain,
% 2.84/3.06 (![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))))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[81, 68])).
% 2.84/3.06 tff(83,plain,
% 2.84/3.06 (((~![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))))))))))),
% 2.84/3.06 inference(rewrite,[status(thm)],[])).
% 2.84/3.06 tff(84,plain,
% 2.84/3.06 ((~![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))))))))))),
% 2.84/3.06 inference(quant_inst,[status(thm)],[])).
% 2.84/3.06 tff(85,plain,
% 2.84/3.06 ((~![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)))))))))),
% 2.84/3.06 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.84/3.06 tff(86,plain,
% 2.84/3.06 (![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)))))))))),
% 2.84/3.06 inference(unit_resolution,[status(thm)],[85, 82, 11])).
% 2.84/3.06 tff(87,plain,
% 2.84/3.06 (((~![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)))))))))),
% 2.90/3.06 inference(rewrite,[status(thm)],[])).
% 2.90/3.06 tff(88,plain,
% 2.90/3.06 ((~![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)))))))))),
% 2.90/3.06 inference(quant_inst,[status(thm)],[])).
% 2.90/3.06 tff(89,plain,
% 2.90/3.06 ((~![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))))))))),
% 2.90/3.06 inference(modus_ponens,[status(thm)],[88, 87])).
% 2.90/3.06 tff(90,plain,
% 2.90/3.06 (~((~((~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)))))))),
% 2.90/3.06 inference(unit_resolution,[status(thm)],[89, 49, 86])).
% 2.90/3.06 tff(91,plain,
% 2.90/3.06 (((~((~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)))))),
% 2.90/3.06 inference(tautology,[status(thm)],[])).
% 2.90/3.06 tff(92,plain,
% 2.90/3.06 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 2.90/3.06 inference(unit_resolution,[status(thm)],[91, 90])).
% 2.90/3.06 tff(93,plain,
% 2.90/3.06 (~segmentP(V!46, U!45)),
% 2.90/3.06 inference(or_elim,[status(thm)],[10])).
% 2.90/3.06 tff(94,plain,
% 2.90/3.06 ((~(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))))),
% 2.90/3.06 inference(tautology,[status(thm)],[])).
% 2.90/3.06 tff(95,plain,
% 2.90/3.06 ((~(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))))),
% 2.90/3.06 inference(unit_resolution,[status(thm)],[94, 93])).
% 2.90/3.08 tff(96,plain,
% 2.90/3.08 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 2.90/3.08 inference(unit_resolution,[status(thm)],[95, 92])).
% 2.90/3.08 tff(97,plain,
% 2.90/3.08 (((~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))),
% 2.90/3.08 inference(tautology,[status(thm)],[])).
% 2.90/3.08 tff(98,plain,
% 2.90/3.08 (ssList(tptp_fun_W_6(U!45, V!46))),
% 2.90/3.08 inference(unit_resolution,[status(thm)],[97, 59])).
% 2.90/3.08 tff(99,plain,
% 2.90/3.08 (((~![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))))),
% 2.90/3.08 inference(rewrite,[status(thm)],[])).
% 2.90/3.08 tff(100,plain,
% 2.90/3.08 ((~![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))))),
% 2.90/3.08 inference(quant_inst,[status(thm)],[])).
% 2.90/3.08 tff(101,plain,
% 2.90/3.08 ((~![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)))),
% 2.90/3.08 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.90/3.08 tff(102,plain,
% 2.90/3.08 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))),
% 2.90/3.08 inference(unit_resolution,[status(thm)],[101, 98, 96])).
% 2.90/3.08 tff(103,plain,
% 2.90/3.08 (ssList(nil) <=> ssList(nil)),
% 2.90/3.08 inference(rewrite,[status(thm)],[])).
% 2.90/3.08 tff(104,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 2.90/3.08 tff(105,plain,
% 2.90/3.08 (ssList(nil)),
% 2.90/3.08 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.90/3.08 tff(106,plain,
% 2.90/3.08 (((~![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)))),
% 2.90/3.08 inference(rewrite,[status(thm)],[])).
% 2.90/3.08 tff(107,plain,
% 2.90/3.08 ((~![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)))),
% 2.90/3.08 inference(quant_inst,[status(thm)],[])).
% 2.90/3.08 tff(108,plain,
% 2.90/3.08 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), X) = V!46)))) | (~ssList(nil)) | (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46))),
% 2.90/3.08 inference(modus_ponens,[status(thm)],[107, 106])).
% 2.90/3.08 tff(109,plain,
% 2.90/3.08 (~(app(app(tptp_fun_W_6(U!45, V!46), U!45), nil) = V!46)),
% 2.90/3.08 inference(unit_resolution,[status(thm)],[108, 105, 102])).
% 2.90/3.08 tff(110,plain,
% 2.90/3.08 ($false),
% 2.90/3.08 inference(unit_resolution,[status(thm)],[109, 63])).
% 2.90/3.08 % SZS output end Proof
% 2.90/3.08 % E exiting
%------------------------------------------------------------------------------