%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC331+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:55 AM UTC 2025
% Result : Theorem 6.88s 7.04s
% Output : Proof 6.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC331+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 09:03:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.88/7.04 % SZS status Theorem
% 6.88/7.04 % SZS output start Proof
% 6.88/7.04 tff(tptp_fun_V_46_type, type, (
% 6.88/7.04 tptp_fun_V_46: $i)).
% 6.88/7.04 tff(app_type, type, (
% 6.88/7.04 app: ( $i * $i ) > $i)).
% 6.88/7.04 tff(tptp_fun_Y_47_type, type, (
% 6.88/7.04 tptp_fun_Y_47: $i)).
% 6.88/7.04 tff(tptp_fun_U_45_type, type, (
% 6.88/7.04 tptp_fun_U_45: $i)).
% 6.88/7.04 tff(tptp_fun_W_6_type, type, (
% 6.88/7.04 tptp_fun_W_6: ( $i * $i ) > $i)).
% 6.88/7.04 tff(nil_type, type, (
% 6.88/7.04 nil: $i)).
% 6.88/7.04 tff(equalelemsP_type, type, (
% 6.88/7.04 equalelemsP: $i > $o)).
% 6.88/7.04 tff(segmentP_type, type, (
% 6.88/7.04 segmentP: ( $i * $i ) > $o)).
% 6.88/7.04 tff(cons_type, type, (
% 6.88/7.04 cons: ( $i * $i ) > $i)).
% 6.88/7.04 tff(ssList_type, type, (
% 6.88/7.04 ssList: $i > $o)).
% 6.88/7.04 tff(ssItem_type, type, (
% 6.88/7.04 ssItem: $i > $o)).
% 6.88/7.04 tff(rearsegP_type, type, (
% 6.88/7.04 rearsegP: ( $i * $i ) > $o)).
% 6.88/7.04 tff(tptp_fun_X_8_type, type, (
% 6.88/7.04 tptp_fun_X_8: ( $i * $i ) > $i)).
% 6.88/7.04 tff(tptp_fun_W_7_type, type, (
% 6.88/7.04 tptp_fun_W_7: ( $i * $i ) > $i)).
% 6.88/7.04 tff(1,plain,
% 6.88/7.04 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(2,plain,
% 6.88/7.04 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(3,plain,
% 6.88/7.04 (((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) <=> ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(4,plain,
% 6.88/7.04 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))),
% 6.88/7.04 inference(monotonicity,[status(thm)],[3])).
% 6.88/7.04 tff(5,plain,
% 6.88/7.04 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))),
% 6.88/7.04 inference(transitivity,[status(thm)],[4, 2])).
% 6.88/7.04 tff(6,plain,
% 6.88/7.04 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45)))))),
% 6.88/7.04 inference(monotonicity,[status(thm)],[5])).
% 6.88/7.04 tff(7,plain,
% 6.88/7.04 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(segmentP(V!46, U!45) & equalelemsP(U!45))))),
% 6.88/7.04 inference(transitivity,[status(thm)],[6, 1])).
% 6.88/7.04 tff(8,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U)))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(9,plain,
% 6.88/7.04 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & equalelemsP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U)))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(10,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & equalelemsP(U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 6.88/7.04 tff(11,plain,
% 6.88/7.04 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[10, 9])).
% 6.88/7.04 tff(12,plain,
% 6.88/7.04 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[11, 8])).
% 6.88/7.04 tff(13,plain,
% 6.88/7.04 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[12, 8])).
% 6.88/7.04 tff(14,plain,
% 6.88/7.04 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (segmentP(V, U) & equalelemsP(U))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[13, 8])).
% 6.88/7.04 tff(15,plain,
% 6.88/7.04 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(segmentP(V!46, U!45) & equalelemsP(U!45)))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[14, 7])).
% 6.88/7.04 tff(16,plain,
% 6.88/7.04 (app(U!45, Y!47) = V!46),
% 6.88/7.04 inference(and_elim,[status(thm)],[15])).
% 6.88/7.04 tff(17,plain,
% 6.88/7.04 (ssList(U!45)),
% 6.88/7.04 inference(and_elim,[status(thm)],[15])).
% 6.88/7.04 tff(18,plain,
% 6.88/7.04 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(19,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[18])).
% 6.88/7.04 tff(20,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(21,plain,
% 6.88/7.04 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(22,plain,
% 6.88/7.04 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[21])).
% 6.88/7.04 tff(23,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 6.88/7.04 tff(24,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[23, 22])).
% 6.88/7.04 tff(25,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[24, 20])).
% 6.88/7.04 tff(26,plain,(
% 6.88/7.04 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(skolemize,[status(sab)],[25])).
% 6.88/7.04 tff(27,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[26, 19])).
% 6.88/7.04 tff(28,plain,
% 6.88/7.04 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(29,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 6.88/7.04 inference(quant_inst,[status(thm)],[])).
% 6.88/7.04 tff(30,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[29, 28])).
% 6.88/7.04 tff(31,plain,
% 6.88/7.04 (app(nil, U!45) = U!45),
% 6.88/7.04 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 6.88/7.04 tff(32,plain,
% 6.88/7.04 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(33,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[32])).
% 6.88/7.04 tff(34,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(35,plain,
% 6.88/7.04 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(36,plain,
% 6.88/7.04 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[35])).
% 6.88/7.04 tff(37,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 6.88/7.04 tff(38,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[37, 36])).
% 6.88/7.04 tff(39,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[38, 34])).
% 6.88/7.04 tff(40,plain,(
% 6.88/7.04 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(skolemize,[status(sab)],[39])).
% 6.88/7.04 tff(41,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[40, 33])).
% 6.88/7.04 tff(42,plain,
% 6.88/7.04 (ssList(nil) <=> ssList(nil)),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(43,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 6.88/7.04 tff(44,plain,
% 6.88/7.04 (ssList(nil)),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[43, 42])).
% 6.88/7.04 tff(45,plain,
% 6.88/7.04 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(46,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 6.88/7.04 inference(quant_inst,[status(thm)],[])).
% 6.88/7.04 tff(47,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[46, 45])).
% 6.88/7.04 tff(48,plain,
% 6.88/7.04 (app(nil, nil) = nil),
% 6.88/7.04 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 6.88/7.04 tff(49,plain,
% 6.88/7.04 (nil = app(nil, nil)),
% 6.88/7.04 inference(symmetry,[status(thm)],[48])).
% 6.88/7.04 tff(50,plain,
% 6.88/7.04 (^[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))))))))))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(51,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[50])).
% 6.88/7.04 tff(52,plain,
% 6.88/7.04 (^[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))))))))))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(53,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[52])).
% 6.88/7.04 tff(54,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(transitivity,[status(thm)],[53, 51])).
% 6.88/7.04 tff(55,plain,
% 6.88/7.04 (^[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))))))))))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(56,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[55])).
% 6.88/7.04 tff(57,plain,
% 6.88/7.04 (![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)))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(58,plain,
% 6.88/7.04 (^[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)))))))),
% 6.88/7.04 inference(bind,[status(th)],[])).
% 6.88/7.04 tff(59,plain,
% 6.88/7.04 (![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)))))),
% 6.88/7.04 inference(quant_intro,[status(thm)],[58])).
% 6.88/7.04 tff(60,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')).
% 6.88/7.04 tff(61,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[60, 59])).
% 6.88/7.04 tff(62,plain,
% 6.88/7.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[61, 57])).
% 6.88/7.04 tff(63,plain,(
% 6.88/7.04 ![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)))))))),
% 6.88/7.04 inference(skolemize,[status(sab)],[62])).
% 6.88/7.04 tff(64,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[63, 56])).
% 6.88/7.04 tff(65,plain,
% 6.88/7.04 (![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)))))))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[64, 54])).
% 6.88/7.04 tff(66,plain,
% 6.88/7.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(67,plain,
% 6.88/7.04 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(68,plain,
% 6.88/7.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))))),
% 6.88/7.04 inference(monotonicity,[status(thm)],[67])).
% 6.88/7.04 tff(69,plain,
% 6.88/7.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil))))))))))),
% 6.88/7.04 inference(transitivity,[status(thm)],[68, 66])).
% 6.88/7.04 tff(70,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))),
% 6.88/7.04 inference(quant_inst,[status(thm)],[])).
% 6.88/7.04 tff(71,plain,
% 6.88/7.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))),
% 6.88/7.04 inference(modus_ponens,[status(thm)],[70, 69])).
% 6.88/7.04 tff(72,plain,
% 6.88/7.04 (![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))),
% 6.88/7.04 inference(unit_resolution,[status(thm)],[71, 65, 44])).
% 6.88/7.04 tff(73,plain,
% 6.88/7.04 (((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | ((~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | (~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))),
% 6.88/7.04 inference(rewrite,[status(thm)],[])).
% 6.88/7.04 tff(74,plain,
% 6.88/7.04 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | ((~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))))),
% 6.88/7.04 inference(quant_inst,[status(thm)],[])).
% 6.88/7.04 tff(75,plain,
% 6.88/7.04 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))) | (~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))))))) | (~ssList(nil)) | (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[74, 73])).
% 6.88/7.05 tff(76,plain,
% 6.88/7.05 (~((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[75, 44, 72])).
% 6.88/7.05 tff(77,plain,
% 6.88/7.05 (((~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))) | (~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))))) | ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))),
% 6.88/7.05 inference(tautology,[status(thm)],[])).
% 6.88/7.05 tff(78,plain,
% 6.88/7.05 ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[77, 76])).
% 6.88/7.05 tff(79,plain,
% 6.88/7.05 (^[U: $i] : refl(((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(80,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[79])).
% 6.88/7.05 tff(81,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(82,plain,
% 6.88/7.05 (^[U: $i] : rewrite((ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(83,plain,
% 6.88/7.05 (![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[82])).
% 6.88/7.05 tff(84,axiom,(![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax52')).
% 6.88/7.05 tff(85,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[84, 83])).
% 6.88/7.05 tff(86,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[85, 81])).
% 6.88/7.05 tff(87,plain,(
% 6.88/7.05 ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(skolemize,[status(sab)],[86])).
% 6.88/7.05 tff(88,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[87, 80])).
% 6.88/7.05 tff(89,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(90,plain,
% 6.88/7.05 (((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil))) <=> ((~ssList(nil)) | rearsegP(nil, nil))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(91,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil)))),
% 6.88/7.05 inference(monotonicity,[status(thm)],[90])).
% 6.88/7.05 tff(92,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 6.88/7.05 inference(transitivity,[status(thm)],[91, 89])).
% 6.88/7.05 tff(93,plain,
% 6.88/7.05 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(94,plain,
% 6.88/7.05 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil)),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[93, 92])).
% 6.88/7.05 tff(95,plain,
% 6.88/7.05 (rearsegP(nil, nil)),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[94, 44, 88])).
% 6.88/7.05 tff(96,plain,
% 6.88/7.05 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 6.88/7.05 inference(tautology,[status(thm)],[])).
% 6.88/7.05 tff(97,plain,
% 6.88/7.05 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[96, 95])).
% 6.88/7.05 tff(98,plain,
% 6.88/7.05 (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[97, 78])).
% 6.88/7.05 tff(99,plain,
% 6.88/7.05 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | (app(tptp_fun_W_6(nil, nil), nil) = nil)),
% 6.88/7.05 inference(tautology,[status(thm)],[])).
% 6.88/7.05 tff(100,plain,
% 6.88/7.05 (app(tptp_fun_W_6(nil, nil), nil) = nil),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[99, 98])).
% 6.88/7.05 tff(101,plain,
% 6.88/7.05 (app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)),
% 6.88/7.05 inference(transitivity,[status(thm)],[100, 49])).
% 6.88/7.05 tff(102,plain,
% 6.88/7.05 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | ssList(tptp_fun_W_6(nil, nil))),
% 6.88/7.05 inference(tautology,[status(thm)],[])).
% 6.88/7.05 tff(103,plain,
% 6.88/7.05 (ssList(tptp_fun_W_6(nil, nil))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[102, 98])).
% 6.88/7.05 tff(104,plain,
% 6.88/7.05 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(105,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[104])).
% 6.88/7.05 tff(106,plain,
% 6.88/7.05 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(107,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[106])).
% 6.88/7.05 tff(108,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(transitivity,[status(thm)],[107, 105])).
% 6.88/7.05 tff(109,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(110,plain,
% 6.88/7.05 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(W, V) = app(U, V)) => (W = U)) <=> ((~(app(W, V) = app(U, V))) | (W = U))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> (ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))))), rewrite((ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), (![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(111,plain,
% 6.88/7.05 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[110])).
% 6.88/7.05 tff(112,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax79')).
% 6.88/7.05 tff(113,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[112, 111])).
% 6.88/7.05 tff(114,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[113, 109])).
% 6.88/7.05 tff(115,plain,(
% 6.88/7.05 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(skolemize,[status(sab)],[114])).
% 6.88/7.05 tff(116,plain,
% 6.88/7.05 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[115, 108])).
% 6.88/7.05 tff(117,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(118,plain,
% 6.88/7.05 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V)))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(119,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))))),
% 6.88/7.05 inference(monotonicity,[status(thm)],[118])).
% 6.88/7.05 tff(120,plain,
% 6.88/7.05 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 6.88/7.05 inference(transitivity,[status(thm)],[119, 117])).
% 6.88/7.05 tff(121,plain,
% 6.88/7.05 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(122,plain,
% 6.88/7.05 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[121, 120])).
% 6.88/7.05 tff(123,plain,
% 6.88/7.05 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[122, 44, 116])).
% 6.88/7.05 tff(124,plain,
% 6.88/7.05 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(125,plain,
% 6.88/7.05 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(126,plain,
% 6.88/7.05 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[125, 124])).
% 6.88/7.05 tff(127,plain,
% 6.88/7.05 (![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[126, 44, 123])).
% 6.88/7.05 tff(128,plain,
% 6.88/7.05 (((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(129,plain,
% 6.88/7.05 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(130,plain,
% 6.88/7.05 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[129, 128])).
% 6.88/7.05 tff(131,plain,
% 6.88/7.05 (tptp_fun_W_6(nil, nil) = nil),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[130, 127, 103, 101])).
% 6.88/7.05 tff(132,plain,
% 6.88/7.05 (app(tptp_fun_W_6(nil, nil), U!45) = app(nil, U!45)),
% 6.88/7.05 inference(monotonicity,[status(thm)],[131])).
% 6.88/7.05 tff(133,plain,
% 6.88/7.05 (app(tptp_fun_W_6(nil, nil), U!45) = U!45),
% 6.88/7.05 inference(transitivity,[status(thm)],[132, 31])).
% 6.88/7.05 tff(134,plain,
% 6.88/7.05 (app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = app(U!45, Y!47)),
% 6.88/7.05 inference(monotonicity,[status(thm)],[133])).
% 6.88/7.05 tff(135,plain,
% 6.88/7.05 (app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46),
% 6.88/7.05 inference(transitivity,[status(thm)],[134, 16])).
% 6.88/7.05 tff(136,plain,
% 6.88/7.05 (ssList(V!46)),
% 6.88/7.05 inference(and_elim,[status(thm)],[15])).
% 6.88/7.05 tff(137,plain,
% 6.88/7.05 (^[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)))))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(138,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[137])).
% 6.88/7.05 tff(139,plain,
% 6.88/7.05 (^[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)))))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(140,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[139])).
% 6.88/7.05 tff(141,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(transitivity,[status(thm)],[140, 138])).
% 6.88/7.05 tff(142,plain,
% 6.88/7.05 (^[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)))))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(143,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[142])).
% 6.88/7.05 tff(144,plain,
% 6.88/7.05 (^[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)))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(145,plain,
% 6.88/7.05 (![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))))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[144])).
% 6.88/7.05 tff(146,plain,
% 6.88/7.05 (![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))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(147,plain,
% 6.88/7.05 (^[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))))))))),
% 6.88/7.05 inference(bind,[status(th)],[])).
% 6.88/7.05 tff(148,plain,
% 6.88/7.05 (![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))))))),
% 6.88/7.05 inference(quant_intro,[status(thm)],[147])).
% 6.88/7.05 tff(149,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')).
% 6.88/7.05 tff(150,plain,
% 6.88/7.05 (![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))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[149, 148])).
% 6.88/7.05 tff(151,plain,
% 6.88/7.05 (![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))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[150, 146])).
% 6.88/7.05 tff(152,plain,(
% 6.88/7.05 ![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))))))))),
% 6.88/7.05 inference(skolemize,[status(sab)],[151])).
% 6.88/7.05 tff(153,plain,
% 6.88/7.05 (![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))))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[152, 145])).
% 6.88/7.05 tff(154,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[153, 143])).
% 6.88/7.05 tff(155,plain,
% 6.88/7.05 (![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))))))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[154, 141])).
% 6.88/7.05 tff(156,plain,
% 6.88/7.05 (((~![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))))))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(157,plain,
% 6.88/7.05 ((~![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))))))))))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(158,plain,
% 6.88/7.05 ((~![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)))))))))),
% 6.88/7.05 inference(modus_ponens,[status(thm)],[157, 156])).
% 6.88/7.05 tff(159,plain,
% 6.88/7.05 (![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)))))))))),
% 6.88/7.05 inference(unit_resolution,[status(thm)],[158, 155, 136])).
% 6.88/7.05 tff(160,plain,
% 6.88/7.05 (((~![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)))))))))),
% 6.88/7.05 inference(rewrite,[status(thm)],[])).
% 6.88/7.05 tff(161,plain,
% 6.88/7.05 ((~![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)))))))))),
% 6.88/7.05 inference(quant_inst,[status(thm)],[])).
% 6.88/7.05 tff(162,plain,
% 6.88/7.05 ((~![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))))))))),
% 6.88/7.06 inference(modus_ponens,[status(thm)],[161, 160])).
% 6.88/7.06 tff(163,plain,
% 6.88/7.06 (~((~((~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)))))))),
% 6.88/7.06 inference(unit_resolution,[status(thm)],[162, 17, 159])).
% 6.88/7.06 tff(164,plain,
% 6.88/7.06 (((~((~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)))))),
% 6.88/7.06 inference(tautology,[status(thm)],[])).
% 6.88/7.06 tff(165,plain,
% 6.88/7.06 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 6.88/7.06 inference(unit_resolution,[status(thm)],[164, 163])).
% 6.88/7.06 tff(166,plain,
% 6.88/7.06 (equalelemsP(U!45)),
% 6.88/7.06 inference(and_elim,[status(thm)],[15])).
% 6.88/7.06 tff(167,plain,
% 6.88/7.06 ((~(~((~equalelemsP(U!45)) | (~segmentP(V!46, U!45))))) <=> ((~equalelemsP(U!45)) | (~segmentP(V!46, U!45)))),
% 6.88/7.06 inference(rewrite,[status(thm)],[])).
% 6.88/7.06 tff(168,plain,
% 6.88/7.06 ((segmentP(V!46, U!45) & equalelemsP(U!45)) <=> (~((~equalelemsP(U!45)) | (~segmentP(V!46, U!45))))),
% 6.88/7.06 inference(rewrite,[status(thm)],[])).
% 6.88/7.06 tff(169,plain,
% 6.88/7.06 ((~(segmentP(V!46, U!45) & equalelemsP(U!45))) <=> (~(~((~equalelemsP(U!45)) | (~segmentP(V!46, U!45)))))),
% 6.88/7.06 inference(monotonicity,[status(thm)],[168])).
% 6.88/7.06 tff(170,plain,
% 6.88/7.06 ((~(segmentP(V!46, U!45) & equalelemsP(U!45))) <=> ((~equalelemsP(U!45)) | (~segmentP(V!46, U!45)))),
% 6.88/7.06 inference(transitivity,[status(thm)],[169, 167])).
% 6.88/7.06 tff(171,plain,
% 6.88/7.06 (~(segmentP(V!46, U!45) & equalelemsP(U!45))),
% 6.88/7.06 inference(and_elim,[status(thm)],[15])).
% 6.88/7.06 tff(172,plain,
% 6.88/7.06 ((~equalelemsP(U!45)) | (~segmentP(V!46, U!45))),
% 6.88/7.06 inference(modus_ponens,[status(thm)],[171, 170])).
% 6.88/7.06 tff(173,plain,
% 6.88/7.06 (~segmentP(V!46, U!45)),
% 6.88/7.06 inference(unit_resolution,[status(thm)],[172, 166])).
% 6.88/7.06 tff(174,plain,
% 6.88/7.06 ((~(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))))),
% 6.88/7.06 inference(tautology,[status(thm)],[])).
% 6.88/7.06 tff(175,plain,
% 6.88/7.06 ((~(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))))),
% 6.88/7.08 inference(unit_resolution,[status(thm)],[174, 173])).
% 6.88/7.08 tff(176,plain,
% 6.88/7.08 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 6.88/7.08 inference(unit_resolution,[status(thm)],[175, 165])).
% 6.88/7.08 tff(177,plain,
% 6.88/7.08 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))),
% 6.88/7.08 inference(rewrite,[status(thm)],[])).
% 6.88/7.08 tff(178,plain,
% 6.88/7.08 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46))))),
% 6.88/7.08 inference(quant_inst,[status(thm)],[])).
% 6.88/7.08 tff(179,plain,
% 6.88/7.08 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))),
% 6.88/7.08 inference(modus_ponens,[status(thm)],[178, 177])).
% 6.88/7.08 tff(180,plain,
% 6.88/7.08 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))),
% 6.88/7.08 inference(unit_resolution,[status(thm)],[179, 103, 176])).
% 6.88/7.08 tff(181,plain,
% 6.88/7.08 (ssList(Y!47)),
% 6.88/7.08 inference(and_elim,[status(thm)],[15])).
% 6.88/7.08 tff(182,plain,
% 6.88/7.08 (((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | ((~ssList(Y!47)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | (~ssList(Y!47)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46)))),
% 6.88/7.08 inference(rewrite,[status(thm)],[])).
% 6.88/7.08 tff(183,plain,
% 6.88/7.08 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | ((~ssList(Y!47)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46)))),
% 6.88/7.08 inference(quant_inst,[status(thm)],[])).
% 6.88/7.08 tff(184,plain,
% 6.88/7.08 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), X) = V!46)))) | (~ssList(Y!47)) | (~(app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46))),
% 6.88/7.08 inference(modus_ponens,[status(thm)],[183, 182])).
% 6.88/7.08 tff(185,plain,
% 6.88/7.08 (~(app(app(tptp_fun_W_6(nil, nil), U!45), Y!47) = V!46)),
% 6.88/7.08 inference(unit_resolution,[status(thm)],[184, 181, 180])).
% 6.88/7.08 tff(186,plain,
% 6.88/7.08 ($false),
% 6.88/7.08 inference(unit_resolution,[status(thm)],[185, 135])).
% 6.88/7.08 % SZS output end Proof
% 6.88/7.09 % E exiting
%------------------------------------------------------------------------------