%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC372+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 6.63s 6.86s
% Output : Proof 6.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC372+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 09:09:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.63/6.86 % SZS status Theorem
% 6.63/6.86 % SZS output start Proof
% 6.63/6.86 tff(tptp_fun_V_46_type, type, (
% 6.63/6.86 tptp_fun_V_46: $i)).
% 6.63/6.86 tff(app_type, type, (
% 6.63/6.86 app: ( $i * $i ) > $i)).
% 6.63/6.86 tff(tptp_fun_Y_47_type, type, (
% 6.63/6.86 tptp_fun_Y_47: $i)).
% 6.63/6.86 tff(tptp_fun_U_45_type, type, (
% 6.63/6.86 tptp_fun_U_45: $i)).
% 6.63/6.86 tff(nil_type, type, (
% 6.63/6.86 nil: $i)).
% 6.63/6.86 tff(lt_type, type, (
% 6.63/6.86 lt: ( $i * $i ) > $o)).
% 6.63/6.86 tff(cons_type, type, (
% 6.63/6.86 cons: ( $i * $i ) > $i)).
% 6.63/6.86 tff(ssList_type, type, (
% 6.63/6.86 ssList: $i > $o)).
% 6.63/6.86 tff(ssItem_type, type, (
% 6.63/6.86 ssItem: $i > $o)).
% 6.63/6.86 tff(strictorderedP_type, type, (
% 6.63/6.86 strictorderedP: $i > $o)).
% 6.63/6.86 tff(segmentP_type, type, (
% 6.63/6.86 segmentP: ( $i * $i ) > $o)).
% 6.63/6.86 tff(tptp_fun_X_8_type, type, (
% 6.63/6.86 tptp_fun_X_8: ( $i * $i ) > $i)).
% 6.63/6.86 tff(tptp_fun_W_7_type, type, (
% 6.63/6.86 tptp_fun_W_7: ( $i * $i ) > $i)).
% 6.63/6.86 tff(1,plain,
% 6.63/6.86 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45))) <=> (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(2,plain,
% 6.63/6.86 (((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45)) <=> ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(3,plain,
% 6.63/6.86 ((strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) <=> (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(4,plain,
% 6.63/6.86 (((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45)) <=> ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[3])).
% 6.63/6.86 tff(5,plain,
% 6.63/6.86 (((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45)) <=> ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45))),
% 6.63/6.86 inference(transitivity,[status(thm)],[4, 2])).
% 6.63/6.86 tff(6,plain,
% 6.63/6.86 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45))) <=> (ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))) & ssList(U!45)))),
% 6.63/6.86 inference(monotonicity,[status(thm)],[5])).
% 6.63/6.86 tff(7,plain,
% 6.63/6.86 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))) & ssList(U!45))) <=> (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z)))))))),
% 6.63/6.86 inference(transitivity,[status(thm)],[6, 1])).
% 6.63/6.86 tff(8,plain,
% 6.63/6.86 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U)))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(9,plain,
% 6.63/6.86 ((~![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)) | (~strictorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & lt(X2, Z)))))))) | segmentP(V, U)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U)))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 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)) | (~strictorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & lt(X2, Z)))))))) | segmentP(V, U)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 6.63/6.86 tff(11,plain,
% 6.63/6.86 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[10, 9])).
% 6.63/6.86 tff(12,plain,
% 6.63/6.86 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[11, 8])).
% 6.63/6.86 tff(13,plain,
% 6.63/6.86 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[12, 8])).
% 6.63/6.86 tff(14,plain,
% 6.63/6.86 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~strictorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & lt(X2, Z)))))) | (~ssList(U))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[13, 8])).
% 6.63/6.86 tff(15,plain,
% 6.63/6.86 (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & strictorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & lt(X2, Z))))))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[14, 7])).
% 6.63/6.86 tff(16,plain,
% 6.63/6.86 (app(U!45, Y!47) = V!46),
% 6.63/6.86 inference(and_elim,[status(thm)],[15])).
% 6.63/6.86 tff(17,plain,
% 6.63/6.86 (ssList(U!45)),
% 6.63/6.86 inference(and_elim,[status(thm)],[15])).
% 6.63/6.86 tff(18,plain,
% 6.63/6.86 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(19,plain,
% 6.63/6.86 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[18])).
% 6.63/6.86 tff(20,plain,
% 6.63/6.86 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(21,plain,
% 6.63/6.86 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(22,plain,
% 6.63/6.86 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[21])).
% 6.63/6.86 tff(23,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 6.63/6.86 tff(24,plain,
% 6.63/6.86 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[23, 22])).
% 6.63/6.86 tff(25,plain,
% 6.63/6.86 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[24, 20])).
% 6.63/6.86 tff(26,plain,(
% 6.63/6.86 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(skolemize,[status(sab)],[25])).
% 6.63/6.86 tff(27,plain,
% 6.63/6.86 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[26, 19])).
% 6.63/6.86 tff(28,plain,
% 6.63/6.86 (((~![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))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(29,plain,
% 6.63/6.86 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 6.63/6.86 inference(quant_inst,[status(thm)],[])).
% 6.63/6.86 tff(30,plain,
% 6.63/6.86 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 6.63/6.86 inference(modus_ponens,[status(thm)],[29, 28])).
% 6.63/6.86 tff(31,plain,
% 6.63/6.86 (app(nil, U!45) = U!45),
% 6.63/6.86 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 6.63/6.86 tff(32,plain,
% 6.63/6.86 (app(app(nil, U!45), Y!47) = app(U!45, Y!47)),
% 6.63/6.86 inference(monotonicity,[status(thm)],[31])).
% 6.63/6.86 tff(33,plain,
% 6.63/6.86 (app(app(nil, U!45), Y!47) = V!46),
% 6.63/6.86 inference(transitivity,[status(thm)],[32, 16])).
% 6.63/6.86 tff(34,plain,
% 6.63/6.86 (ssList(V!46)),
% 6.63/6.86 inference(and_elim,[status(thm)],[15])).
% 6.63/6.86 tff(35,plain,
% 6.63/6.86 (^[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)))))))))))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(36,plain,
% 6.63/6.86 (![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))))))))))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[35])).
% 6.63/6.86 tff(37,plain,
% 6.63/6.86 (^[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)))))))))))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(38,plain,
% 6.63/6.86 (![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))))))))))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[37])).
% 6.63/6.86 tff(39,plain,
% 6.63/6.86 (![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))))))))))),
% 6.63/6.86 inference(transitivity,[status(thm)],[38, 36])).
% 6.63/6.86 tff(40,plain,
% 6.63/6.86 (^[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)))))))))))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(41,plain,
% 6.63/6.86 (![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))))))))))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[40])).
% 6.63/6.86 tff(42,plain,
% 6.63/6.86 (^[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)))))))))),
% 6.63/6.86 inference(bind,[status(th)],[])).
% 6.63/6.86 tff(43,plain,
% 6.63/6.86 (![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))))))))),
% 6.63/6.86 inference(quant_intro,[status(thm)],[42])).
% 6.63/6.86 tff(44,plain,
% 6.63/6.86 (![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))))))),
% 6.63/6.86 inference(rewrite,[status(thm)],[])).
% 6.63/6.86 tff(45,plain,
% 6.63/6.86 (^[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))))))))),
% 6.63/6.87 inference(bind,[status(th)],[])).
% 6.63/6.87 tff(46,plain,
% 6.63/6.87 (![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))))))),
% 6.63/6.87 inference(quant_intro,[status(thm)],[45])).
% 6.63/6.87 tff(47,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')).
% 6.63/6.87 tff(48,plain,
% 6.63/6.87 (![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))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[47, 46])).
% 6.63/6.87 tff(49,plain,
% 6.63/6.87 (![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))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[48, 44])).
% 6.63/6.87 tff(50,plain,(
% 6.63/6.87 ![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))))))))),
% 6.63/6.87 inference(skolemize,[status(sab)],[49])).
% 6.63/6.87 tff(51,plain,
% 6.63/6.87 (![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))))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[50, 43])).
% 6.63/6.87 tff(52,plain,
% 6.63/6.87 (![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))))))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[51, 41])).
% 6.63/6.87 tff(53,plain,
% 6.63/6.87 (![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))))))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[52, 39])).
% 6.63/6.87 tff(54,plain,
% 6.63/6.87 (((~![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))))))))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(55,plain,
% 6.63/6.87 ((~![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))))))))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(56,plain,
% 6.63/6.87 ((~![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)))))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[55, 54])).
% 6.63/6.87 tff(57,plain,
% 6.63/6.87 (![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)))))))))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[56, 53, 34])).
% 6.63/6.87 tff(58,plain,
% 6.63/6.87 (((~![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)))))))))),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(59,plain,
% 6.63/6.87 ((~![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)))))))))),
% 6.63/6.87 inference(quant_inst,[status(thm)],[])).
% 6.63/6.87 tff(60,plain,
% 6.63/6.87 ((~![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))))))))),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[59, 58])).
% 6.63/6.87 tff(61,plain,
% 6.63/6.87 (~((~((~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)))))))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[60, 17, 57])).
% 6.63/6.87 tff(62,plain,
% 6.63/6.87 (((~((~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)))))),
% 6.63/6.87 inference(tautology,[status(thm)],[])).
% 6.63/6.87 tff(63,plain,
% 6.63/6.87 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[62, 61])).
% 6.63/6.87 tff(64,plain,
% 6.63/6.87 (~segmentP(V!46, U!45)),
% 6.63/6.87 inference(and_elim,[status(thm)],[15])).
% 6.63/6.87 tff(65,plain,
% 6.63/6.87 ((~(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))))),
% 6.63/6.87 inference(tautology,[status(thm)],[])).
% 6.63/6.87 tff(66,plain,
% 6.63/6.87 ((~(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))))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[65, 64])).
% 6.63/6.87 tff(67,plain,
% 6.63/6.87 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 6.63/6.87 inference(unit_resolution,[status(thm)],[66, 63])).
% 6.63/6.87 tff(68,plain,
% 6.63/6.87 (ssList(nil) <=> ssList(nil)),
% 6.63/6.87 inference(rewrite,[status(thm)],[])).
% 6.63/6.87 tff(69,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 6.63/6.87 tff(70,plain,
% 6.63/6.87 (ssList(nil)),
% 6.63/6.87 inference(modus_ponens,[status(thm)],[69, 68])).
% 6.72/6.89 tff(71,plain,
% 6.72/6.89 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 6.72/6.89 inference(rewrite,[status(thm)],[])).
% 6.72/6.89 tff(72,plain,
% 6.72/6.89 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 6.72/6.89 inference(quant_inst,[status(thm)],[])).
% 6.72/6.89 tff(73,plain,
% 6.72/6.89 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 6.72/6.89 inference(modus_ponens,[status(thm)],[72, 71])).
% 6.72/6.89 tff(74,plain,
% 6.72/6.89 (![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 6.72/6.89 inference(unit_resolution,[status(thm)],[73, 70, 67])).
% 6.72/6.89 tff(75,plain,
% 6.72/6.89 (ssList(Y!47)),
% 6.72/6.89 inference(and_elim,[status(thm)],[15])).
% 6.72/6.89 tff(76,plain,
% 6.72/6.89 (((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(Y!47)) | (~(app(app(nil, U!45), Y!47) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(Y!47)) | (~(app(app(nil, U!45), Y!47) = V!46)))),
% 6.72/6.89 inference(rewrite,[status(thm)],[])).
% 6.72/6.89 tff(77,plain,
% 6.72/6.89 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(Y!47)) | (~(app(app(nil, U!45), Y!47) = V!46)))),
% 6.72/6.89 inference(quant_inst,[status(thm)],[])).
% 6.72/6.89 tff(78,plain,
% 6.72/6.89 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(Y!47)) | (~(app(app(nil, U!45), Y!47) = V!46))),
% 6.72/6.89 inference(modus_ponens,[status(thm)],[77, 76])).
% 6.72/6.89 tff(79,plain,
% 6.72/6.89 (~(app(app(nil, U!45), Y!47) = V!46)),
% 6.72/6.89 inference(unit_resolution,[status(thm)],[78, 75, 74])).
% 6.72/6.89 tff(80,plain,
% 6.72/6.89 ($false),
% 6.72/6.89 inference(unit_resolution,[status(thm)],[79, 33])).
% 6.72/6.89 % SZS output end Proof
% 6.72/6.89 % E exiting
%------------------------------------------------------------------------------