%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC308+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:30:52 AM UTC 2025
% Result : Theorem 80.04s 80.28s
% Output : Proof 80.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC308+1 : TPTP v9.0.0. Released v2.4.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 08:58:42 EDT 2025
% 0.13/0.33 % CPUTime :
% 80.04/80.28 % SZS status Theorem
% 80.04/80.28 % SZS output start Proof
% 80.04/80.28 tff(tptp_fun_V_46_type, type, (
% 80.04/80.28 tptp_fun_V_46: $i)).
% 80.04/80.28 tff(app_type, type, (
% 80.04/80.28 app: ( $i * $i ) > $i)).
% 80.04/80.28 tff(tptp_fun_V_43_type, type, (
% 80.04/80.28 tptp_fun_V_43: $i > $i)).
% 80.04/80.28 tff(cons_type, type, (
% 80.04/80.28 cons: ( $i * $i ) > $i)).
% 80.04/80.28 tff(nil_type, type, (
% 80.04/80.28 nil: $i)).
% 80.04/80.28 tff(tptp_fun_W_44_type, type, (
% 80.04/80.28 tptp_fun_W_44: $i > $i)).
% 80.04/80.28 tff(ssItem_type, type, (
% 80.04/80.28 ssItem: $i > $o)).
% 80.04/80.28 tff(ssList_type, type, (
% 80.04/80.28 ssList: $i > $o)).
% 80.04/80.28 tff(segmentP_type, type, (
% 80.04/80.28 segmentP: ( $i * $i ) > $o)).
% 80.04/80.28 tff(tptp_fun_U_45_type, type, (
% 80.04/80.28 tptp_fun_U_45: $i)).
% 80.04/80.28 tff(hd_type, type, (
% 80.04/80.28 hd: $i > $i)).
% 80.04/80.28 tff(tl_type, type, (
% 80.04/80.28 tl: $i > $i)).
% 80.04/80.28 tff(neq_type, type, (
% 80.04/80.28 neq: ( $i * $i ) > $o)).
% 80.04/80.28 tff(1,plain,
% 80.04/80.28 ((app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) <=> (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)))),
% 80.04/80.28 inference(commutativity,[status(thm)],[])).
% 80.04/80.28 tff(2,plain,
% 80.04/80.28 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(3,plain,
% 80.04/80.28 (((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45)))) <=> ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(4,plain,
% 80.04/80.28 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45)))))),
% 80.04/80.28 inference(monotonicity,[status(thm)],[3])).
% 80.04/80.28 tff(5,plain,
% 80.04/80.28 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & ssList(U!45) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))))),
% 80.04/80.28 inference(transitivity,[status(thm)],[4, 2])).
% 80.04/80.28 tff(6,plain,
% 80.04/80.28 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U)))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(7,plain,
% 80.04/80.28 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : ((ssList(Y) & (U = Y)) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((((ssList(X1) & (tl(V) = Z)) & (app(Z, X1) = Y)) & ?[X2: $i] : (((ssItem(X2) & (cons(X2, nil) = X1)) & (hd(V) = X2)) & neq(nil, V))) & neq(nil, V))))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (~(app(X4, cons(X3, nil)) = W))) & (app(cons(X3, nil), X4) = X)))) | ((~(nil = W)) & (nil = X)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U)))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(8,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : ((ssList(Y) & (U = Y)) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((((ssList(X1) & (tl(V) = Z)) & (app(Z, X1) = Y)) & ?[X2: $i] : (((ssItem(X2) & (cons(X2, nil) = X1)) & (hd(V) = X2)) & neq(nil, V))) & neq(nil, V))))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (~(app(X4, cons(X3, nil)) = W))) & (app(cons(X3, nil), X4) = X)))) | ((~(nil = W)) & (nil = X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 80.04/80.28 tff(9,plain,
% 80.04/80.28 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[8, 7])).
% 80.04/80.28 tff(10,plain,
% 80.04/80.28 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[9, 6])).
% 80.04/80.28 tff(11,plain,
% 80.04/80.28 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[10, 6])).
% 80.04/80.28 tff(12,plain,
% 80.04/80.28 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (~(app(X4, cons(X3, nil)) = U)) & (app(cons(X3, nil), X4) = V))) | (~ssList(U)) | (~neq(V, nil)) | (neq(nil, V) & ssList(U) & ssItem(hd(V)) & ssList(tl(V)) & ssList(cons(hd(V), nil)) & (app(tl(V), cons(hd(V), nil)) = U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[11, 6])).
% 80.04/80.28 tff(13,plain,
% 80.04/80.28 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) & neq(V!46, nil) & (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45)))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[12, 5])).
% 80.04/80.28 tff(14,plain,
% 80.04/80.28 (ssList(V!46)),
% 80.04/80.28 inference(and_elim,[status(thm)],[13])).
% 80.04/80.28 tff(15,plain,
% 80.04/80.28 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(16,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[15])).
% 80.04/80.28 tff(17,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(18,plain,
% 80.04/80.28 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(19,plain,
% 80.04/80.28 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[18])).
% 80.04/80.28 tff(20,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 80.04/80.28 tff(21,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[20, 19])).
% 80.04/80.28 tff(22,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[21, 17])).
% 80.04/80.28 tff(23,plain,(
% 80.04/80.28 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(skolemize,[status(sab)],[22])).
% 80.04/80.28 tff(24,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[23, 16])).
% 80.04/80.28 tff(25,plain,
% 80.04/80.28 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(26,plain,
% 80.04/80.28 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 80.04/80.28 inference(quant_inst,[status(thm)],[])).
% 80.04/80.28 tff(27,plain,
% 80.04/80.28 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[26, 25])).
% 80.04/80.28 tff(28,plain,
% 80.04/80.28 (segmentP(nil, V!46) <=> (nil = V!46)),
% 80.04/80.28 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 80.04/80.28 tff(29,plain,
% 80.04/80.28 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(30,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[29])).
% 80.04/80.28 tff(31,plain,
% 80.04/80.28 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(32,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[31])).
% 80.04/80.28 tff(33,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(transitivity,[status(thm)],[32, 30])).
% 80.04/80.28 tff(34,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(35,plain,
% 80.04/80.28 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(36,plain,
% 80.04/80.28 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[35])).
% 80.04/80.28 tff(37,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 80.04/80.28 tff(38,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[37, 36])).
% 80.04/80.28 tff(39,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[38, 34])).
% 80.04/80.28 tff(40,plain,(
% 80.04/80.28 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(skolemize,[status(sab)],[39])).
% 80.04/80.28 tff(41,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[40, 33])).
% 80.04/80.28 tff(42,plain,
% 80.04/80.28 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(43,plain,
% 80.04/80.28 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 80.04/80.28 inference(quant_inst,[status(thm)],[])).
% 80.04/80.28 tff(44,plain,
% 80.04/80.28 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[43, 42])).
% 80.04/80.28 tff(45,plain,
% 80.04/80.28 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 80.04/80.28 inference(unit_resolution,[status(thm)],[44, 41, 14])).
% 80.04/80.28 tff(46,plain,
% 80.04/80.28 (ssList(nil) <=> ssList(nil)),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(47,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 80.04/80.28 tff(48,plain,
% 80.04/80.28 (ssList(nil)),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[47, 46])).
% 80.04/80.28 tff(49,plain,
% 80.04/80.28 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(50,plain,
% 80.04/80.28 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 80.04/80.28 inference(quant_inst,[status(thm)],[])).
% 80.04/80.28 tff(51,plain,
% 80.04/80.28 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[50, 49])).
% 80.04/80.28 tff(52,plain,
% 80.04/80.28 (~((V!46 = nil) <=> neq(V!46, nil))),
% 80.04/80.28 inference(unit_resolution,[status(thm)],[51, 48, 45])).
% 80.04/80.28 tff(53,plain,
% 80.04/80.28 (neq(V!46, nil)),
% 80.04/80.28 inference(and_elim,[status(thm)],[13])).
% 80.04/80.28 tff(54,plain,
% 80.04/80.28 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 80.04/80.28 inference(tautology,[status(thm)],[])).
% 80.04/80.28 tff(55,plain,
% 80.04/80.28 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 80.04/80.28 inference(unit_resolution,[status(thm)],[54, 53])).
% 80.04/80.28 tff(56,plain,
% 80.04/80.28 (~(V!46 = nil)),
% 80.04/80.28 inference(unit_resolution,[status(thm)],[55, 52])).
% 80.04/80.28 tff(57,plain,
% 80.04/80.28 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(58,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[57])).
% 80.04/80.28 tff(59,plain,
% 80.04/80.28 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(60,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[59])).
% 80.04/80.28 tff(61,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(transitivity,[status(thm)],[60, 58])).
% 80.04/80.28 tff(62,plain,
% 80.04/80.28 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(63,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[62])).
% 80.04/80.28 tff(64,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(65,plain,
% 80.04/80.28 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 80.04/80.28 inference(bind,[status(th)],[])).
% 80.04/80.28 tff(66,plain,
% 80.04/80.28 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 80.04/80.28 inference(quant_intro,[status(thm)],[65])).
% 80.04/80.28 tff(67,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 80.04/80.28 tff(68,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[67, 66])).
% 80.04/80.28 tff(69,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[68, 64])).
% 80.04/80.28 tff(70,plain,(
% 80.04/80.28 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 80.04/80.28 inference(skolemize,[status(sab)],[69])).
% 80.04/80.28 tff(71,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[70, 63])).
% 80.04/80.28 tff(72,plain,
% 80.04/80.28 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 80.04/80.28 inference(modus_ponens,[status(thm)],[71, 61])).
% 80.04/80.28 tff(73,plain,
% 80.04/80.28 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(74,plain,
% 80.04/80.28 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 80.04/80.28 inference(rewrite,[status(thm)],[])).
% 80.04/80.28 tff(75,plain,
% 80.04/80.28 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 80.13/80.28 inference(monotonicity,[status(thm)],[74])).
% 80.13/80.28 tff(76,plain,
% 80.13/80.28 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 80.13/80.28 inference(transitivity,[status(thm)],[75, 73])).
% 80.13/80.28 tff(77,plain,
% 80.13/80.28 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 80.13/80.28 inference(quant_inst,[status(thm)],[])).
% 80.13/80.28 tff(78,plain,
% 80.13/80.28 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 80.13/80.28 inference(modus_ponens,[status(thm)],[77, 76])).
% 80.13/80.28 tff(79,plain,
% 80.13/80.28 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 80.13/80.28 inference(unit_resolution,[status(thm)],[78, 72, 14])).
% 80.13/80.28 tff(80,plain,
% 80.13/80.28 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 80.13/80.28 inference(bind,[status(th)],[])).
% 80.13/80.28 tff(81,plain,
% 80.13/80.28 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(quant_intro,[status(thm)],[80])).
% 80.13/80.28 tff(82,plain,
% 80.13/80.28 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(rewrite,[status(thm)],[])).
% 80.13/80.28 tff(83,plain,
% 80.13/80.28 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 80.13/80.28 inference(bind,[status(th)],[])).
% 80.13/80.28 tff(84,plain,
% 80.13/80.28 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(quant_intro,[status(thm)],[83])).
% 80.13/80.28 tff(85,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 80.13/80.28 tff(86,plain,
% 80.13/80.28 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(modus_ponens,[status(thm)],[85, 84])).
% 80.13/80.28 tff(87,plain,
% 80.13/80.28 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(modus_ponens,[status(thm)],[86, 82])).
% 80.13/80.28 tff(88,plain,(
% 80.13/80.28 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(skolemize,[status(sab)],[87])).
% 80.13/80.28 tff(89,plain,
% 80.13/80.28 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 80.13/80.28 inference(modus_ponens,[status(thm)],[88, 81])).
% 80.13/80.28 tff(90,plain,
% 80.13/80.28 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 80.13/80.28 inference(rewrite,[status(thm)],[])).
% 80.13/80.28 tff(91,plain,
% 80.13/80.28 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 80.13/80.28 inference(quant_inst,[status(thm)],[])).
% 80.13/80.28 tff(92,plain,
% 80.13/80.28 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 80.13/80.28 inference(modus_ponens,[status(thm)],[91, 90])).
% 80.13/80.28 tff(93,plain,
% 80.13/80.28 (segmentP(V!46, nil)),
% 80.13/80.28 inference(unit_resolution,[status(thm)],[92, 89, 14])).
% 80.13/80.28 tff(94,plain,
% 80.13/80.28 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 80.13/80.28 inference(rewrite,[status(thm)],[])).
% 80.13/80.28 tff(95,plain,
% 80.13/80.28 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 80.13/80.28 inference(rewrite,[status(thm)],[])).
% 80.13/80.28 tff(96,plain,
% 80.13/80.28 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 80.13/80.28 inference(monotonicity,[status(thm)],[95])).
% 80.13/80.28 tff(97,plain,
% 80.13/80.28 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 80.13/80.28 inference(transitivity,[status(thm)],[96, 94])).
% 80.13/80.28 tff(98,plain,
% 80.13/80.28 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(99,plain,
% 80.13/80.29 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[98, 97])).
% 80.13/80.29 tff(100,plain,
% 80.13/80.29 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[99, 48, 93, 79])).
% 80.13/80.29 tff(101,plain,
% 80.13/80.29 (~segmentP(nil, V!46)),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[100, 56])).
% 80.13/80.29 tff(102,plain,
% 80.13/80.29 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 80.13/80.29 inference(tautology,[status(thm)],[])).
% 80.13/80.29 tff(103,plain,
% 80.13/80.29 (~(nil = V!46)),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[102, 101, 28])).
% 80.13/80.29 tff(104,plain,
% 80.13/80.29 (^[U: $i] : refl(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(105,plain,
% 80.13/80.29 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[104])).
% 80.13/80.29 tff(106,plain,
% 80.13/80.29 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) <=> (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))), rewrite(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(107,plain,
% 80.13/80.29 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[106])).
% 80.13/80.29 tff(108,plain,
% 80.13/80.29 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))))), rewrite(((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(109,plain,
% 80.13/80.29 (![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[108])).
% 80.13/80.29 tff(110,plain,
% 80.13/80.29 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(111,plain,
% 80.13/80.29 (^[U: $i] : trans(monotonicity(rewrite(((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))))), rewrite((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(112,plain,
% 80.13/80.29 (![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[111])).
% 80.13/80.29 tff(113,axiom,(![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax20')).
% 80.13/80.29 tff(114,plain,
% 80.13/80.29 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[113, 112])).
% 80.13/80.29 tff(115,plain,
% 80.13/80.29 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[114, 110])).
% 80.13/80.29 tff(116,plain,(
% 80.13/80.29 ![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U)))),
% 80.13/80.29 inference(skolemize,[status(sab)],[115])).
% 80.13/80.29 tff(117,plain,
% 80.13/80.29 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[116, 109])).
% 80.13/80.29 tff(118,plain,
% 80.13/80.29 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[117, 107])).
% 80.13/80.29 tff(119,plain,
% 80.13/80.29 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[118, 105])).
% 80.13/80.29 tff(120,plain,
% 80.13/80.29 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(121,plain,
% 80.13/80.29 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(122,plain,
% 80.13/80.29 ((~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))) <=> (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(123,plain,
% 80.13/80.29 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(monotonicity,[status(thm)],[122])).
% 80.13/80.29 tff(124,plain,
% 80.13/80.29 (((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))) <=> ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(transitivity,[status(thm)],[123, 121])).
% 80.13/80.29 tff(125,plain,
% 80.13/80.29 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))))),
% 80.13/80.29 inference(monotonicity,[status(thm)],[124])).
% 80.13/80.29 tff(126,plain,
% 80.13/80.29 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(transitivity,[status(thm)],[125, 120])).
% 80.13/80.29 tff(127,plain,
% 80.13/80.29 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = V!46) | (~ssList(V!46)) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(128,plain,
% 80.13/80.29 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(V!46)) | (nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[127, 126])).
% 80.13/80.29 tff(129,plain,
% 80.13/80.29 ((nil = V!46) | (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[128, 119, 14])).
% 80.13/80.29 tff(130,plain,
% 80.13/80.29 (~((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[129, 103])).
% 80.13/80.29 tff(131,plain,
% 80.13/80.29 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46)),
% 80.13/80.29 inference(tautology,[status(thm)],[])).
% 80.13/80.29 tff(132,plain,
% 80.13/80.29 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[131, 130])).
% 80.13/80.29 tff(133,plain,
% 80.13/80.29 (V!46 = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))),
% 80.13/80.29 inference(symmetry,[status(thm)],[132])).
% 80.13/80.29 tff(134,plain,
% 80.13/80.29 ((app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46) <=> (app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 80.13/80.29 inference(monotonicity,[status(thm)],[133])).
% 80.13/80.29 tff(135,plain,
% 80.13/80.29 ((app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46) <=> (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)))),
% 80.13/80.29 inference(transitivity,[status(thm)],[134, 1])).
% 80.13/80.29 tff(136,plain,
% 80.13/80.29 ((cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))) <=> (app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)),
% 80.13/80.29 inference(symmetry,[status(thm)],[135])).
% 80.13/80.29 tff(137,plain,
% 80.13/80.29 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | ssList(tptp_fun_V_43(V!46))),
% 80.13/80.29 inference(tautology,[status(thm)],[])).
% 80.13/80.29 tff(138,plain,
% 80.13/80.29 (ssList(tptp_fun_V_43(V!46))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[137, 130])).
% 80.13/80.29 tff(139,plain,
% 80.13/80.29 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(140,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[139])).
% 80.13/80.29 tff(141,plain,
% 80.13/80.29 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(142,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[141])).
% 80.13/80.29 tff(143,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(transitivity,[status(thm)],[142, 140])).
% 80.13/80.29 tff(144,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(145,plain,
% 80.13/80.29 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(146,plain,
% 80.13/80.29 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[145])).
% 80.13/80.29 tff(147,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax81')).
% 80.13/80.29 tff(148,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[147, 146])).
% 80.13/80.29 tff(149,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[148, 144])).
% 80.13/80.29 tff(150,plain,(
% 80.13/80.29 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(skolemize,[status(sab)],[149])).
% 80.13/80.29 tff(151,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[150, 143])).
% 80.13/80.29 tff(152,plain,
% 80.13/80.29 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(153,plain,
% 80.13/80.29 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46)))))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(154,plain,
% 80.13/80.29 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[153, 152])).
% 80.13/80.29 tff(155,plain,
% 80.13/80.29 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[154, 151, 138])).
% 80.13/80.29 tff(156,plain,
% 80.13/80.29 (((~ssList(tptp_fun_V_43(V!46))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46))) | ssItem(tptp_fun_W_44(V!46))),
% 80.13/80.29 inference(tautology,[status(thm)],[])).
% 80.13/80.29 tff(157,plain,
% 80.13/80.29 (ssItem(tptp_fun_W_44(V!46))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[156, 130])).
% 80.13/80.29 tff(158,plain,
% 80.13/80.29 (((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(159,plain,
% 80.13/80.29 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(160,plain,
% 80.13/80.29 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[159, 158])).
% 80.13/80.29 tff(161,plain,
% 80.13/80.29 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[160, 157, 155])).
% 80.13/80.29 tff(162,plain,
% 80.13/80.29 (app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[161, 136])).
% 80.13/80.29 tff(163,plain,
% 80.13/80.29 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(164,plain,
% 80.13/80.29 (((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(165,plain,
% 80.13/80.29 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))))),
% 80.13/80.29 inference(monotonicity,[status(thm)],[164])).
% 80.13/80.29 tff(166,plain,
% 80.13/80.29 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 80.13/80.29 inference(transitivity,[status(thm)],[165, 163])).
% 80.13/80.29 tff(167,plain,
% 80.13/80.29 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(168,plain,
% 80.13/80.29 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[167, 166])).
% 80.13/80.29 tff(169,plain,
% 80.13/80.29 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[168, 48, 151])).
% 80.13/80.29 tff(170,plain,
% 80.13/80.29 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), nil)))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(171,plain,
% 80.13/80.29 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), nil)))),
% 80.13/80.29 inference(quant_inst,[status(thm)],[])).
% 80.13/80.29 tff(172,plain,
% 80.13/80.29 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), nil))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[171, 170])).
% 80.13/80.29 tff(173,plain,
% 80.13/80.29 (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), nil)),
% 80.13/80.29 inference(unit_resolution,[status(thm)],[172, 169, 157])).
% 80.13/80.29 tff(174,plain,
% 80.13/80.29 (app(cons(tptp_fun_W_44(V!46), nil), nil) = cons(tptp_fun_W_44(V!46), nil)),
% 80.13/80.29 inference(symmetry,[status(thm)],[173])).
% 80.13/80.29 tff(175,plain,
% 80.13/80.29 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(176,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[175])).
% 80.13/80.29 tff(177,plain,
% 80.13/80.29 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(178,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[177])).
% 80.13/80.29 tff(179,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(transitivity,[status(thm)],[178, 176])).
% 80.13/80.29 tff(180,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(rewrite,[status(thm)],[])).
% 80.13/80.29 tff(181,plain,
% 80.13/80.29 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))), ((ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> (ssList(V) => ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))))), rewrite((ssList(V) => ((nil = U) | (tl(app(U, V)) = app(tl(U), V)))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))), ((ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))), (![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))) <=> ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> (ssList(U) => ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))))), rewrite((ssList(U) => ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))))),
% 80.13/80.29 inference(bind,[status(th)],[])).
% 80.13/80.29 tff(182,plain,
% 80.13/80.29 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(quant_intro,[status(thm)],[181])).
% 80.13/80.29 tff(183,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (tl(app(U, V)) = app(tl(U), V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax86')).
% 80.13/80.29 tff(184,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[183, 182])).
% 80.13/80.29 tff(185,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[184, 180])).
% 80.13/80.29 tff(186,plain,(
% 80.13/80.29 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(skolemize,[status(sab)],[185])).
% 80.13/80.29 tff(187,plain,
% 80.13/80.29 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))),
% 80.13/80.29 inference(modus_ponens,[status(thm)],[186, 179])).
% 80.13/80.29 tff(188,plain,
% 80.13/80.29 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(189,plain,
% 80.13/80.30 (((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(190,plain,
% 80.13/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[189])).
% 80.13/80.30 tff(191,plain,
% 80.13/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V))))),
% 80.13/80.30 inference(transitivity,[status(thm)],[190, 188])).
% 80.13/80.30 tff(192,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | ((~ssList(V!46)) | ![V: $i] : ((nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)) | (~ssList(V))))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(193,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (tl(app(U, V)) = app(tl(U), V)) | (~ssList(V))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[192, 191])).
% 80.13/80.30 tff(194,plain,
% 80.13/80.30 (![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[193, 187, 14])).
% 80.13/80.30 tff(195,plain,
% 80.13/80.30 (((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | ((~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | (~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(196,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | ((~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil)))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(197,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssList(V)) | (nil = V!46) | (tl(app(V!46, V)) = app(tl(V!46), V)))) | (~ssList(nil)) | (nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[196, 195])).
% 80.13/80.30 tff(198,plain,
% 80.13/80.30 ((nil = V!46) | (tl(app(V!46, nil)) = app(tl(V!46), nil))),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[197, 48, 194])).
% 80.13/80.30 tff(199,plain,
% 80.13/80.30 (tl(app(V!46, nil)) = app(tl(V!46), nil)),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[198, 103])).
% 80.13/80.30 tff(200,plain,
% 80.13/80.30 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(201,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[200])).
% 80.13/80.30 tff(202,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(203,plain,
% 80.13/80.30 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(204,plain,
% 80.13/80.30 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[203])).
% 80.13/80.30 tff(205,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 80.13/80.30 tff(206,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[205, 204])).
% 80.13/80.30 tff(207,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[206, 202])).
% 80.13/80.30 tff(208,plain,(
% 80.13/80.30 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(skolemize,[status(sab)],[207])).
% 80.13/80.30 tff(209,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[208, 201])).
% 80.13/80.30 tff(210,plain,
% 80.13/80.30 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(211,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(V!46)) | (app(V!46, nil) = V!46))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(212,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(V!46)) | (app(V!46, nil) = V!46)),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[211, 210])).
% 80.13/80.30 tff(213,plain,
% 80.13/80.30 (app(V!46, nil) = V!46),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[212, 209, 14])).
% 80.13/80.30 tff(214,plain,
% 80.13/80.30 (V!46 = app(V!46, nil)),
% 80.13/80.30 inference(symmetry,[status(thm)],[213])).
% 80.13/80.30 tff(215,plain,
% 80.13/80.30 (tl(V!46) = tl(app(V!46, nil))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[214])).
% 80.13/80.30 tff(216,plain,
% 80.13/80.30 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tl(V!46)),
% 80.13/80.30 inference(monotonicity,[status(thm)],[132])).
% 80.13/80.30 tff(217,plain,
% 80.13/80.30 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(218,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[217])).
% 80.13/80.30 tff(219,plain,
% 80.13/80.30 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(220,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[219])).
% 80.13/80.30 tff(221,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(transitivity,[status(thm)],[220, 218])).
% 80.13/80.30 tff(222,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(223,plain,
% 80.13/80.30 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (tl(cons(V, U)) = U)) <=> ((~ssItem(V)) | (tl(cons(V, U)) = U)))), (![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)) <=> ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(224,plain,
% 80.13/80.30 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[223])).
% 80.13/80.30 tff(225,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax25')).
% 80.13/80.30 tff(226,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[225, 224])).
% 80.13/80.30 tff(227,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[226, 222])).
% 80.13/80.30 tff(228,plain,(
% 80.13/80.30 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(skolemize,[status(sab)],[227])).
% 80.13/80.30 tff(229,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[228, 221])).
% 80.13/80.30 tff(230,plain,
% 80.13/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(231,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(232,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[231, 230])).
% 80.13/80.30 tff(233,plain,
% 80.13/80.30 (![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[232, 229, 138])).
% 80.13/80.30 tff(234,plain,
% 80.13/80.30 (((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) <=> ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | (~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(235,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(236,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)))) | (~ssItem(tptp_fun_W_44(V!46))) | (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[235, 234])).
% 80.13/80.30 tff(237,plain,
% 80.13/80.30 (tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[236, 157, 233])).
% 80.13/80.30 tff(238,plain,
% 80.13/80.30 (tptp_fun_V_43(V!46) = tl(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(symmetry,[status(thm)],[237])).
% 80.13/80.30 tff(239,plain,
% 80.13/80.30 (tptp_fun_V_43(V!46) = app(tl(V!46), nil)),
% 80.13/80.30 inference(transitivity,[status(thm)],[238, 216, 215, 199])).
% 80.13/80.30 tff(240,plain,
% 80.13/80.30 (app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), nil)) = app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[239, 174])).
% 80.13/80.30 tff(241,plain,
% 80.13/80.30 (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), nil))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[173])).
% 80.13/80.30 tff(242,plain,
% 80.13/80.30 (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil))),
% 80.13/80.30 inference(transitivity,[status(thm)],[241, 240])).
% 80.13/80.30 tff(243,plain,
% 80.13/80.30 ((app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45) <=> (app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.13/80.30 inference(monotonicity,[status(thm)],[242])).
% 80.13/80.30 tff(244,plain,
% 80.13/80.30 ((app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil)) = U!45) <=> (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.13/80.30 inference(symmetry,[status(thm)],[243])).
% 80.13/80.30 tff(245,plain,
% 80.13/80.30 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = hd(V!46)),
% 80.13/80.30 inference(monotonicity,[status(thm)],[132])).
% 80.13/80.30 tff(246,plain,
% 80.13/80.30 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(247,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[246])).
% 80.13/80.30 tff(248,plain,
% 80.13/80.30 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(249,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[248])).
% 80.13/80.30 tff(250,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(transitivity,[status(thm)],[249, 247])).
% 80.13/80.30 tff(251,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(252,plain,
% 80.13/80.30 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (hd(cons(V, U)) = V)) <=> ((~ssItem(V)) | (hd(cons(V, U)) = V)))), (![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)) <=> ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(253,plain,
% 80.13/80.30 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[252])).
% 80.13/80.30 tff(254,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax23')).
% 80.13/80.30 tff(255,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[254, 253])).
% 80.13/80.30 tff(256,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[255, 251])).
% 80.13/80.30 tff(257,plain,(
% 80.13/80.30 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(skolemize,[status(sab)],[256])).
% 80.13/80.30 tff(258,plain,
% 80.13/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[257, 250])).
% 80.13/80.30 tff(259,plain,
% 80.13/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(260,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(261,plain,
% 80.13/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[260, 259])).
% 80.13/80.30 tff(262,plain,
% 80.13/80.30 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[261, 258, 138])).
% 80.13/80.30 tff(263,plain,
% 80.13/80.30 (((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(264,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 80.13/80.30 inference(quant_inst,[status(thm)],[])).
% 80.13/80.30 tff(265,plain,
% 80.13/80.30 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46))),
% 80.13/80.30 inference(modus_ponens,[status(thm)],[264, 263])).
% 80.13/80.30 tff(266,plain,
% 80.13/80.30 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)),
% 80.13/80.30 inference(unit_resolution,[status(thm)],[265, 157, 262])).
% 80.13/80.30 tff(267,plain,
% 80.13/80.30 (tptp_fun_W_44(V!46) = hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 80.13/80.30 inference(symmetry,[status(thm)],[266])).
% 80.13/80.30 tff(268,plain,
% 80.13/80.30 (tptp_fun_W_44(V!46) = hd(V!46)),
% 80.13/80.30 inference(transitivity,[status(thm)],[267, 245])).
% 80.13/80.30 tff(269,plain,
% 80.13/80.30 (cons(tptp_fun_W_44(V!46), nil) = cons(hd(V!46), nil)),
% 80.13/80.30 inference(monotonicity,[status(thm)],[268])).
% 80.13/80.30 tff(270,plain,
% 80.13/80.30 (tl(app(V!46, nil)) = tl(V!46)),
% 80.13/80.30 inference(symmetry,[status(thm)],[215])).
% 80.13/80.30 tff(271,plain,
% 80.13/80.30 (app(tl(V!46), nil) = tl(app(V!46, nil))),
% 80.13/80.30 inference(symmetry,[status(thm)],[199])).
% 80.13/80.30 tff(272,plain,
% 80.13/80.30 (app(tl(V!46), nil) = tl(V!46)),
% 80.13/80.30 inference(transitivity,[status(thm)],[271, 270])).
% 80.13/80.30 tff(273,plain,
% 80.13/80.30 (app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil)) = app(tl(V!46), cons(hd(V!46), nil))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[272, 269])).
% 80.13/80.30 tff(274,plain,
% 80.13/80.30 ((app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil)) = U!45) <=> (app(tl(V!46), cons(hd(V!46), nil)) = U!45)),
% 80.13/80.30 inference(monotonicity,[status(thm)],[273])).
% 80.13/80.30 tff(275,plain,
% 80.13/80.30 ((app(tl(V!46), cons(hd(V!46), nil)) = U!45) <=> (app(app(tl(V!46), nil), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.13/80.30 inference(symmetry,[status(thm)],[274])).
% 80.13/80.30 tff(276,plain,
% 80.13/80.30 ((app(tl(V!46), cons(hd(V!46), nil)) = U!45) <=> (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.13/80.30 inference(transitivity,[status(thm)],[275, 244])).
% 80.13/80.30 tff(277,plain,
% 80.13/80.30 ((~(app(tl(V!46), cons(hd(V!46), nil)) = U!45)) <=> (~(app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 80.13/80.30 inference(monotonicity,[status(thm)],[276])).
% 80.13/80.30 tff(278,plain,
% 80.13/80.30 (^[U: $i] : refl(((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(279,plain,
% 80.13/80.30 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.13/80.30 inference(quant_intro,[status(thm)],[278])).
% 80.13/80.30 tff(280,plain,
% 80.13/80.30 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.13/80.30 inference(rewrite,[status(thm)],[])).
% 80.13/80.30 tff(281,plain,
% 80.13/80.30 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssList(tl(U))) <=> ((nil = U) | ssList(tl(U)))), ((ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> (ssList(U) => ((nil = U) | ssList(tl(U)))))), rewrite((ssList(U) => ((nil = U) | ssList(tl(U)))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ((nil = U) | ssList(tl(U)) | (~ssList(U)))))),
% 80.13/80.30 inference(bind,[status(th)],[])).
% 80.13/80.30 tff(282,plain,
% 80.13/80.30 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U)))) <=> ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[281])).
% 80.15/80.30 tff(283,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssList(tl(U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax24')).
% 80.15/80.30 tff(284,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[283, 282])).
% 80.15/80.30 tff(285,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[284, 280])).
% 80.15/80.30 tff(286,plain,(
% 80.15/80.30 ![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.15/80.30 inference(skolemize,[status(sab)],[285])).
% 80.15/80.30 tff(287,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[286, 279])).
% 80.15/80.30 tff(288,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(289,plain,
% 80.15/80.30 (((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46))) <=> (ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(290,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | (ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46)))),
% 80.15/80.30 inference(monotonicity,[status(thm)],[289])).
% 80.15/80.30 tff(291,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(transitivity,[status(thm)],[290, 288])).
% 80.15/80.30 tff(292,plain,
% 80.15/80.30 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ((nil = V!46) | ssList(tl(V!46)) | (~ssList(V!46)))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(293,plain,
% 80.15/80.30 ((~![U: $i] : ((nil = U) | ssList(tl(U)) | (~ssList(U)))) | ssList(tl(V!46)) | (~ssList(V!46)) | (nil = V!46)),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[292, 291])).
% 80.15/80.30 tff(294,plain,
% 80.15/80.30 (ssList(tl(V!46))),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[293, 287, 103, 14])).
% 80.15/80.30 tff(295,plain,
% 80.15/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(296,plain,
% 80.15/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(297,plain,
% 80.15/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[296, 295])).
% 80.15/80.30 tff(298,plain,
% 80.15/80.30 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[297, 41, 48])).
% 80.15/80.30 tff(299,plain,
% 80.15/80.30 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(300,plain,
% 80.15/80.30 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(301,plain,
% 80.15/80.30 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[300, 299])).
% 80.15/80.30 tff(302,plain,
% 80.15/80.30 (~((nil = V!46) <=> neq(nil, V!46))),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[301, 14, 298])).
% 80.15/80.30 tff(303,plain,
% 80.15/80.30 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 80.15/80.30 inference(tautology,[status(thm)],[])).
% 80.15/80.30 tff(304,plain,
% 80.15/80.30 (neq(nil, V!46)),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[303, 103, 302])).
% 80.15/80.30 tff(305,plain,
% 80.15/80.30 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 80.15/80.30 inference(bind,[status(th)],[])).
% 80.15/80.30 tff(306,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[305])).
% 80.15/80.30 tff(307,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(308,plain,
% 80.15/80.30 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssItem(hd(U))) <=> ((nil = U) | ssItem(hd(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> (ssList(U) => ((nil = U) | ssItem(hd(U)))))), rewrite((ssList(U) => ((nil = U) | ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))))),
% 80.15/80.30 inference(bind,[status(th)],[])).
% 80.15/80.30 tff(309,plain,
% 80.15/80.30 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[308])).
% 80.15/80.30 tff(310,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax22')).
% 80.15/80.30 tff(311,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[310, 309])).
% 80.15/80.30 tff(312,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[311, 307])).
% 80.15/80.30 tff(313,plain,(
% 80.15/80.30 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(skolemize,[status(sab)],[312])).
% 80.15/80.30 tff(314,plain,
% 80.15/80.30 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[313, 306])).
% 80.15/80.30 tff(315,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(316,plain,
% 80.15/80.30 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(317,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46)))),
% 80.15/80.30 inference(monotonicity,[status(thm)],[316])).
% 80.15/80.30 tff(318,plain,
% 80.15/80.30 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 80.15/80.30 inference(transitivity,[status(thm)],[317, 315])).
% 80.15/80.30 tff(319,plain,
% 80.15/80.30 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(320,plain,
% 80.15/80.30 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46)),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[319, 318])).
% 80.15/80.30 tff(321,plain,
% 80.15/80.30 (ssItem(hd(V!46)) | (nil = V!46)),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[320, 314, 14])).
% 80.15/80.30 tff(322,plain,
% 80.15/80.30 (ssItem(hd(V!46))),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[321, 103])).
% 80.15/80.30 tff(323,plain,
% 80.15/80.30 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 80.15/80.30 inference(bind,[status(th)],[])).
% 80.15/80.30 tff(324,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[323])).
% 80.15/80.30 tff(325,plain,
% 80.15/80.30 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 80.15/80.30 inference(bind,[status(th)],[])).
% 80.15/80.30 tff(326,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[325])).
% 80.15/80.30 tff(327,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(transitivity,[status(thm)],[326, 324])).
% 80.15/80.30 tff(328,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(329,plain,
% 80.15/80.30 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 80.15/80.30 inference(bind,[status(th)],[])).
% 80.15/80.30 tff(330,plain,
% 80.15/80.30 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(quant_intro,[status(thm)],[329])).
% 80.15/80.30 tff(331,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax16')).
% 80.15/80.30 tff(332,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[331, 330])).
% 80.15/80.30 tff(333,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[332, 328])).
% 80.15/80.30 tff(334,plain,(
% 80.15/80.30 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(skolemize,[status(sab)],[333])).
% 80.15/80.30 tff(335,plain,
% 80.15/80.30 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[334, 327])).
% 80.15/80.30 tff(336,plain,
% 80.15/80.30 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(337,plain,
% 80.15/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(338,plain,
% 80.15/80.30 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 80.15/80.30 inference(modus_ponens,[status(thm)],[337, 336])).
% 80.15/80.30 tff(339,plain,
% 80.15/80.30 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 80.15/80.30 inference(unit_resolution,[status(thm)],[338, 335, 48])).
% 80.15/80.30 tff(340,plain,
% 80.15/80.30 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 80.15/80.30 inference(rewrite,[status(thm)],[])).
% 80.15/80.30 tff(341,plain,
% 80.15/80.30 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 80.15/80.30 inference(quant_inst,[status(thm)],[])).
% 80.15/80.30 tff(342,plain,
% 80.15/80.31 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[341, 340])).
% 80.15/80.31 tff(343,plain,
% 80.15/80.31 (ssList(cons(hd(V!46), nil))),
% 80.15/80.31 inference(unit_resolution,[status(thm)],[342, 322, 339])).
% 80.15/80.31 tff(344,plain,
% 80.15/80.31 (ssList(U!45)),
% 80.15/80.31 inference(and_elim,[status(thm)],[13])).
% 80.15/80.31 tff(345,plain,
% 80.15/80.31 ((~(~((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45))))) <=> ((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45)))),
% 80.15/80.31 inference(rewrite,[status(thm)],[])).
% 80.15/80.31 tff(346,plain,
% 80.15/80.31 ((neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45)) <=> (~((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45))))),
% 80.15/80.31 inference(rewrite,[status(thm)],[])).
% 80.15/80.31 tff(347,plain,
% 80.15/80.31 ((~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))) <=> (~(~((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45)))))),
% 80.15/80.31 inference(monotonicity,[status(thm)],[346])).
% 80.15/80.31 tff(348,plain,
% 80.15/80.31 ((~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))) <=> ((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45)))),
% 80.15/80.31 inference(transitivity,[status(thm)],[347, 345])).
% 80.15/80.31 tff(349,plain,
% 80.15/80.31 (~(neq(nil, V!46) & ssList(U!45) & ssItem(hd(V!46)) & ssList(tl(V!46)) & ssList(cons(hd(V!46), nil)) & (app(tl(V!46), cons(hd(V!46), nil)) = U!45))),
% 80.15/80.31 inference(and_elim,[status(thm)],[13])).
% 80.15/80.31 tff(350,plain,
% 80.15/80.31 ((~ssList(U!45)) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45))),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[349, 348])).
% 80.15/80.31 tff(351,plain,
% 80.15/80.31 ((~neq(nil, V!46)) | (~ssItem(hd(V!46))) | (~ssList(tl(V!46))) | (~ssList(cons(hd(V!46), nil))) | (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45))),
% 80.15/80.31 inference(unit_resolution,[status(thm)],[350, 344])).
% 80.15/80.31 tff(352,plain,
% 80.15/80.31 (~(app(tl(V!46), cons(hd(V!46), nil)) = U!45)),
% 80.15/80.31 inference(unit_resolution,[status(thm)],[351, 343, 322, 304, 294])).
% 80.15/80.31 tff(353,plain,
% 80.15/80.31 (~(app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[352, 277])).
% 80.15/80.31 tff(354,plain,
% 80.15/80.31 (^[X3: $i] : refl(((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))) <=> ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))))),
% 80.15/80.31 inference(bind,[status(th)],[])).
% 80.15/80.31 tff(355,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))) <=> ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(quant_intro,[status(thm)],[354])).
% 80.15/80.31 tff(356,plain,
% 80.15/80.31 (^[X3: $i] : rewrite(((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))) <=> ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))))),
% 80.15/80.31 inference(bind,[status(th)],[])).
% 80.15/80.31 tff(357,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))) <=> ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(quant_intro,[status(thm)],[356])).
% 80.15/80.31 tff(358,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))) <=> ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(transitivity,[status(thm)],[357, 355])).
% 80.15/80.31 tff(359,plain,
% 80.15/80.31 (^[X3: $i] : rewrite(((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) <=> ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46)))))),
% 80.15/80.31 inference(bind,[status(th)],[])).
% 80.15/80.31 tff(360,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46)))) <=> ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(quant_intro,[status(thm)],[359])).
% 80.15/80.31 tff(361,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (~(app(X4, cons(X3, nil)) = U!45)) & (app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(and_elim,[status(thm)],[13])).
% 80.15/80.31 tff(362,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[361, 360])).
% 80.15/80.31 tff(363,plain,
% 80.15/80.31 (![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[362, 358])).
% 80.15/80.31 tff(364,plain,
% 80.15/80.31 (((~![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46))))) <=> ((~![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46))))),
% 80.15/80.31 inference(rewrite,[status(thm)],[])).
% 80.15/80.31 tff(365,plain,
% 80.15/80.31 ((~![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46))))),
% 80.15/80.31 inference(quant_inst,[status(thm)],[])).
% 80.15/80.31 tff(366,plain,
% 80.15/80.31 ((~![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(X3, nil)) = U!45) | (~(app(cons(X3, nil), X4) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))),
% 80.15/80.31 inference(modus_ponens,[status(thm)],[365, 364])).
% 80.15/80.31 tff(367,plain,
% 80.15/80.31 (![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))),
% 80.15/80.31 inference(unit_resolution,[status(thm)],[366, 363, 157])).
% 80.15/80.31 tff(368,plain,
% 80.15/80.31 (((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))) <=> ((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 80.15/80.31 inference(rewrite,[status(thm)],[])).
% 80.15/80.31 tff(369,plain,
% 80.15/80.31 (((~ssList(tptp_fun_V_43(V!46))) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46))) <=> ((~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 80.34/80.56 inference(rewrite,[status(thm)],[])).
% 80.34/80.56 tff(370,plain,
% 80.34/80.56 (((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)))) <=> ((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 80.34/80.56 inference(monotonicity,[status(thm)],[369])).
% 80.34/80.56 tff(371,plain,
% 80.34/80.56 (((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)))) <=> ((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 80.34/80.56 inference(transitivity,[status(thm)],[370, 368])).
% 80.34/80.56 tff(372,plain,
% 80.34/80.56 ((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)))),
% 80.34/80.56 inference(quant_inst,[status(thm)],[])).
% 80.34/80.56 tff(373,plain,
% 80.34/80.56 ((~![X4: $i] : ((~ssList(X4)) | (app(X4, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X4) = V!46)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.34/80.56 inference(modus_ponens,[status(thm)],[372, 371])).
% 80.34/80.56 tff(374,plain,
% 80.34/80.56 ((~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45)),
% 80.34/80.56 inference(unit_resolution,[status(thm)],[373, 138, 367])).
% 80.34/80.56 tff(375,plain,
% 80.34/80.56 ($false),
% 80.34/80.56 inference(unit_resolution,[status(thm)],[374, 353, 162])).
% 80.34/80.56 % SZS output end Proof
% 80.34/80.56 % E exiting
%------------------------------------------------------------------------------