%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC309+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 77.82s 78.09s
% Output : Proof 78.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC309+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:58:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 77.82/78.09 % SZS status Theorem
% 77.82/78.09 % SZS output start Proof
% 77.82/78.09 tff(tptp_fun_V_46_type, type, (
% 77.82/78.09 tptp_fun_V_46: $i)).
% 77.82/78.09 tff(app_type, type, (
% 77.82/78.09 app: ( $i * $i ) > $i)).
% 77.82/78.09 tff(tptp_fun_V_43_type, type, (
% 77.82/78.09 tptp_fun_V_43: $i > $i)).
% 77.82/78.09 tff(cons_type, type, (
% 77.82/78.09 cons: ( $i * $i ) > $i)).
% 77.82/78.09 tff(nil_type, type, (
% 77.82/78.09 nil: $i)).
% 77.82/78.09 tff(tptp_fun_W_44_type, type, (
% 77.82/78.09 tptp_fun_W_44: $i > $i)).
% 77.82/78.09 tff(ssItem_type, type, (
% 77.82/78.09 ssItem: $i > $o)).
% 77.82/78.09 tff(ssList_type, type, (
% 77.82/78.09 ssList: $i > $o)).
% 77.82/78.09 tff(segmentP_type, type, (
% 77.82/78.09 segmentP: ( $i * $i ) > $o)).
% 77.82/78.09 tff(tptp_fun_U_45_type, type, (
% 77.82/78.09 tptp_fun_U_45: $i)).
% 77.82/78.09 tff(neq_type, type, (
% 77.82/78.09 neq: ( $i * $i ) > $o)).
% 77.82/78.09 tff(1,plain,
% 77.82/78.09 ((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)))),
% 77.82/78.09 inference(commutativity,[status(thm)],[])).
% 77.82/78.09 tff(2,plain,
% 77.82/78.09 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))),
% 77.82/78.09 inference(rewrite,[status(thm)],[])).
% 77.82/78.09 tff(3,plain,
% 77.82/78.09 (((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45))))) <=> ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))),
% 77.82/78.09 inference(rewrite,[status(thm)],[])).
% 77.82/78.09 tff(4,plain,
% 77.82/78.09 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45))))))),
% 77.82/78.09 inference(monotonicity,[status(thm)],[3])).
% 77.82/78.09 tff(5,plain,
% 77.82/78.09 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & ssList(U!45) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))))),
% 77.82/78.09 inference(transitivity,[status(thm)],[4, 2])).
% 77.82/78.09 tff(6,plain,
% 77.82/78.09 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U))))))),
% 77.82/78.09 inference(rewrite,[status(thm)],[])).
% 77.82/78.09 tff(7,plain,
% 77.82/78.09 ((~![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] : (ssItem(Y) & ?[Z: $i] : ((ssList(Z) & (app(cons(Y, nil), Z) = V)) & (app(Z, cons(Y, nil)) = U)))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (~(app(X2, cons(X1, nil)) = W))) & (app(cons(X1, nil), X2) = X)))) | ((~(nil = W)) & (nil = X)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U))))))),
% 77.82/78.09 inference(rewrite,[status(thm)],[])).
% 77.82/78.09 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] : (ssItem(Y) & ?[Z: $i] : ((ssList(Z) & (app(cons(Y, nil), Z) = V)) & (app(Z, cons(Y, nil)) = U)))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (~(app(X2, cons(X1, nil)) = W))) & (app(cons(X1, nil), X2) = X)))) | ((~(nil = W)) & (nil = X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 77.82/78.09 tff(9,plain,
% 77.82/78.09 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U)))))),
% 77.82/78.09 inference(modus_ponens,[status(thm)],[8, 7])).
% 77.82/78.09 tff(10,plain,
% 77.82/78.09 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U)))))),
% 77.82/78.09 inference(modus_ponens,[status(thm)],[9, 6])).
% 77.82/78.09 tff(11,plain,
% 77.82/78.09 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U)))))),
% 77.82/78.09 inference(modus_ponens,[status(thm)],[10, 6])).
% 77.82/78.09 tff(12,plain,
% 77.82/78.09 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (~(app(X2, cons(X1, nil)) = U)) & (app(cons(X1, nil), X2) = V))) | (~ssList(U)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (app(cons(Y, nil), Z) = V) & (app(Z, cons(Y, nil)) = U)))))),
% 77.82/78.09 inference(modus_ponens,[status(thm)],[11, 6])).
% 77.82/78.09 tff(13,plain,
% 77.82/78.09 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) & neq(V!46, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45))))),
% 77.82/78.09 inference(modus_ponens,[status(thm)],[12, 5])).
% 77.82/78.09 tff(14,plain,
% 77.82/78.09 (ssList(V!46)),
% 77.82/78.09 inference(and_elim,[status(thm)],[13])).
% 77.82/78.09 tff(15,plain,
% 77.82/78.09 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 77.82/78.10 inference(bind,[status(th)],[])).
% 77.82/78.10 tff(16,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(quant_intro,[status(thm)],[15])).
% 77.82/78.10 tff(17,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(18,plain,
% 77.82/78.10 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 77.82/78.10 inference(bind,[status(th)],[])).
% 77.82/78.10 tff(19,plain,
% 77.82/78.10 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(quant_intro,[status(thm)],[18])).
% 77.82/78.10 tff(20,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 77.82/78.10 tff(21,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[20, 19])).
% 77.82/78.10 tff(22,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[21, 17])).
% 77.82/78.10 tff(23,plain,(
% 77.82/78.10 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(skolemize,[status(sab)],[22])).
% 77.82/78.10 tff(24,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[23, 16])).
% 77.82/78.10 tff(25,plain,
% 77.82/78.10 (((~![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)))),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(26,plain,
% 77.82/78.10 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 77.82/78.10 inference(quant_inst,[status(thm)],[])).
% 77.82/78.10 tff(27,plain,
% 77.82/78.10 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[26, 25])).
% 77.82/78.10 tff(28,plain,
% 77.82/78.10 (segmentP(nil, V!46) <=> (nil = V!46)),
% 77.82/78.10 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 77.82/78.10 tff(29,plain,
% 77.82/78.10 (^[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))))))),
% 77.82/78.10 inference(bind,[status(th)],[])).
% 77.82/78.10 tff(30,plain,
% 77.82/78.10 (![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)))))),
% 77.82/78.10 inference(quant_intro,[status(thm)],[29])).
% 77.82/78.10 tff(31,plain,
% 77.82/78.10 (^[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))))))),
% 77.82/78.10 inference(bind,[status(th)],[])).
% 77.82/78.10 tff(32,plain,
% 77.82/78.10 (![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)))))),
% 77.82/78.10 inference(quant_intro,[status(thm)],[31])).
% 77.82/78.10 tff(33,plain,
% 77.82/78.10 (![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)))))),
% 77.82/78.10 inference(transitivity,[status(thm)],[32, 30])).
% 77.82/78.10 tff(34,plain,
% 77.82/78.10 (![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)))))),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(35,plain,
% 77.82/78.10 (^[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)))))))),
% 77.82/78.10 inference(bind,[status(th)],[])).
% 77.82/78.10 tff(36,plain,
% 77.82/78.10 (![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)))))),
% 77.82/78.10 inference(quant_intro,[status(thm)],[35])).
% 77.82/78.10 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')).
% 77.82/78.10 tff(38,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[37, 36])).
% 77.82/78.10 tff(39,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[38, 34])).
% 77.82/78.10 tff(40,plain,(
% 77.82/78.10 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 77.82/78.10 inference(skolemize,[status(sab)],[39])).
% 77.82/78.10 tff(41,plain,
% 77.82/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[40, 33])).
% 77.82/78.10 tff(42,plain,
% 77.82/78.10 (((~![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)))))),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(43,plain,
% 77.82/78.10 ((~![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)))))),
% 77.82/78.10 inference(quant_inst,[status(thm)],[])).
% 77.82/78.10 tff(44,plain,
% 77.82/78.10 ((~![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))))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[43, 42])).
% 77.82/78.10 tff(45,plain,
% 77.82/78.10 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 77.82/78.10 inference(unit_resolution,[status(thm)],[44, 41, 14])).
% 77.82/78.10 tff(46,plain,
% 77.82/78.10 (ssList(nil) <=> ssList(nil)),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(47,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 77.82/78.10 tff(48,plain,
% 77.82/78.10 (ssList(nil)),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[47, 46])).
% 77.82/78.10 tff(49,plain,
% 77.82/78.10 (((~![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))))),
% 77.82/78.10 inference(rewrite,[status(thm)],[])).
% 77.82/78.10 tff(50,plain,
% 77.82/78.10 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 77.82/78.10 inference(quant_inst,[status(thm)],[])).
% 77.82/78.10 tff(51,plain,
% 77.82/78.10 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 77.82/78.10 inference(modus_ponens,[status(thm)],[50, 49])).
% 77.82/78.10 tff(52,plain,
% 77.82/78.10 (~((V!46 = nil) <=> neq(V!46, nil))),
% 77.82/78.10 inference(unit_resolution,[status(thm)],[51, 48, 45])).
% 77.82/78.10 tff(53,plain,
% 77.82/78.10 (neq(V!46, nil)),
% 77.91/78.10 inference(and_elim,[status(thm)],[13])).
% 77.91/78.10 tff(54,plain,
% 77.91/78.10 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 77.91/78.10 inference(tautology,[status(thm)],[])).
% 77.91/78.10 tff(55,plain,
% 77.91/78.10 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[54, 53])).
% 77.91/78.10 tff(56,plain,
% 77.91/78.10 (~(V!46 = nil)),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[55, 52])).
% 77.91/78.10 tff(57,plain,
% 77.91/78.10 (^[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)))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(58,plain,
% 77.91/78.10 (![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))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[57])).
% 77.91/78.10 tff(59,plain,
% 77.91/78.10 (^[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)))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(60,plain,
% 77.91/78.10 (![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))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[59])).
% 77.91/78.10 tff(61,plain,
% 77.91/78.10 (![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))))),
% 77.91/78.10 inference(transitivity,[status(thm)],[60, 58])).
% 77.91/78.10 tff(62,plain,
% 77.91/78.10 (^[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)))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(63,plain,
% 77.91/78.10 (![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))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[62])).
% 77.91/78.10 tff(64,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(65,plain,
% 77.91/78.10 (^[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)))))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(66,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[65])).
% 77.91/78.10 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')).
% 77.91/78.10 tff(68,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[67, 66])).
% 77.91/78.10 tff(69,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[68, 64])).
% 77.91/78.10 tff(70,plain,(
% 77.91/78.10 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 77.91/78.10 inference(skolemize,[status(sab)],[69])).
% 77.91/78.10 tff(71,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[70, 63])).
% 77.91/78.10 tff(72,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[71, 61])).
% 77.91/78.10 tff(73,plain,
% 77.91/78.10 (((~![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))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(74,plain,
% 77.91/78.10 (((~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))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(75,plain,
% 77.91/78.10 (((~![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)))))),
% 77.91/78.10 inference(monotonicity,[status(thm)],[74])).
% 77.91/78.10 tff(76,plain,
% 77.91/78.10 (((~![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))))),
% 77.91/78.10 inference(transitivity,[status(thm)],[75, 73])).
% 77.91/78.10 tff(77,plain,
% 77.91/78.10 ((~![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))))),
% 77.91/78.10 inference(quant_inst,[status(thm)],[])).
% 77.91/78.10 tff(78,plain,
% 77.91/78.10 ((~![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)))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[77, 76])).
% 77.91/78.10 tff(79,plain,
% 77.91/78.10 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[78, 72, 14])).
% 77.91/78.10 tff(80,plain,
% 77.91/78.10 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(81,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[80])).
% 77.91/78.10 tff(82,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(83,plain,
% 77.91/78.10 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(84,plain,
% 77.91/78.10 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[83])).
% 77.91/78.10 tff(85,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 77.91/78.10 tff(86,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[85, 84])).
% 77.91/78.10 tff(87,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[86, 82])).
% 77.91/78.10 tff(88,plain,(
% 77.91/78.10 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(skolemize,[status(sab)],[87])).
% 77.91/78.10 tff(89,plain,
% 77.91/78.10 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[88, 81])).
% 77.91/78.10 tff(90,plain,
% 77.91/78.10 (((~![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))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(91,plain,
% 77.91/78.10 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 77.91/78.10 inference(quant_inst,[status(thm)],[])).
% 77.91/78.10 tff(92,plain,
% 77.91/78.10 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[91, 90])).
% 77.91/78.10 tff(93,plain,
% 77.91/78.10 (segmentP(V!46, nil)),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[92, 89, 14])).
% 77.91/78.10 tff(94,plain,
% 77.91/78.10 (((~![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)))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(95,plain,
% 77.91/78.10 (((~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)))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(96,plain,
% 77.91/78.10 (((~![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))))),
% 77.91/78.10 inference(monotonicity,[status(thm)],[95])).
% 77.91/78.10 tff(97,plain,
% 77.91/78.10 (((~![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)))),
% 77.91/78.10 inference(transitivity,[status(thm)],[96, 94])).
% 77.91/78.10 tff(98,plain,
% 77.91/78.10 ((~![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)))),
% 77.91/78.10 inference(quant_inst,[status(thm)],[])).
% 77.91/78.10 tff(99,plain,
% 77.91/78.10 ((~![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))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[98, 97])).
% 77.91/78.10 tff(100,plain,
% 77.91/78.10 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[99, 48, 93, 79])).
% 77.91/78.10 tff(101,plain,
% 77.91/78.10 (~segmentP(nil, V!46)),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[100, 56])).
% 77.91/78.10 tff(102,plain,
% 77.91/78.10 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 77.91/78.10 inference(tautology,[status(thm)],[])).
% 77.91/78.10 tff(103,plain,
% 77.91/78.10 (~(nil = V!46)),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[102, 101, 28])).
% 77.91/78.10 tff(104,plain,
% 77.91/78.10 (^[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))))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(105,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[104])).
% 77.91/78.10 tff(106,plain,
% 77.91/78.10 (^[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)))))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(107,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[106])).
% 77.91/78.10 tff(108,plain,
% 77.91/78.10 (^[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)))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(109,plain,
% 77.91/78.10 (![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)))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[108])).
% 77.91/78.10 tff(110,plain,
% 77.91/78.10 (![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)))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(111,plain,
% 77.91/78.10 (^[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)))))),
% 77.91/78.10 inference(bind,[status(th)],[])).
% 77.91/78.10 tff(112,plain,
% 77.91/78.10 (![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)))),
% 77.91/78.10 inference(quant_intro,[status(thm)],[111])).
% 77.91/78.10 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')).
% 77.91/78.10 tff(114,plain,
% 77.91/78.10 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[113, 112])).
% 77.91/78.10 tff(115,plain,
% 77.91/78.10 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[114, 110])).
% 77.91/78.10 tff(116,plain,(
% 77.91/78.10 ![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)))),
% 77.91/78.10 inference(skolemize,[status(sab)],[115])).
% 77.91/78.10 tff(117,plain,
% 77.91/78.10 (![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)))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[116, 109])).
% 77.91/78.10 tff(118,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[117, 107])).
% 77.91/78.10 tff(119,plain,
% 77.91/78.10 (![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)))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[118, 105])).
% 77.91/78.10 tff(120,plain,
% 77.91/78.10 (((~![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)))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(121,plain,
% 77.91/78.10 (((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)))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(122,plain,
% 77.91/78.10 ((~((~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))))),
% 77.91/78.10 inference(rewrite,[status(thm)],[])).
% 77.91/78.10 tff(123,plain,
% 77.91/78.10 (((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)))))),
% 77.91/78.10 inference(monotonicity,[status(thm)],[122])).
% 77.91/78.10 tff(124,plain,
% 77.91/78.10 (((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)))))),
% 77.91/78.10 inference(transitivity,[status(thm)],[123, 121])).
% 77.91/78.10 tff(125,plain,
% 77.91/78.10 (((~![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))))))),
% 77.91/78.10 inference(monotonicity,[status(thm)],[124])).
% 77.91/78.10 tff(126,plain,
% 77.91/78.10 (((~![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)))))),
% 77.91/78.10 inference(transitivity,[status(thm)],[125, 120])).
% 77.91/78.10 tff(127,plain,
% 77.91/78.10 ((~![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)))))),
% 77.91/78.10 inference(quant_inst,[status(thm)],[])).
% 77.91/78.10 tff(128,plain,
% 77.91/78.10 ((~![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))))),
% 77.91/78.10 inference(modus_ponens,[status(thm)],[127, 126])).
% 77.91/78.10 tff(129,plain,
% 77.91/78.10 ((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))))),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[128, 119, 14])).
% 77.91/78.10 tff(130,plain,
% 77.91/78.10 (~((~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)))),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[129, 103])).
% 77.91/78.10 tff(131,plain,
% 77.91/78.10 (((~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)),
% 77.91/78.10 inference(tautology,[status(thm)],[])).
% 77.91/78.10 tff(132,plain,
% 77.91/78.10 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 77.91/78.10 inference(unit_resolution,[status(thm)],[131, 130])).
% 77.91/78.10 tff(133,plain,
% 77.91/78.10 (V!46 = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))),
% 77.91/78.10 inference(symmetry,[status(thm)],[132])).
% 77.91/78.10 tff(134,plain,
% 77.91/78.10 ((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)))),
% 77.91/78.11 inference(monotonicity,[status(thm)],[133])).
% 77.91/78.11 tff(135,plain,
% 77.91/78.11 ((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)))),
% 77.91/78.11 inference(transitivity,[status(thm)],[134, 1])).
% 77.91/78.11 tff(136,plain,
% 77.91/78.11 ((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)),
% 77.91/78.11 inference(symmetry,[status(thm)],[135])).
% 77.91/78.11 tff(137,plain,
% 77.91/78.11 (((~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))),
% 77.91/78.11 inference(tautology,[status(thm)],[])).
% 77.91/78.11 tff(138,plain,
% 77.91/78.11 (ssList(tptp_fun_V_43(V!46))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[137, 130])).
% 77.91/78.11 tff(139,plain,
% 77.91/78.11 (^[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)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(140,plain,
% 77.91/78.11 (![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))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[139])).
% 77.91/78.11 tff(141,plain,
% 77.91/78.11 (^[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)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(142,plain,
% 77.91/78.11 (![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))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[141])).
% 77.91/78.11 tff(143,plain,
% 77.91/78.11 (![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))))),
% 77.91/78.11 inference(transitivity,[status(thm)],[142, 140])).
% 77.91/78.11 tff(144,plain,
% 77.91/78.11 (![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))))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(145,plain,
% 77.91/78.11 (^[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))))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(146,plain,
% 77.91/78.11 (![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))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[145])).
% 77.91/78.11 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')).
% 77.91/78.11 tff(148,plain,
% 77.91/78.11 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[147, 146])).
% 77.91/78.11 tff(149,plain,
% 77.91/78.11 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[148, 144])).
% 77.91/78.11 tff(150,plain,(
% 77.91/78.11 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 77.91/78.11 inference(skolemize,[status(sab)],[149])).
% 77.91/78.11 tff(151,plain,
% 77.91/78.11 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[150, 143])).
% 77.91/78.11 tff(152,plain,
% 77.91/78.11 (((~![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)))))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(153,plain,
% 77.91/78.11 ((~![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)))))),
% 77.91/78.11 inference(quant_inst,[status(thm)],[])).
% 77.91/78.11 tff(154,plain,
% 77.91/78.11 ((~![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))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[153, 152])).
% 77.91/78.11 tff(155,plain,
% 77.91/78.11 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[154, 151, 138])).
% 77.91/78.11 tff(156,plain,
% 77.91/78.11 (((~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))),
% 77.91/78.11 inference(tautology,[status(thm)],[])).
% 77.91/78.11 tff(157,plain,
% 77.91/78.11 (ssItem(tptp_fun_W_44(V!46))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[156, 130])).
% 77.91/78.11 tff(158,plain,
% 77.91/78.11 (((~![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))))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(159,plain,
% 77.91/78.11 ((~![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))))),
% 77.91/78.11 inference(quant_inst,[status(thm)],[])).
% 77.91/78.11 tff(160,plain,
% 77.91/78.11 ((~![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)))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[159, 158])).
% 77.91/78.11 tff(161,plain,
% 77.91/78.11 (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))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[160, 157, 155])).
% 77.91/78.11 tff(162,plain,
% 77.91/78.11 (app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[161, 136])).
% 77.91/78.11 tff(163,plain,
% 77.91/78.11 (^[X1: $i] : refl(((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))) <=> ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(164,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))) <=> ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[163])).
% 77.91/78.11 tff(165,plain,
% 77.91/78.11 (^[X1: $i] : rewrite(((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))) <=> ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(166,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))) <=> ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[165])).
% 77.91/78.11 tff(167,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))) <=> ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(transitivity,[status(thm)],[166, 164])).
% 77.91/78.11 tff(168,plain,
% 77.91/78.11 (^[X1: $i] : rewrite(((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) <=> ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(169,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46)))) <=> ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[168])).
% 77.91/78.11 tff(170,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : (~(ssList(X2) & (~(app(X2, cons(X1, nil)) = U!45)) & (app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(and_elim,[status(thm)],[13])).
% 77.91/78.11 tff(171,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[170, 169])).
% 77.91/78.11 tff(172,plain,
% 77.91/78.11 (![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[171, 167])).
% 77.91/78.11 tff(173,plain,
% 77.91/78.11 (((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45)))) <=> ((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(174,plain,
% 77.91/78.11 (((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)))) <=> ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(175,plain,
% 77.91/78.11 (((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46))))) <=> ((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))))),
% 77.91/78.11 inference(monotonicity,[status(thm)],[174])).
% 77.91/78.11 tff(176,plain,
% 77.91/78.11 (((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46))))) <=> ((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 77.91/78.11 inference(transitivity,[status(thm)],[175, 173])).
% 77.91/78.11 tff(177,plain,
% 77.91/78.11 ((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46))))),
% 77.91/78.11 inference(quant_inst,[status(thm)],[])).
% 77.91/78.11 tff(178,plain,
% 77.91/78.11 ((~![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (app(X2, cons(X1, nil)) = U!45) | (~(app(cons(X1, nil), X2) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[177, 176])).
% 77.91/78.11 tff(179,plain,
% 77.91/78.11 (![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[178, 172, 157])).
% 77.91/78.11 tff(180,plain,
% 77.91/78.11 (((~![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))) | ((~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))) <=> ((~![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))) | (~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))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(181,plain,
% 77.91/78.11 ((~![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))) | ((~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))),
% 77.91/78.11 inference(quant_inst,[status(thm)],[])).
% 77.91/78.11 tff(182,plain,
% 77.91/78.11 ((~![X2: $i] : ((~ssList(X2)) | (~(app(cons(tptp_fun_W_44(V!46), nil), X2) = V!46)) | (app(X2, cons(tptp_fun_W_44(V!46), nil)) = U!45))) | (~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)),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[181, 180])).
% 77.91/78.11 tff(183,plain,
% 77.91/78.11 ((~(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)),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[182, 138, 179])).
% 77.91/78.11 tff(184,plain,
% 77.91/78.11 (app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[183, 162])).
% 77.91/78.11 tff(185,plain,
% 77.91/78.11 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(186,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[185])).
% 77.91/78.11 tff(187,plain,
% 77.91/78.11 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(188,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[187])).
% 77.91/78.11 tff(189,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(transitivity,[status(thm)],[188, 186])).
% 77.91/78.11 tff(190,plain,
% 77.91/78.11 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45)))))),
% 77.91/78.11 inference(bind,[status(th)],[])).
% 77.91/78.11 tff(191,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(quant_intro,[status(thm)],[190])).
% 77.91/78.11 tff(192,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (app(cons(Y, nil), Z) = V!46) & (app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(and_elim,[status(thm)],[13])).
% 77.91/78.11 tff(193,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[192, 191])).
% 77.91/78.11 tff(194,plain,
% 77.91/78.11 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[193, 189])).
% 77.91/78.11 tff(195,plain,
% 77.91/78.11 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45))))),
% 77.91/78.11 inference(rewrite,[status(thm)],[])).
% 77.91/78.11 tff(196,plain,
% 77.91/78.11 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45))))),
% 77.91/78.11 inference(quant_inst,[status(thm)],[])).
% 77.91/78.11 tff(197,plain,
% 77.91/78.11 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = V!46)) | (~(app(Z, cons(Y, nil)) = U!45))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 77.91/78.11 inference(modus_ponens,[status(thm)],[196, 195])).
% 77.91/78.11 tff(198,plain,
% 77.91/78.11 (![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))),
% 77.91/78.11 inference(unit_resolution,[status(thm)],[197, 194, 157])).
% 77.91/78.11 tff(199,plain,
% 77.91/78.11 (((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))) | ((~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)))) <=> ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))) | (~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)))),
% 78.14/78.37 inference(rewrite,[status(thm)],[])).
% 78.14/78.37 tff(200,plain,
% 78.14/78.37 ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))) | ((~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)))),
% 78.14/78.37 inference(quant_inst,[status(thm)],[])).
% 78.14/78.37 tff(201,plain,
% 78.14/78.37 ((~![Z: $i] : ((~ssList(Z)) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)) | (~(app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (~(app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 78.14/78.37 inference(modus_ponens,[status(thm)],[200, 199])).
% 78.14/78.37 tff(202,plain,
% 78.14/78.37 ((~(app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46)) = V!46)) | (~(app(tptp_fun_V_43(V!46), cons(tptp_fun_W_44(V!46), nil)) = U!45))),
% 78.14/78.37 inference(unit_resolution,[status(thm)],[201, 138, 198])).
% 78.14/78.37 tff(203,plain,
% 78.14/78.37 ($false),
% 78.14/78.37 inference(unit_resolution,[status(thm)],[202, 184, 162])).
% 78.14/78.37 % SZS output end Proof
% 78.14/78.37 % E exiting
%------------------------------------------------------------------------------