%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC211+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:31 AM UTC 2025
% Result : Theorem 18.16s 18.38s
% Output : Proof 18.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC211+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:38:09 EDT 2025
% 0.19/0.34 % CPUTime :
% 18.16/18.38 % SZS status Theorem
% 18.16/18.38 % SZS output start Proof
% 18.16/18.38 tff(app_type, type, (
% 18.16/18.38 app: ( $i * $i ) > $i)).
% 18.16/18.38 tff(tptp_fun_U_45_type, type, (
% 18.16/18.38 tptp_fun_U_45: $i)).
% 18.16/18.38 tff(cons_type, type, (
% 18.16/18.38 cons: ( $i * $i ) > $i)).
% 18.16/18.38 tff(nil_type, type, (
% 18.16/18.38 nil: $i)).
% 18.16/18.38 tff(tptp_fun_W_44_type, type, (
% 18.16/18.38 tptp_fun_W_44: $i > $i)).
% 18.16/18.38 tff(tptp_fun_V_46_type, type, (
% 18.16/18.38 tptp_fun_V_46: $i)).
% 18.16/18.38 tff(tptp_fun_V_43_type, type, (
% 18.16/18.38 tptp_fun_V_43: $i > $i)).
% 18.16/18.38 tff(neq_type, type, (
% 18.16/18.38 neq: ( $i * $i ) > $o)).
% 18.16/18.38 tff(ssList_type, type, (
% 18.16/18.38 ssList: $i > $o)).
% 18.16/18.38 tff(ssItem_type, type, (
% 18.16/18.38 ssItem: $i > $o)).
% 18.16/18.38 tff(segmentP_type, type, (
% 18.16/18.38 segmentP: ( $i * $i ) > $o)).
% 18.16/18.38 tff(1,plain,
% 18.16/18.38 ((app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)) = nil) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.16/18.38 inference(commutativity,[status(thm)],[])).
% 18.16/18.38 tff(2,plain,
% 18.16/18.38 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 18.16/18.38 inference(rewrite,[status(thm)],[])).
% 18.16/18.38 tff(3,plain,
% 18.16/18.38 (((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 18.16/18.38 inference(rewrite,[status(thm)],[])).
% 18.16/18.38 tff(4,plain,
% 18.16/18.38 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)))),
% 18.16/18.38 inference(monotonicity,[status(thm)],[3])).
% 18.16/18.38 tff(5,plain,
% 18.16/18.38 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 18.16/18.38 inference(transitivity,[status(thm)],[4, 2])).
% 18.16/18.38 tff(6,plain,
% 18.16/18.38 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 18.16/18.38 inference(rewrite,[status(thm)],[])).
% 18.16/18.38 tff(7,plain,
% 18.16/18.38 ((~![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(Z, cons(Y, nil)) = W))) & (app(cons(Y, nil), Z) = X)))) | neq(U, nil)) | ((~(nil = W)) & (nil = X)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 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(Z, cons(Y, nil)) = W))) & (app(cons(Y, nil), Z) = X)))) | neq(U, nil)) | ((~(nil = W)) & (nil = X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 18.16/18.39 tff(9,plain,
% 18.16/18.39 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 18.16/18.39 tff(10,plain,
% 18.16/18.39 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 18.16/18.39 tff(11,plain,
% 18.16/18.39 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 18.16/18.39 tff(12,plain,
% 18.16/18.39 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & (~(app(Z, cons(Y, nil)) = U)) & (app(cons(Y, nil), Z) = V))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[11, 6])).
% 18.16/18.39 tff(13,plain,
% 18.16/18.39 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) & (~neq(U!45, nil)) & neq(V!46, nil)),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 18.16/18.39 tff(14,plain,
% 18.16/18.39 (ssList(U!45)),
% 18.16/18.39 inference(and_elim,[status(thm)],[13])).
% 18.16/18.39 tff(15,plain,
% 18.16/18.39 (^[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))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(16,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[15])).
% 18.16/18.39 tff(17,plain,
% 18.16/18.39 (^[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))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(18,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[17])).
% 18.16/18.39 tff(19,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[18, 16])).
% 18.16/18.39 tff(20,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(21,plain,
% 18.16/18.39 (^[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)))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(22,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[21])).
% 18.16/18.39 tff(23,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 18.16/18.39 tff(24,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 18.16/18.39 tff(25,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 18.16/18.39 tff(26,plain,(
% 18.16/18.39 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 18.16/18.39 inference(skolemize,[status(sab)],[25])).
% 18.16/18.39 tff(27,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 18.16/18.39 tff(28,plain,
% 18.16/18.39 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(29,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(30,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 18.16/18.39 tff(31,plain,
% 18.16/18.39 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 18.16/18.39 tff(32,plain,
% 18.16/18.39 (ssList(nil) <=> ssList(nil)),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(33,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 18.16/18.39 tff(34,plain,
% 18.16/18.39 (ssList(nil)),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 18.16/18.39 tff(35,plain,
% 18.16/18.39 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(36,plain,
% 18.16/18.39 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(37,plain,
% 18.16/18.39 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 18.16/18.39 tff(38,plain,
% 18.16/18.39 (~((U!45 = nil) <=> neq(U!45, nil))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[37, 34, 31])).
% 18.16/18.39 tff(39,plain,
% 18.16/18.39 (~neq(U!45, nil)),
% 18.16/18.39 inference(and_elim,[status(thm)],[13])).
% 18.16/18.39 tff(40,plain,
% 18.16/18.39 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 18.16/18.39 inference(tautology,[status(thm)],[])).
% 18.16/18.39 tff(41,plain,
% 18.16/18.39 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 18.16/18.39 tff(42,plain,
% 18.16/18.39 (U!45 = nil),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[41, 38])).
% 18.16/18.39 tff(43,plain,
% 18.16/18.39 (ssList(V!46)),
% 18.16/18.39 inference(and_elim,[status(thm)],[13])).
% 18.16/18.39 tff(44,plain,
% 18.16/18.39 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(45,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[44])).
% 18.16/18.39 tff(46,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(47,plain,
% 18.16/18.39 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(48,plain,
% 18.16/18.39 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[47])).
% 18.16/18.39 tff(49,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 18.16/18.39 tff(50,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 18.16/18.39 tff(51,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 18.16/18.39 tff(52,plain,(
% 18.16/18.39 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(skolemize,[status(sab)],[51])).
% 18.16/18.39 tff(53,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 18.16/18.39 tff(54,plain,
% 18.16/18.39 (((~![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)))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(55,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(56,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 18.16/18.39 tff(57,plain,
% 18.16/18.39 (segmentP(nil, V!46) <=> (nil = V!46)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 18.16/18.39 tff(58,plain,
% 18.16/18.39 (((~![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)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(59,plain,
% 18.16/18.39 ((~![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)))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(60,plain,
% 18.16/18.39 ((~![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))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 18.16/18.39 tff(61,plain,
% 18.16/18.39 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[60, 27, 43])).
% 18.16/18.39 tff(62,plain,
% 18.16/18.39 (((~![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))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(63,plain,
% 18.16/18.39 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(64,plain,
% 18.16/18.39 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 18.16/18.39 tff(65,plain,
% 18.16/18.39 (~((V!46 = nil) <=> neq(V!46, nil))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[64, 34, 61])).
% 18.16/18.39 tff(66,plain,
% 18.16/18.39 (neq(V!46, nil)),
% 18.16/18.39 inference(and_elim,[status(thm)],[13])).
% 18.16/18.39 tff(67,plain,
% 18.16/18.39 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 18.16/18.39 inference(tautology,[status(thm)],[])).
% 18.16/18.39 tff(68,plain,
% 18.16/18.39 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 18.16/18.39 tff(69,plain,
% 18.16/18.39 (~(V!46 = nil)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[68, 65])).
% 18.16/18.39 tff(70,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(71,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[70])).
% 18.16/18.39 tff(72,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(73,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[72])).
% 18.16/18.39 tff(74,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[73, 71])).
% 18.16/18.39 tff(75,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(76,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[75])).
% 18.16/18.39 tff(77,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(78,plain,
% 18.16/18.39 (^[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)))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(79,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[78])).
% 18.16/18.39 tff(80,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')).
% 18.16/18.39 tff(81,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 18.16/18.39 tff(82,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 18.16/18.39 tff(83,plain,(
% 18.16/18.39 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 18.16/18.39 inference(skolemize,[status(sab)],[82])).
% 18.16/18.39 tff(84,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[83, 76])).
% 18.16/18.39 tff(85,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[84, 74])).
% 18.16/18.39 tff(86,plain,
% 18.16/18.39 (((~![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))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(87,plain,
% 18.16/18.39 (((~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))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(88,plain,
% 18.16/18.39 (((~![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)))))),
% 18.16/18.39 inference(monotonicity,[status(thm)],[87])).
% 18.16/18.39 tff(89,plain,
% 18.16/18.39 (((~![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))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[88, 86])).
% 18.16/18.39 tff(90,plain,
% 18.16/18.39 ((~![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))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(91,plain,
% 18.16/18.39 ((~![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)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 18.16/18.39 tff(92,plain,
% 18.16/18.39 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[91, 85, 43])).
% 18.16/18.39 tff(93,plain,
% 18.16/18.39 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(94,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[93])).
% 18.16/18.39 tff(95,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(96,plain,
% 18.16/18.39 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(97,plain,
% 18.16/18.39 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[96])).
% 18.16/18.39 tff(98,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 18.16/18.39 tff(99,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 18.16/18.39 tff(100,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[99, 95])).
% 18.16/18.39 tff(101,plain,(
% 18.16/18.39 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(skolemize,[status(sab)],[100])).
% 18.16/18.39 tff(102,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[101, 94])).
% 18.16/18.39 tff(103,plain,
% 18.16/18.39 (((~![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))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(104,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(105,plain,
% 18.16/18.39 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 18.16/18.39 tff(106,plain,
% 18.16/18.39 (segmentP(V!46, nil)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[105, 102, 43])).
% 18.16/18.39 tff(107,plain,
% 18.16/18.39 (((~![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)))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(108,plain,
% 18.16/18.39 (((~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)))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(109,plain,
% 18.16/18.39 (((~![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))))),
% 18.16/18.39 inference(monotonicity,[status(thm)],[108])).
% 18.16/18.39 tff(110,plain,
% 18.16/18.39 (((~![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)))),
% 18.16/18.39 inference(transitivity,[status(thm)],[109, 107])).
% 18.16/18.39 tff(111,plain,
% 18.16/18.39 ((~![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)))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(112,plain,
% 18.16/18.39 ((~![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))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 18.16/18.39 tff(113,plain,
% 18.16/18.39 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[112, 34, 106, 92])).
% 18.16/18.39 tff(114,plain,
% 18.16/18.39 (~segmentP(nil, V!46)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[113, 69])).
% 18.16/18.39 tff(115,plain,
% 18.16/18.39 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 18.16/18.39 inference(tautology,[status(thm)],[])).
% 18.16/18.39 tff(116,plain,
% 18.16/18.39 (~(nil = V!46)),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[115, 114, 57])).
% 18.16/18.39 tff(117,plain,
% 18.16/18.39 (^[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))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(118,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[117])).
% 18.16/18.39 tff(119,plain,
% 18.16/18.39 (^[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)))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(120,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[119])).
% 18.16/18.39 tff(121,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(122,plain,
% 18.16/18.39 (![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)))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[121])).
% 18.16/18.39 tff(123,plain,
% 18.16/18.39 (![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)))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(124,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(125,plain,
% 18.16/18.39 (![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)))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[124])).
% 18.16/18.39 tff(126,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')).
% 18.16/18.39 tff(127,plain,
% 18.16/18.39 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[126, 125])).
% 18.16/18.39 tff(128,plain,
% 18.16/18.39 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[127, 123])).
% 18.16/18.39 tff(129,plain,(
% 18.16/18.39 ![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)))),
% 18.16/18.39 inference(skolemize,[status(sab)],[128])).
% 18.16/18.39 tff(130,plain,
% 18.16/18.39 (![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)))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[129, 122])).
% 18.16/18.39 tff(131,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[130, 120])).
% 18.16/18.39 tff(132,plain,
% 18.16/18.39 (![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)))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[131, 118])).
% 18.16/18.39 tff(133,plain,
% 18.16/18.39 (((~![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)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(134,plain,
% 18.16/18.39 (((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)))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(135,plain,
% 18.16/18.39 ((~((~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))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(136,plain,
% 18.16/18.39 (((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)))))),
% 18.16/18.39 inference(monotonicity,[status(thm)],[135])).
% 18.16/18.39 tff(137,plain,
% 18.16/18.39 (((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)))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[136, 134])).
% 18.16/18.39 tff(138,plain,
% 18.16/18.39 (((~![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))))))),
% 18.16/18.39 inference(monotonicity,[status(thm)],[137])).
% 18.16/18.39 tff(139,plain,
% 18.16/18.39 (((~![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)))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[138, 133])).
% 18.16/18.39 tff(140,plain,
% 18.16/18.39 ((~![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)))))),
% 18.16/18.39 inference(quant_inst,[status(thm)],[])).
% 18.16/18.39 tff(141,plain,
% 18.16/18.39 ((~![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))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[140, 139])).
% 18.16/18.39 tff(142,plain,
% 18.16/18.39 ((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))))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[141, 132, 43])).
% 18.16/18.39 tff(143,plain,
% 18.16/18.39 (~((~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)))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[142, 116])).
% 18.16/18.39 tff(144,plain,
% 18.16/18.39 (((~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))),
% 18.16/18.39 inference(tautology,[status(thm)],[])).
% 18.16/18.39 tff(145,plain,
% 18.16/18.39 (ssItem(tptp_fun_W_44(V!46))),
% 18.16/18.39 inference(unit_resolution,[status(thm)],[144, 143])).
% 18.16/18.39 tff(146,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(147,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[146])).
% 18.16/18.39 tff(148,plain,
% 18.16/18.39 (^[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)))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(149,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[148])).
% 18.16/18.39 tff(150,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(transitivity,[status(thm)],[149, 147])).
% 18.16/18.39 tff(151,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(rewrite,[status(thm)],[])).
% 18.16/18.39 tff(152,plain,
% 18.16/18.39 (^[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))))))),
% 18.16/18.39 inference(bind,[status(th)],[])).
% 18.16/18.39 tff(153,plain,
% 18.16/18.39 (![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))))),
% 18.16/18.39 inference(quant_intro,[status(thm)],[152])).
% 18.16/18.39 tff(154,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')).
% 18.16/18.39 tff(155,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[154, 153])).
% 18.16/18.39 tff(156,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[155, 151])).
% 18.16/18.39 tff(157,plain,(
% 18.16/18.39 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 18.16/18.39 inference(skolemize,[status(sab)],[156])).
% 18.16/18.39 tff(158,plain,
% 18.16/18.39 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 18.16/18.39 inference(modus_ponens,[status(thm)],[157, 150])).
% 18.16/18.39 tff(159,plain,
% 18.16/18.39 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(160,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(161,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[160, 159])).
% 18.16/18.40 tff(162,plain,
% 18.16/18.40 (![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[161, 158, 14])).
% 18.16/18.40 tff(163,plain,
% 18.16/18.40 (((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), U!45) = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), U!45) = app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(164,plain,
% 18.16/18.40 ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), U!45) = app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(165,plain,
% 18.16/18.40 ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | (cons(tptp_fun_W_44(V!46), U!45) = app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[164, 163])).
% 18.16/18.40 tff(166,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), U!45) = app(cons(tptp_fun_W_44(V!46), nil), U!45)),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[165, 162, 145])).
% 18.16/18.40 tff(167,plain,
% 18.16/18.40 (app(U!45, U!45) = app(nil, nil)),
% 18.16/18.40 inference(monotonicity,[status(thm)],[42, 42])).
% 18.16/18.40 tff(168,plain,
% 18.16/18.40 (app(nil, nil) = app(U!45, U!45)),
% 18.16/18.40 inference(symmetry,[status(thm)],[167])).
% 18.16/18.40 tff(169,plain,
% 18.16/18.40 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(170,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[169])).
% 18.16/18.40 tff(171,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(172,plain,
% 18.16/18.40 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(173,plain,
% 18.16/18.40 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[172])).
% 18.16/18.40 tff(174,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 18.16/18.40 tff(175,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[174, 173])).
% 18.16/18.40 tff(176,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[175, 171])).
% 18.16/18.40 tff(177,plain,(
% 18.16/18.40 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(skolemize,[status(sab)],[176])).
% 18.16/18.40 tff(178,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[177, 170])).
% 18.16/18.40 tff(179,plain,
% 18.16/18.40 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(180,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(181,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[180, 179])).
% 18.16/18.40 tff(182,plain,
% 18.16/18.40 (app(nil, nil) = nil),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[181, 34, 178])).
% 18.16/18.40 tff(183,plain,
% 18.16/18.40 (nil = app(nil, nil)),
% 18.16/18.40 inference(symmetry,[status(thm)],[182])).
% 18.16/18.40 tff(184,plain,
% 18.16/18.40 (U!45 = app(U!45, U!45)),
% 18.16/18.40 inference(transitivity,[status(thm)],[42, 183, 168])).
% 18.16/18.40 tff(185,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), U!45) = cons(tptp_fun_W_44(V!46), app(U!45, U!45))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[184])).
% 18.16/18.40 tff(186,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), app(U!45, U!45)) = cons(tptp_fun_W_44(V!46), U!45)),
% 18.16/18.40 inference(symmetry,[status(thm)],[185])).
% 18.16/18.40 tff(187,plain,
% 18.16/18.40 (nil = app(U!45, U!45)),
% 18.16/18.40 inference(transitivity,[status(thm)],[183, 168])).
% 18.16/18.40 tff(188,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), nil) = cons(tptp_fun_W_44(V!46), app(U!45, U!45))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[187])).
% 18.16/18.40 tff(189,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), nil) = app(cons(tptp_fun_W_44(V!46), nil), U!45)),
% 18.16/18.40 inference(transitivity,[status(thm)],[188, 186, 166])).
% 18.16/18.40 tff(190,plain,
% 18.16/18.40 (((~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))),
% 18.16/18.40 inference(tautology,[status(thm)],[])).
% 18.16/18.40 tff(191,plain,
% 18.16/18.40 (ssList(tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[190, 143])).
% 18.16/18.40 tff(192,plain,
% 18.16/18.40 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(193,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[192])).
% 18.16/18.40 tff(194,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(195,plain,
% 18.16/18.40 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(196,plain,
% 18.16/18.40 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[195])).
% 18.16/18.40 tff(197,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 18.16/18.40 tff(198,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[197, 196])).
% 18.16/18.40 tff(199,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[198, 194])).
% 18.16/18.40 tff(200,plain,(
% 18.16/18.40 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(skolemize,[status(sab)],[199])).
% 18.16/18.40 tff(201,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[200, 193])).
% 18.16/18.40 tff(202,plain,
% 18.16/18.40 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(203,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(204,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(tptp_fun_V_43(V!46))) | (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[203, 202])).
% 18.16/18.40 tff(205,plain,
% 18.16/18.40 (app(nil, tptp_fun_V_43(V!46)) = tptp_fun_V_43(V!46)),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[204, 201, 191])).
% 18.16/18.40 tff(206,plain,
% 18.16/18.40 (app(U!45, tptp_fun_V_43(V!46)) = app(nil, tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[42])).
% 18.16/18.40 tff(207,plain,
% 18.16/18.40 (nil = U!45),
% 18.16/18.40 inference(symmetry,[status(thm)],[42])).
% 18.16/18.40 tff(208,plain,
% 18.16/18.40 (app(U!45, U!45) = U!45),
% 18.16/18.40 inference(transitivity,[status(thm)],[167, 182, 207])).
% 18.16/18.40 tff(209,plain,
% 18.16/18.40 (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[208])).
% 18.16/18.40 tff(210,plain,
% 18.16/18.40 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(211,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[210])).
% 18.16/18.40 tff(212,plain,
% 18.16/18.40 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(213,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[212])).
% 18.16/18.40 tff(214,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(transitivity,[status(thm)],[213, 211])).
% 18.16/18.40 tff(215,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(216,plain,
% 18.16/18.40 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(217,plain,
% 18.16/18.40 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[216])).
% 18.16/18.40 tff(218,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax82')).
% 18.16/18.40 tff(219,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[218, 217])).
% 18.16/18.40 tff(220,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[219, 215])).
% 18.16/18.40 tff(221,plain,(
% 18.16/18.40 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(skolemize,[status(sab)],[220])).
% 18.16/18.40 tff(222,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[221, 214])).
% 18.16/18.40 tff(223,plain,
% 18.16/18.40 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W))))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(224,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W))))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(225,plain,
% 18.16/18.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[224, 223])).
% 18.16/18.40 tff(226,plain,
% 18.16/18.40 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[225, 222, 14])).
% 18.16/18.40 tff(227,plain,
% 18.16/18.40 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W)))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(228,plain,
% 18.16/18.40 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W)))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(229,plain,
% 18.16/18.40 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, V), W) = app(U!45, app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[228, 227])).
% 18.16/18.40 tff(230,plain,
% 18.16/18.40 (![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[229, 14, 226])).
% 18.16/18.40 tff(231,plain,
% 18.16/18.40 (((~![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, app(U!45, tptp_fun_V_43(V!46)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))) | (~ssList(tptp_fun_V_43(V!46))) | (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, app(U!45, tptp_fun_V_43(V!46)))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(232,plain,
% 18.16/18.40 ((~![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))) | ((~ssList(tptp_fun_V_43(V!46))) | (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, app(U!45, tptp_fun_V_43(V!46)))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(233,plain,
% 18.16/18.40 ((~![W: $i] : ((~ssList(W)) | (app(app(U!45, U!45), W) = app(U!45, app(U!45, W))))) | (~ssList(tptp_fun_V_43(V!46))) | (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, app(U!45, tptp_fun_V_43(V!46))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[232, 231])).
% 18.16/18.40 tff(234,plain,
% 18.16/18.40 (app(app(U!45, U!45), tptp_fun_V_43(V!46)) = app(U!45, app(U!45, tptp_fun_V_43(V!46)))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[233, 191, 230])).
% 18.16/18.40 tff(235,plain,
% 18.16/18.40 (app(U!45, app(U!45, tptp_fun_V_43(V!46))) = app(app(U!45, U!45), tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(symmetry,[status(thm)],[234])).
% 18.16/18.40 tff(236,plain,
% 18.16/18.40 (app(U!45, app(U!45, tptp_fun_V_43(V!46))) = tptp_fun_V_43(V!46)),
% 18.16/18.40 inference(transitivity,[status(thm)],[235, 209, 206, 205])).
% 18.16/18.40 tff(237,plain,
% 18.16/18.40 (app(app(U!45, app(U!45, 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), U!45))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[236, 189])).
% 18.16/18.40 tff(238,plain,
% 18.16/18.40 ((app(app(U!45, app(U!45, tptp_fun_V_43(V!46))), cons(tptp_fun_W_44(V!46), nil)) = U!45) <=> (app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)) = nil)),
% 18.16/18.40 inference(monotonicity,[status(thm)],[237, 42])).
% 18.16/18.40 tff(239,plain,
% 18.16/18.40 ((app(app(U!45, app(U!45, tptp_fun_V_43(V!46))), cons(tptp_fun_W_44(V!46), nil)) = U!45) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.16/18.40 inference(transitivity,[status(thm)],[238, 1])).
% 18.16/18.40 tff(240,plain,
% 18.16/18.40 (((~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)),
% 18.16/18.40 inference(tautology,[status(thm)],[])).
% 18.16/18.40 tff(241,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[240, 143])).
% 18.16/18.40 tff(242,plain,
% 18.16/18.40 (((~![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)))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(243,plain,
% 18.16/18.40 ((~![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)))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(244,plain,
% 18.16/18.40 ((~![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))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[243, 242])).
% 18.16/18.40 tff(245,plain,
% 18.16/18.40 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[244, 158, 191])).
% 18.16/18.40 tff(246,plain,
% 18.16/18.40 (((~![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))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(247,plain,
% 18.16/18.40 ((~![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))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(248,plain,
% 18.16/18.40 ((~![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)))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[247, 246])).
% 18.16/18.40 tff(249,plain,
% 18.16/18.40 (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))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[248, 145, 245])).
% 18.16/18.40 tff(250,plain,
% 18.16/18.40 (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))),
% 18.16/18.40 inference(symmetry,[status(thm)],[249])).
% 18.16/18.40 tff(251,plain,
% 18.16/18.40 (cons(tptp_fun_W_44(V!46), app(U!45, U!45)) = cons(tptp_fun_W_44(V!46), nil)),
% 18.16/18.40 inference(symmetry,[status(thm)],[188])).
% 18.16/18.40 tff(252,plain,
% 18.16/18.40 (app(cons(tptp_fun_W_44(V!46), nil), U!45) = cons(tptp_fun_W_44(V!46), U!45)),
% 18.16/18.40 inference(symmetry,[status(thm)],[166])).
% 18.16/18.40 tff(253,plain,
% 18.16/18.40 (app(cons(tptp_fun_W_44(V!46), nil), U!45) = cons(tptp_fun_W_44(V!46), nil)),
% 18.16/18.40 inference(transitivity,[status(thm)],[252, 185, 251])).
% 18.16/18.40 tff(254,plain,
% 18.16/18.40 (app(app(cons(tptp_fun_W_44(V!46), nil), U!45), tptp_fun_V_43(V!46)) = app(cons(tptp_fun_W_44(V!46), nil), tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[253])).
% 18.16/18.40 tff(255,plain,
% 18.16/18.40 (app(cons(tptp_fun_W_44(V!46), nil), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = app(app(cons(tptp_fun_W_44(V!46), nil), U!45), tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[189, 236])).
% 18.16/18.40 tff(256,plain,
% 18.16/18.40 (app(cons(tptp_fun_W_44(V!46), nil), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46),
% 18.16/18.40 inference(transitivity,[status(thm)],[255, 254, 250, 241])).
% 18.16/18.40 tff(257,plain,
% 18.16/18.40 (ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46)))) <=> ssList(tptp_fun_V_43(V!46))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[236])).
% 18.16/18.40 tff(258,plain,
% 18.16/18.40 (ssList(tptp_fun_V_43(V!46)) <=> ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))),
% 18.16/18.40 inference(symmetry,[status(thm)],[257])).
% 18.16/18.40 tff(259,plain,
% 18.16/18.40 (ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[191, 258])).
% 18.16/18.40 tff(260,plain,
% 18.16/18.40 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(261,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[260])).
% 18.16/18.40 tff(262,plain,
% 18.16/18.40 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(263,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[262])).
% 18.16/18.40 tff(264,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(transitivity,[status(thm)],[263, 261])).
% 18.16/18.40 tff(265,plain,
% 18.16/18.40 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46)))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(266,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46)))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[265])).
% 18.16/18.40 tff(267,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : (~(ssList(Z) & (~(app(Z, cons(Y, nil)) = U!45)) & (app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(and_elim,[status(thm)],[13])).
% 18.16/18.40 tff(268,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[267, 266])).
% 18.16/18.40 tff(269,plain,
% 18.16/18.40 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[268, 264])).
% 18.16/18.40 tff(270,plain,
% 18.16/18.40 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(271,plain,
% 18.16/18.40 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))) | ((~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46))))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(272,plain,
% 18.16/18.40 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(Y, nil)) = U!45) | (~(app(cons(Y, nil), Z) = V!46))))) | (~ssItem(tptp_fun_W_44(V!46))) | ![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[271, 270])).
% 18.16/18.40 tff(273,plain,
% 18.16/18.40 (![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[272, 269, 145])).
% 18.16/18.40 tff(274,plain,
% 18.16/18.40 (((~![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))) | ((~ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))) | (app(app(U!45, app(U!45, 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), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46)))) <=> ((~![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))) | (~ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))) | (app(app(U!45, app(U!45, 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), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46)))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(275,plain,
% 18.16/18.40 ((~![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))) | ((~ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))) | (app(app(U!45, app(U!45, 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), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46)))),
% 18.16/18.40 inference(quant_inst,[status(thm)],[])).
% 18.16/18.40 tff(276,plain,
% 18.16/18.40 ((~![Z: $i] : ((~ssList(Z)) | (app(Z, cons(tptp_fun_W_44(V!46), nil)) = U!45) | (~(app(cons(tptp_fun_W_44(V!46), nil), Z) = V!46)))) | (~ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))) | (app(app(U!45, app(U!45, 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), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[275, 274])).
% 18.16/18.40 tff(277,plain,
% 18.16/18.40 ((~ssList(app(U!45, app(U!45, tptp_fun_V_43(V!46))))) | (app(app(U!45, app(U!45, 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), app(U!45, app(U!45, tptp_fun_V_43(V!46)))) = V!46))),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[276, 273])).
% 18.16/18.40 tff(278,plain,
% 18.16/18.40 (app(app(U!45, app(U!45, tptp_fun_V_43(V!46))), cons(tptp_fun_W_44(V!46), nil)) = U!45),
% 18.16/18.40 inference(unit_resolution,[status(thm)],[277, 259, 256])).
% 18.16/18.40 tff(279,plain,
% 18.16/18.40 (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[278, 239])).
% 18.16/18.40 tff(280,plain,
% 18.16/18.40 (ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45)) <=> ssList(cons(tptp_fun_W_44(V!46), U!45))),
% 18.16/18.40 inference(monotonicity,[status(thm)],[252])).
% 18.16/18.40 tff(281,plain,
% 18.16/18.40 (ssList(cons(tptp_fun_W_44(V!46), U!45)) <=> ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.16/18.40 inference(symmetry,[status(thm)],[280])).
% 18.16/18.40 tff(282,plain,
% 18.16/18.40 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(283,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[282])).
% 18.16/18.40 tff(284,plain,
% 18.16/18.40 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(285,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[284])).
% 18.16/18.40 tff(286,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(transitivity,[status(thm)],[285, 283])).
% 18.16/18.40 tff(287,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(rewrite,[status(thm)],[])).
% 18.16/18.40 tff(288,plain,
% 18.16/18.40 (^[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))))))),
% 18.16/18.40 inference(bind,[status(th)],[])).
% 18.16/18.40 tff(289,plain,
% 18.16/18.40 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(quant_intro,[status(thm)],[288])).
% 18.16/18.40 tff(290,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax16')).
% 18.16/18.40 tff(291,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[290, 289])).
% 18.16/18.40 tff(292,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(modus_ponens,[status(thm)],[291, 287])).
% 18.16/18.40 tff(293,plain,(
% 18.16/18.40 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.40 inference(skolemize,[status(sab)],[292])).
% 18.16/18.40 tff(294,plain,
% 18.16/18.40 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[293, 286])).
% 18.16/18.41 tff(295,plain,
% 18.16/18.41 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(296,plain,
% 18.16/18.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))),
% 18.16/18.41 inference(quant_inst,[status(thm)],[])).
% 18.16/18.41 tff(297,plain,
% 18.16/18.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[296, 295])).
% 18.16/18.41 tff(298,plain,
% 18.16/18.41 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))),
% 18.16/18.41 inference(unit_resolution,[status(thm)],[297, 294, 14])).
% 18.16/18.41 tff(299,plain,
% 18.16/18.41 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | ssList(cons(tptp_fun_W_44(V!46), U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | ssList(cons(tptp_fun_W_44(V!46), U!45)))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(300,plain,
% 18.16/18.41 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | ssList(cons(tptp_fun_W_44(V!46), U!45)))),
% 18.16/18.41 inference(quant_inst,[status(thm)],[])).
% 18.16/18.41 tff(301,plain,
% 18.16/18.41 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | ssList(cons(tptp_fun_W_44(V!46), U!45))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[300, 299])).
% 18.16/18.41 tff(302,plain,
% 18.16/18.41 (ssList(cons(tptp_fun_W_44(V!46), U!45))),
% 18.16/18.41 inference(unit_resolution,[status(thm)],[301, 298, 145])).
% 18.16/18.41 tff(303,plain,
% 18.16/18.41 (ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[302, 281])).
% 18.16/18.41 tff(304,plain,
% 18.16/18.41 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(305,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[304])).
% 18.16/18.41 tff(306,plain,
% 18.16/18.41 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(307,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[306])).
% 18.16/18.41 tff(308,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(transitivity,[status(thm)],[307, 305])).
% 18.16/18.41 tff(309,plain,
% 18.16/18.41 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(310,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[309])).
% 18.16/18.41 tff(311,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(312,plain,
% 18.16/18.41 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(313,plain,
% 18.16/18.41 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[312])).
% 18.16/18.41 tff(314,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax83')).
% 18.16/18.41 tff(315,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[314, 313])).
% 18.16/18.41 tff(316,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[315, 311])).
% 18.16/18.41 tff(317,plain,(
% 18.16/18.41 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 18.16/18.41 inference(skolemize,[status(sab)],[316])).
% 18.16/18.41 tff(318,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[317, 310])).
% 18.16/18.41 tff(319,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[318, 308])).
% 18.16/18.41 tff(320,plain,
% 18.16/18.41 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V))))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(321,plain,
% 18.16/18.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V))))))),
% 18.16/18.41 inference(quant_inst,[status(thm)],[])).
% 18.16/18.41 tff(322,plain,
% 18.16/18.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[321, 320])).
% 18.16/18.41 tff(323,plain,
% 18.16/18.41 (![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))),
% 18.16/18.41 inference(unit_resolution,[status(thm)],[322, 319, 191])).
% 18.16/18.41 tff(324,plain,
% 18.16/18.41 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | (~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(325,plain,
% 18.16/18.41 (((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))))) <=> ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(326,plain,
% 18.16/18.41 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))))))),
% 18.16/18.41 inference(monotonicity,[status(thm)],[325])).
% 18.16/18.41 tff(327,plain,
% 18.16/18.41 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | (~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))),
% 18.16/18.41 inference(transitivity,[status(thm)],[326, 324])).
% 18.16/18.41 tff(328,plain,
% 18.16/18.41 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))))),
% 18.16/18.41 inference(quant_inst,[status(thm)],[])).
% 18.16/18.41 tff(329,plain,
% 18.16/18.41 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = tptp_fun_V_43(V!46)))) <=> (nil = app(tptp_fun_V_43(V!46), V)))))) | (~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[328, 327])).
% 18.16/18.41 tff(330,plain,
% 18.16/18.41 ((~ssList(app(cons(tptp_fun_W_44(V!46), nil), U!45))) | (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))))),
% 18.16/18.41 inference(unit_resolution,[status(thm)],[329, 323])).
% 18.16/18.41 tff(331,plain,
% 18.16/18.41 (~(((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))),
% 18.16/18.41 inference(unit_resolution,[status(thm)],[330, 303])).
% 18.16/18.41 tff(332,plain,
% 18.16/18.41 ((U!45 = cons(tptp_fun_W_44(V!46), U!45)) <=> (cons(tptp_fun_W_44(V!46), U!45) = U!45)),
% 18.16/18.41 inference(commutativity,[status(thm)],[])).
% 18.16/18.41 tff(333,plain,
% 18.16/18.41 ((nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)) <=> (U!45 = cons(tptp_fun_W_44(V!46), U!45))),
% 18.16/18.41 inference(monotonicity,[status(thm)],[207, 252])).
% 18.16/18.41 tff(334,plain,
% 18.16/18.41 ((nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)) <=> (cons(tptp_fun_W_44(V!46), U!45) = U!45)),
% 18.16/18.41 inference(transitivity,[status(thm)],[333, 332])).
% 18.16/18.41 tff(335,plain,
% 18.16/18.41 ((cons(tptp_fun_W_44(V!46), U!45) = U!45) <=> (nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.16/18.41 inference(symmetry,[status(thm)],[334])).
% 18.16/18.41 tff(336,plain,
% 18.16/18.41 ((~(cons(tptp_fun_W_44(V!46), U!45) = U!45)) <=> (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.16/18.41 inference(monotonicity,[status(thm)],[335])).
% 18.16/18.41 tff(337,plain,
% 18.16/18.41 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(338,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[337])).
% 18.16/18.41 tff(339,plain,
% 18.16/18.41 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(340,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[339])).
% 18.16/18.41 tff(341,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(transitivity,[status(thm)],[340, 338])).
% 18.16/18.41 tff(342,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(rewrite,[status(thm)],[])).
% 18.16/18.41 tff(343,plain,
% 18.16/18.41 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 18.16/18.41 inference(bind,[status(th)],[])).
% 18.16/18.41 tff(344,plain,
% 18.16/18.41 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(quant_intro,[status(thm)],[343])).
% 18.16/18.41 tff(345,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax18')).
% 18.16/18.41 tff(346,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[345, 344])).
% 18.16/18.41 tff(347,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[346, 342])).
% 18.16/18.41 tff(348,plain,(
% 18.16/18.41 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(skolemize,[status(sab)],[347])).
% 18.16/18.41 tff(349,plain,
% 18.16/18.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 18.16/18.41 inference(modus_ponens,[status(thm)],[348, 341])).
% 18.24/18.46 tff(350,plain,
% 18.24/18.46 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45))))),
% 18.24/18.46 inference(rewrite,[status(thm)],[])).
% 18.24/18.46 tff(351,plain,
% 18.24/18.46 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45))))),
% 18.24/18.46 inference(quant_inst,[status(thm)],[])).
% 18.24/18.46 tff(352,plain,
% 18.24/18.46 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))),
% 18.24/18.46 inference(modus_ponens,[status(thm)],[351, 350])).
% 18.24/18.46 tff(353,plain,
% 18.24/18.46 (![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))),
% 18.24/18.46 inference(unit_resolution,[status(thm)],[352, 349, 14])).
% 18.24/18.46 tff(354,plain,
% 18.24/18.46 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), U!45) = U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), U!45) = U!45)))),
% 18.24/18.46 inference(rewrite,[status(thm)],[])).
% 18.24/18.46 tff(355,plain,
% 18.24/18.46 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))) | ((~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), U!45) = U!45)))),
% 18.24/18.46 inference(quant_inst,[status(thm)],[])).
% 18.24/18.46 tff(356,plain,
% 18.24/18.46 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, U!45) = U!45)))) | (~ssItem(tptp_fun_W_44(V!46))) | (~(cons(tptp_fun_W_44(V!46), U!45) = U!45))),
% 18.24/18.46 inference(modus_ponens,[status(thm)],[355, 354])).
% 18.24/18.46 tff(357,plain,
% 18.24/18.46 (~(cons(tptp_fun_W_44(V!46), U!45) = U!45)),
% 18.24/18.46 inference(unit_resolution,[status(thm)],[356, 353, 145])).
% 18.24/18.46 tff(358,plain,
% 18.24/18.46 (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.24/18.46 inference(modus_ponens,[status(thm)],[357, 336])).
% 18.24/18.46 tff(359,plain,
% 18.24/18.46 (((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) | (nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))),
% 18.24/18.46 inference(tautology,[status(thm)],[])).
% 18.24/18.46 tff(360,plain,
% 18.24/18.46 ((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.24/18.46 inference(unit_resolution,[status(thm)],[359, 358])).
% 18.24/18.46 tff(361,plain,
% 18.24/18.46 ((((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45)))) <=> (nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))) | (~((~(nil = tptp_fun_V_43(V!46))) | (~(nil = app(cons(tptp_fun_W_44(V!46), nil), U!45))))) | (~(nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45))))),
% 18.24/18.46 inference(tautology,[status(thm)],[])).
% 18.24/18.46 tff(362,plain,
% 18.24/18.46 (~(nil = app(tptp_fun_V_43(V!46), app(cons(tptp_fun_W_44(V!46), nil), U!45)))),
% 18.24/18.46 inference(unit_resolution,[status(thm)],[361, 360, 331])).
% 18.24/18.46 tff(363,plain,
% 18.24/18.46 ($false),
% 18.24/18.46 inference(unit_resolution,[status(thm)],[362, 279])).
% 18.24/18.46 % SZS output end Proof
% 18.24/18.47 % E exiting
%------------------------------------------------------------------------------