%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC354+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:59 AM UTC 2025
% Result : Theorem 3.28s 3.49s
% Output : Proof 3.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC354+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:06:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.28/3.49 % SZS status Theorem
% 3.28/3.49 % SZS output start Proof
% 3.28/3.49 tff(tptp_fun_V_46_type, type, (
% 3.28/3.49 tptp_fun_V_46: $i)).
% 3.28/3.49 tff(app_type, type, (
% 3.28/3.49 app: ( $i * $i ) > $i)).
% 3.28/3.49 tff(tptp_fun_V_43_type, type, (
% 3.28/3.49 tptp_fun_V_43: $i > $i)).
% 3.28/3.49 tff(tptp_fun_U_45_type, type, (
% 3.28/3.49 tptp_fun_U_45: $i)).
% 3.28/3.49 tff(nil_type, type, (
% 3.28/3.49 nil: $i)).
% 3.28/3.49 tff(cons_type, type, (
% 3.28/3.49 cons: ( $i * $i ) > $i)).
% 3.28/3.49 tff(tptp_fun_W_44_type, type, (
% 3.28/3.49 tptp_fun_W_44: $i > $i)).
% 3.28/3.49 tff(ssItem_type, type, (
% 3.28/3.49 ssItem: $i > $o)).
% 3.28/3.49 tff(ssList_type, type, (
% 3.28/3.49 ssList: $i > $o)).
% 3.28/3.49 tff(segmentP_type, type, (
% 3.28/3.49 segmentP: ( $i * $i ) > $o)).
% 3.28/3.49 tff(neq_type, type, (
% 3.28/3.49 neq: ( $i * $i ) > $o)).
% 3.28/3.49 tff(hd_type, type, (
% 3.28/3.49 hd: $i > $i)).
% 3.28/3.49 tff(tptp_fun_X_8_type, type, (
% 3.28/3.49 tptp_fun_X_8: ( $i * $i ) > $i)).
% 3.28/3.49 tff(tptp_fun_W_7_type, type, (
% 3.28/3.49 tptp_fun_W_7: ( $i * $i ) > $i)).
% 3.28/3.49 tff(1,plain,
% 3.28/3.49 ((ssList(U!45) & (~(segmentP(V!46, U!45) | (~ssList(V!46)) | (~ssList(U!45)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)))))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(2,plain,
% 3.28/3.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)))))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(3,plain,
% 3.28/3.49 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssList(Y) & (~(W = Y))) & ?[Z: $i] : (((ssItem(Z) & (cons(Z, nil) = Y)) & (hd(X) = Z)) & neq(nil, X)))) | segmentP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)))))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssList(Y) & (~(W = Y))) & ?[Z: $i] : (((ssItem(Z) & (cons(Z, nil) = Y)) & (hd(X) = Z)) & neq(nil, X)))) | segmentP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 3.28/3.49 tff(5,plain,
% 3.28/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.28/3.49 tff(6,plain,
% 3.28/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[5, 2])).
% 3.28/3.49 tff(7,plain,
% 3.28/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.28/3.49 tff(8,plain,
% 3.28/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[7, 2])).
% 3.28/3.49 tff(9,plain,
% 3.28/3.49 (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[8, 1])).
% 3.28/3.49 tff(10,plain,
% 3.28/3.49 (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)))),
% 3.28/3.49 inference(and_elim,[status(thm)],[9])).
% 3.28/3.49 tff(11,plain,
% 3.28/3.49 (ssList(V!46)),
% 3.28/3.49 inference(or_elim,[status(thm)],[10])).
% 3.28/3.49 tff(12,plain,
% 3.28/3.49 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(13,plain,
% 3.28/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[12])).
% 3.28/3.49 tff(14,plain,
% 3.28/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(15,plain,
% 3.28/3.49 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(16,plain,
% 3.28/3.49 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[15])).
% 3.28/3.49 tff(17,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 3.28/3.49 tff(18,plain,
% 3.28/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.28/3.49 tff(19,plain,
% 3.28/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.28/3.49 tff(20,plain,(
% 3.28/3.49 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(skolemize,[status(sab)],[19])).
% 3.28/3.49 tff(21,plain,
% 3.28/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[20, 13])).
% 3.28/3.49 tff(22,plain,
% 3.28/3.49 (((~![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)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(23,plain,
% 3.28/3.49 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 3.28/3.49 inference(quant_inst,[status(thm)],[])).
% 3.28/3.49 tff(24,plain,
% 3.28/3.49 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.28/3.49 tff(25,plain,
% 3.28/3.49 (segmentP(nil, V!46) <=> (nil = V!46)),
% 3.28/3.49 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 3.28/3.49 tff(26,plain,
% 3.28/3.49 (^[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))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(27,plain,
% 3.28/3.49 (![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)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[26])).
% 3.28/3.49 tff(28,plain,
% 3.28/3.49 (^[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))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(29,plain,
% 3.28/3.49 (![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)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[28])).
% 3.28/3.49 tff(30,plain,
% 3.28/3.49 (![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)))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[29, 27])).
% 3.28/3.49 tff(31,plain,
% 3.28/3.49 (![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)))))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(32,plain,
% 3.28/3.50 (^[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)))))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(33,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[32])).
% 3.28/3.50 tff(34,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 3.28/3.50 tff(35,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.28/3.50 tff(36,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[35, 31])).
% 3.28/3.50 tff(37,plain,(
% 3.28/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.28/3.50 inference(skolemize,[status(sab)],[36])).
% 3.28/3.50 tff(38,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[37, 30])).
% 3.28/3.50 tff(39,plain,
% 3.28/3.50 (((~![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)))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(40,plain,
% 3.28/3.50 ((~![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)))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(41,plain,
% 3.28/3.50 ((~![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))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.28/3.50 tff(42,plain,
% 3.28/3.50 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[41, 38, 11])).
% 3.28/3.50 tff(43,plain,
% 3.28/3.50 (ssList(nil) <=> ssList(nil)),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(44,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.28/3.50 tff(45,plain,
% 3.28/3.50 (ssList(nil)),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[44, 43])).
% 3.28/3.50 tff(46,plain,
% 3.28/3.50 (((~![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))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(47,plain,
% 3.28/3.50 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(48,plain,
% 3.28/3.50 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[47, 46])).
% 3.28/3.50 tff(49,plain,
% 3.28/3.50 (~((V!46 = nil) <=> neq(V!46, nil))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 3.28/3.50 tff(50,plain,
% 3.28/3.50 (neq(V!46, nil)),
% 3.28/3.50 inference(or_elim,[status(thm)],[10])).
% 3.28/3.50 tff(51,plain,
% 3.28/3.50 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(52,plain,
% 3.28/3.50 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[51, 50])).
% 3.28/3.50 tff(53,plain,
% 3.28/3.50 (~(V!46 = nil)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[52, 49])).
% 3.28/3.50 tff(54,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(55,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[54])).
% 3.28/3.50 tff(56,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(57,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[56])).
% 3.28/3.50 tff(58,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(transitivity,[status(thm)],[57, 55])).
% 3.28/3.50 tff(59,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(60,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[59])).
% 3.28/3.50 tff(61,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(62,plain,
% 3.28/3.50 (^[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)))))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(63,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[62])).
% 3.28/3.50 tff(64,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 3.28/3.50 tff(65,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[64, 63])).
% 3.28/3.50 tff(66,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[65, 61])).
% 3.28/3.50 tff(67,plain,(
% 3.28/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.28/3.50 inference(skolemize,[status(sab)],[66])).
% 3.28/3.50 tff(68,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[67, 60])).
% 3.28/3.50 tff(69,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[68, 58])).
% 3.28/3.50 tff(70,plain,
% 3.28/3.50 (((~![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))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(71,plain,
% 3.28/3.50 (((~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))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(72,plain,
% 3.28/3.50 (((~![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)))))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[71])).
% 3.28/3.50 tff(73,plain,
% 3.28/3.50 (((~![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))))),
% 3.28/3.50 inference(transitivity,[status(thm)],[72, 70])).
% 3.28/3.50 tff(74,plain,
% 3.28/3.50 ((~![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))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(75,plain,
% 3.28/3.50 ((~![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)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[74, 73])).
% 3.28/3.50 tff(76,plain,
% 3.28/3.50 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[75, 69, 11])).
% 3.28/3.50 tff(77,plain,
% 3.28/3.50 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(78,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[77])).
% 3.28/3.50 tff(79,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(80,plain,
% 3.28/3.50 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(81,plain,
% 3.28/3.50 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[80])).
% 3.28/3.50 tff(82,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 3.28/3.50 tff(83,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.28/3.50 tff(84,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[83, 79])).
% 3.28/3.50 tff(85,plain,(
% 3.28/3.50 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(skolemize,[status(sab)],[84])).
% 3.28/3.50 tff(86,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[85, 78])).
% 3.28/3.50 tff(87,plain,
% 3.28/3.50 (((~![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))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(88,plain,
% 3.28/3.50 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(89,plain,
% 3.28/3.50 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.28/3.50 tff(90,plain,
% 3.28/3.50 (segmentP(V!46, nil)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[89, 86, 11])).
% 3.28/3.50 tff(91,plain,
% 3.28/3.50 (((~![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)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(92,plain,
% 3.28/3.50 (((~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)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(93,plain,
% 3.28/3.50 (((~![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))))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[92])).
% 3.28/3.50 tff(94,plain,
% 3.28/3.50 (((~![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)))),
% 3.28/3.50 inference(transitivity,[status(thm)],[93, 91])).
% 3.28/3.50 tff(95,plain,
% 3.28/3.50 ((~![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)))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(96,plain,
% 3.28/3.50 ((~![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))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 3.28/3.50 tff(97,plain,
% 3.28/3.50 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[96, 45, 90, 76])).
% 3.28/3.50 tff(98,plain,
% 3.28/3.50 (~segmentP(nil, V!46)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[97, 53])).
% 3.28/3.50 tff(99,plain,
% 3.28/3.50 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(100,plain,
% 3.28/3.50 (~(nil = V!46)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[99, 98, 25])).
% 3.28/3.50 tff(101,plain,
% 3.28/3.50 (^[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))))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(102,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[101])).
% 3.28/3.50 tff(103,plain,
% 3.28/3.50 (^[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)))))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(104,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[103])).
% 3.28/3.50 tff(105,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(106,plain,
% 3.28/3.50 (![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)))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[105])).
% 3.28/3.50 tff(107,plain,
% 3.28/3.50 (![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)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(108,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(109,plain,
% 3.28/3.50 (![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)))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[108])).
% 3.28/3.50 tff(110,axiom,(![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax20')).
% 3.28/3.50 tff(111,plain,
% 3.28/3.50 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[110, 109])).
% 3.28/3.50 tff(112,plain,
% 3.28/3.50 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[111, 107])).
% 3.28/3.50 tff(113,plain,(
% 3.28/3.50 ![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)))),
% 3.28/3.50 inference(skolemize,[status(sab)],[112])).
% 3.28/3.50 tff(114,plain,
% 3.28/3.50 (![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)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[113, 106])).
% 3.28/3.50 tff(115,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[114, 104])).
% 3.28/3.50 tff(116,plain,
% 3.28/3.50 (![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)))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[115, 102])).
% 3.28/3.50 tff(117,plain,
% 3.28/3.50 (((~![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)))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(118,plain,
% 3.28/3.50 (((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)))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(119,plain,
% 3.28/3.50 ((~((~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))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(120,plain,
% 3.28/3.50 (((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)))))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[119])).
% 3.28/3.50 tff(121,plain,
% 3.28/3.50 (((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)))))),
% 3.28/3.50 inference(transitivity,[status(thm)],[120, 118])).
% 3.28/3.50 tff(122,plain,
% 3.28/3.50 (((~![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))))))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[121])).
% 3.28/3.50 tff(123,plain,
% 3.28/3.50 (((~![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)))))),
% 3.28/3.50 inference(transitivity,[status(thm)],[122, 117])).
% 3.28/3.50 tff(124,plain,
% 3.28/3.50 ((~![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)))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(125,plain,
% 3.28/3.50 ((~![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))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[124, 123])).
% 3.28/3.50 tff(126,plain,
% 3.28/3.50 ((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))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[125, 116, 11])).
% 3.28/3.50 tff(127,plain,
% 3.28/3.50 (~((~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)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[126, 100])).
% 3.28/3.50 tff(128,plain,
% 3.28/3.50 (((~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)),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(129,plain,
% 3.28/3.50 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[128, 127])).
% 3.28/3.50 tff(130,plain,
% 3.28/3.50 (((~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))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(131,plain,
% 3.28/3.50 (ssList(tptp_fun_V_43(V!46))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[130, 127])).
% 3.28/3.50 tff(132,plain,
% 3.28/3.50 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(133,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[132])).
% 3.28/3.50 tff(134,plain,
% 3.28/3.50 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(135,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[134])).
% 3.28/3.50 tff(136,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(transitivity,[status(thm)],[135, 133])).
% 3.28/3.50 tff(137,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(138,plain,
% 3.28/3.50 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (hd(cons(V, U)) = V)) <=> ((~ssItem(V)) | (hd(cons(V, U)) = V)))), (![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)) <=> ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(139,plain,
% 3.28/3.50 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[138])).
% 3.28/3.50 tff(140,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax23')).
% 3.28/3.50 tff(141,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[140, 139])).
% 3.28/3.50 tff(142,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[141, 137])).
% 3.28/3.50 tff(143,plain,(
% 3.28/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(skolemize,[status(sab)],[142])).
% 3.28/3.50 tff(144,plain,
% 3.28/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[143, 136])).
% 3.28/3.50 tff(145,plain,
% 3.28/3.50 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(146,plain,
% 3.28/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V)))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(147,plain,
% 3.28/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(V!46))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.28/3.50 tff(148,plain,
% 3.28/3.50 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[147, 144, 131])).
% 3.28/3.50 tff(149,plain,
% 3.28/3.50 (((~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))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(150,plain,
% 3.28/3.50 (ssItem(tptp_fun_W_44(V!46))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[149, 127])).
% 3.28/3.50 tff(151,plain,
% 3.28/3.50 (((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(152,plain,
% 3.28/3.50 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | ((~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(153,plain,
% 3.28/3.50 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))) | (~ssItem(tptp_fun_W_44(V!46))) | (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.28/3.50 tff(154,plain,
% 3.28/3.50 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[153, 150, 148])).
% 3.28/3.50 tff(155,plain,
% 3.28/3.50 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = hd(V!46)),
% 3.28/3.50 inference(monotonicity,[status(thm)],[129])).
% 3.28/3.50 tff(156,plain,
% 3.28/3.50 (hd(V!46) = hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 3.28/3.50 inference(symmetry,[status(thm)],[155])).
% 3.28/3.50 tff(157,plain,
% 3.28/3.50 (hd(V!46) = tptp_fun_W_44(V!46)),
% 3.28/3.50 inference(transitivity,[status(thm)],[156, 154])).
% 3.28/3.50 tff(158,plain,
% 3.28/3.50 (cons(hd(V!46), tptp_fun_V_43(V!46)) = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[157])).
% 3.28/3.50 tff(159,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(160,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[159])).
% 3.28/3.50 tff(161,plain,
% 3.28/3.50 (^[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)))))),
% 3.28/3.50 inference(bind,[status(th)],[])).
% 3.28/3.50 tff(162,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(quant_intro,[status(thm)],[161])).
% 3.28/3.50 tff(163,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(transitivity,[status(thm)],[162, 160])).
% 3.28/3.50 tff(164,plain,
% 3.28/3.50 (![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))))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(165,plain,
% 3.28/3.50 (^[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))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(166,plain,
% 3.28/3.51 (![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))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[165])).
% 3.28/3.51 tff(167,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 3.28/3.51 tff(168,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[167, 166])).
% 3.28/3.51 tff(169,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[168, 164])).
% 3.28/3.51 tff(170,plain,(
% 3.28/3.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.28/3.51 inference(skolemize,[status(sab)],[169])).
% 3.28/3.51 tff(171,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[170, 163])).
% 3.28/3.51 tff(172,plain,
% 3.28/3.51 (((~![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)))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(173,plain,
% 3.28/3.51 ((~![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)))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(174,plain,
% 3.28/3.51 ((~![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))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.28/3.51 tff(175,plain,
% 3.28/3.51 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[174, 171, 131])).
% 3.28/3.51 tff(176,plain,
% 3.28/3.51 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(177,plain,
% 3.28/3.51 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[176])).
% 3.28/3.51 tff(178,plain,
% 3.28/3.51 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(179,plain,
% 3.28/3.51 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssItem(hd(U))) <=> ((nil = U) | ssItem(hd(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> (ssList(U) => ((nil = U) | ssItem(hd(U)))))), rewrite((ssList(U) => ((nil = U) | ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(180,plain,
% 3.28/3.51 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[179])).
% 3.28/3.51 tff(181,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax22')).
% 3.28/3.51 tff(182,plain,
% 3.28/3.51 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[181, 180])).
% 3.28/3.51 tff(183,plain,
% 3.28/3.51 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[182, 178])).
% 3.28/3.51 tff(184,plain,(
% 3.28/3.51 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(skolemize,[status(sab)],[183])).
% 3.28/3.51 tff(185,plain,
% 3.28/3.51 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[184, 177])).
% 3.28/3.51 tff(186,plain,
% 3.28/3.51 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(187,plain,
% 3.28/3.51 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(188,plain,
% 3.28/3.51 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)))),
% 3.28/3.51 inference(monotonicity,[status(thm)],[187])).
% 3.28/3.51 tff(189,plain,
% 3.28/3.51 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 3.28/3.51 inference(transitivity,[status(thm)],[188, 186])).
% 3.28/3.51 tff(190,plain,
% 3.28/3.51 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(191,plain,
% 3.28/3.51 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[190, 189])).
% 3.28/3.51 tff(192,plain,
% 3.28/3.51 (ssItem(hd(V!46)) | (nil = V!46)),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[191, 185, 11])).
% 3.28/3.51 tff(193,plain,
% 3.28/3.51 (ssItem(hd(V!46))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[192, 100])).
% 3.28/3.51 tff(194,plain,
% 3.28/3.51 (((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(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(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(195,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(196,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[195, 194])).
% 3.28/3.51 tff(197,plain,
% 3.28/3.51 (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[196, 193, 175])).
% 3.28/3.51 tff(198,plain,
% 3.28/3.51 (app(cons(hd(V!46), nil), tptp_fun_V_43(V!46)) = cons(hd(V!46), tptp_fun_V_43(V!46))),
% 3.28/3.51 inference(symmetry,[status(thm)],[197])).
% 3.28/3.51 tff(199,plain,
% 3.28/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(200,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(201,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[200, 199])).
% 3.28/3.51 tff(202,plain,
% 3.28/3.51 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[201, 38, 45])).
% 3.28/3.51 tff(203,plain,
% 3.28/3.51 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(204,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(205,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.28/3.51 tff(206,plain,
% 3.28/3.51 (~((nil = V!46) <=> neq(nil, V!46))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[205, 11, 202])).
% 3.28/3.51 tff(207,plain,
% 3.28/3.51 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 3.28/3.51 inference(tautology,[status(thm)],[])).
% 3.28/3.51 tff(208,plain,
% 3.28/3.51 (neq(nil, V!46)),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[207, 100, 206])).
% 3.28/3.51 tff(209,plain,
% 3.28/3.51 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(210,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[209])).
% 3.28/3.51 tff(211,plain,
% 3.28/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(212,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[211])).
% 3.28/3.51 tff(213,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(transitivity,[status(thm)],[212, 210])).
% 3.28/3.51 tff(214,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(215,plain,
% 3.28/3.51 (^[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))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(216,plain,
% 3.28/3.51 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[215])).
% 3.28/3.51 tff(217,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 3.28/3.51 tff(218,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[217, 216])).
% 3.28/3.51 tff(219,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[218, 214])).
% 3.28/3.51 tff(220,plain,(
% 3.28/3.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(skolemize,[status(sab)],[219])).
% 3.28/3.51 tff(221,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[220, 213])).
% 3.28/3.51 tff(222,plain,
% 3.28/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(223,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(224,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[223, 222])).
% 3.28/3.51 tff(225,plain,
% 3.28/3.51 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[224, 221, 45])).
% 3.28/3.51 tff(226,plain,
% 3.28/3.51 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(227,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(228,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[227, 226])).
% 3.28/3.51 tff(229,plain,
% 3.28/3.51 (ssList(cons(hd(V!46), nil))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[228, 193, 225])).
% 3.28/3.51 tff(230,plain,
% 3.28/3.51 ((~(~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))) <=> ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(231,plain,
% 3.28/3.51 ((ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) <=> (~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(232,plain,
% 3.28/3.51 ((~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> (~(~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))))),
% 3.28/3.51 inference(monotonicity,[status(thm)],[231])).
% 3.28/3.51 tff(233,plain,
% 3.28/3.51 ((~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 3.28/3.51 inference(transitivity,[status(thm)],[232, 230])).
% 3.28/3.51 tff(234,plain,
% 3.28/3.51 (~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))),
% 3.28/3.51 inference(or_elim,[status(thm)],[10])).
% 3.28/3.51 tff(235,plain,
% 3.28/3.51 ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[234, 233])).
% 3.28/3.51 tff(236,plain,
% 3.28/3.51 (U!45 = cons(hd(V!46), nil)),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[235, 229, 208, 193])).
% 3.28/3.51 tff(237,plain,
% 3.28/3.51 (app(U!45, tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 3.28/3.51 inference(monotonicity,[status(thm)],[236])).
% 3.28/3.51 tff(238,plain,
% 3.28/3.51 (ssList(U!45)),
% 3.28/3.51 inference(and_elim,[status(thm)],[9])).
% 3.28/3.51 tff(239,plain,
% 3.28/3.51 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(240,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[239])).
% 3.28/3.51 tff(241,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(242,plain,
% 3.28/3.51 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(243,plain,
% 3.28/3.51 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[242])).
% 3.28/3.51 tff(244,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 3.28/3.51 tff(245,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[244, 243])).
% 3.28/3.51 tff(246,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[245, 241])).
% 3.28/3.51 tff(247,plain,(
% 3.28/3.51 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(skolemize,[status(sab)],[246])).
% 3.28/3.51 tff(248,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[247, 240])).
% 3.28/3.51 tff(249,plain,
% 3.28/3.51 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(250,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(251,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[250, 249])).
% 3.28/3.51 tff(252,plain,
% 3.28/3.51 (app(nil, U!45) = U!45),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[251, 248, 238])).
% 3.28/3.51 tff(253,plain,
% 3.28/3.51 (app(app(nil, U!45), tptp_fun_V_43(V!46)) = app(U!45, tptp_fun_V_43(V!46))),
% 3.28/3.51 inference(monotonicity,[status(thm)],[252])).
% 3.28/3.51 tff(254,plain,
% 3.28/3.51 (app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46),
% 3.28/3.51 inference(transitivity,[status(thm)],[253, 237, 198, 158, 129])).
% 3.28/3.51 tff(255,plain,
% 3.28/3.51 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(256,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[255])).
% 3.28/3.51 tff(257,plain,
% 3.28/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(258,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[257])).
% 3.28/3.51 tff(259,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(transitivity,[status(thm)],[258, 256])).
% 3.28/3.51 tff(260,plain,
% 3.28/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(261,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[260])).
% 3.28/3.51 tff(262,plain,
% 3.28/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(263,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[262])).
% 3.28/3.51 tff(264,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(265,plain,
% 3.28/3.51 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.28/3.51 inference(bind,[status(th)],[])).
% 3.28/3.51 tff(266,plain,
% 3.28/3.51 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.28/3.51 inference(quant_intro,[status(thm)],[265])).
% 3.28/3.51 tff(267,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 3.28/3.51 tff(268,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[267, 266])).
% 3.28/3.51 tff(269,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[268, 264])).
% 3.28/3.51 tff(270,plain,(
% 3.28/3.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.28/3.51 inference(skolemize,[status(sab)],[269])).
% 3.28/3.51 tff(271,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[270, 263])).
% 3.28/3.51 tff(272,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[271, 261])).
% 3.28/3.51 tff(273,plain,
% 3.28/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[272, 259])).
% 3.28/3.51 tff(274,plain,
% 3.28/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(275,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(276,plain,
% 3.28/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[275, 274])).
% 3.28/3.51 tff(277,plain,
% 3.28/3.51 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 3.28/3.51 inference(unit_resolution,[status(thm)],[276, 273, 11])).
% 3.28/3.51 tff(278,plain,
% 3.28/3.51 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 3.28/3.51 inference(rewrite,[status(thm)],[])).
% 3.28/3.51 tff(279,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 3.28/3.51 inference(quant_inst,[status(thm)],[])).
% 3.28/3.51 tff(280,plain,
% 3.28/3.51 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))))),
% 3.28/3.51 inference(modus_ponens,[status(thm)],[279, 278])).
% 3.28/3.51 tff(281,plain,
% 3.28/3.51 (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[280, 238, 277])).
% 3.36/3.53 tff(282,plain,
% 3.36/3.53 (((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))) | (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))),
% 3.36/3.53 inference(tautology,[status(thm)],[])).
% 3.36/3.53 tff(283,plain,
% 3.36/3.53 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[282, 281])).
% 3.36/3.53 tff(284,plain,
% 3.36/3.53 (~segmentP(V!46, U!45)),
% 3.36/3.53 inference(or_elim,[status(thm)],[10])).
% 3.36/3.53 tff(285,plain,
% 3.36/3.53 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.36/3.53 inference(tautology,[status(thm)],[])).
% 3.36/3.53 tff(286,plain,
% 3.36/3.53 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[285, 284])).
% 3.36/3.53 tff(287,plain,
% 3.36/3.53 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[286, 283])).
% 3.36/3.53 tff(288,plain,
% 3.36/3.53 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 3.36/3.53 inference(rewrite,[status(thm)],[])).
% 3.36/3.53 tff(289,plain,
% 3.36/3.53 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46))))),
% 3.36/3.53 inference(quant_inst,[status(thm)],[])).
% 3.36/3.53 tff(290,plain,
% 3.36/3.53 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 3.36/3.53 inference(modus_ponens,[status(thm)],[289, 288])).
% 3.36/3.53 tff(291,plain,
% 3.36/3.53 (![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[290, 45, 287])).
% 3.36/3.53 tff(292,plain,
% 3.36/3.53 (((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (~(app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46)))),
% 3.36/3.53 inference(rewrite,[status(thm)],[])).
% 3.36/3.53 tff(293,plain,
% 3.36/3.53 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | ((~ssList(tptp_fun_V_43(V!46))) | (~(app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46)))),
% 3.36/3.53 inference(quant_inst,[status(thm)],[])).
% 3.36/3.53 tff(294,plain,
% 3.36/3.53 ((~![X: $i] : ((~ssList(X)) | (~(app(app(nil, U!45), X) = V!46)))) | (~ssList(tptp_fun_V_43(V!46))) | (~(app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46))),
% 3.36/3.53 inference(modus_ponens,[status(thm)],[293, 292])).
% 3.36/3.53 tff(295,plain,
% 3.36/3.53 (~(app(app(nil, U!45), tptp_fun_V_43(V!46)) = V!46)),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[294, 131, 291])).
% 3.36/3.53 tff(296,plain,
% 3.36/3.53 ($false),
% 3.36/3.53 inference(unit_resolution,[status(thm)],[295, 254])).
% 3.36/3.53 % SZS output end Proof
% 3.36/3.53 % E exiting
%------------------------------------------------------------------------------