%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC022+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:29:57 AM UTC 2025
% Result : Theorem 3.33s 3.49s
% Output : Proof 3.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC022+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:02:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.33/3.49 % SZS status Theorem
% 3.33/3.49 % SZS output start Proof
% 3.33/3.49 tff(frontsegP_type, type, (
% 3.33/3.49 frontsegP: ( $i * $i ) > $o)).
% 3.33/3.49 tff(tptp_fun_U_45_type, type, (
% 3.33/3.49 tptp_fun_U_45: $i)).
% 3.33/3.49 tff(app_type, type, (
% 3.33/3.49 app: ( $i * $i ) > $i)).
% 3.33/3.49 tff(tptp_fun_V_43_type, type, (
% 3.33/3.49 tptp_fun_V_43: $i > $i)).
% 3.33/3.49 tff(tptp_fun_V_46_type, type, (
% 3.33/3.49 tptp_fun_V_46: $i)).
% 3.33/3.49 tff(cons_type, type, (
% 3.33/3.49 cons: ( $i * $i ) > $i)).
% 3.33/3.49 tff(tptp_fun_W_44_type, type, (
% 3.33/3.49 tptp_fun_W_44: $i > $i)).
% 3.33/3.49 tff(ssItem_type, type, (
% 3.33/3.49 ssItem: $i > $o)).
% 3.33/3.49 tff(ssList_type, type, (
% 3.33/3.49 ssList: $i > $o)).
% 3.33/3.49 tff(nil_type, type, (
% 3.33/3.49 nil: $i)).
% 3.33/3.49 tff(segmentP_type, type, (
% 3.33/3.49 segmentP: ( $i * $i ) > $o)).
% 3.33/3.49 tff(neq_type, type, (
% 3.33/3.49 neq: ( $i * $i ) > $o)).
% 3.33/3.49 tff(hd_type, type, (
% 3.33/3.49 hd: $i > $i)).
% 3.33/3.49 tff(1,plain,
% 3.33/3.49 ((ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(2,plain,
% 3.33/3.49 ((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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))) <=> (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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(3,plain,
% 3.33/3.49 ((ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))))),
% 3.33/3.49 inference(monotonicity,[status(thm)],[2])).
% 3.33/3.49 tff(4,plain,
% 3.33/3.49 ((ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))) <=> (ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))))),
% 3.33/3.49 inference(transitivity,[status(thm)],[3, 1])).
% 3.33/3.49 tff(5,plain,
% 3.33/3.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(6,plain,
% 3.33/3.49 ((~![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) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ?[Z: $i] : ((ssList(Z) & (~(W = Z))) & ?[X1: $i] : (((ssItem(X1) & (cons(X1, nil) = Z)) & (hd(X) = X1)) & neq(nil, X)))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y)))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(7,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) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ?[Z: $i] : ((ssList(Z) & (~(W = Z))) & ?[X1: $i] : (((ssItem(X1) & (cons(X1, nil) = Z)) & (hd(X) = X1)) & neq(nil, X)))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 3.33/3.49 tff(8,plain,
% 3.33/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 3.33/3.49 tff(9,plain,
% 3.33/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[8, 5])).
% 3.33/3.49 tff(10,plain,
% 3.33/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 3.33/3.49 tff(11,plain,
% 3.33/3.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(V, Y) & frontsegP(U, Y))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[10, 5])).
% 3.33/3.49 tff(12,plain,
% 3.33/3.49 (ssList(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) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[11, 4])).
% 3.33/3.49 tff(13,plain,
% 3.33/3.49 (ssList(V!46)),
% 3.33/3.49 inference(and_elim,[status(thm)],[12])).
% 3.33/3.49 tff(14,plain,
% 3.33/3.49 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(15,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[14])).
% 3.33/3.49 tff(16,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(17,plain,
% 3.33/3.49 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(18,plain,
% 3.33/3.49 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[17])).
% 3.33/3.49 tff(19,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 3.33/3.49 tff(20,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[19, 18])).
% 3.33/3.49 tff(21,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[20, 16])).
% 3.33/3.49 tff(22,plain,(
% 3.33/3.49 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(skolemize,[status(sab)],[21])).
% 3.33/3.49 tff(23,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[22, 15])).
% 3.33/3.49 tff(24,plain,
% 3.33/3.49 (((~![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)))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(25,plain,
% 3.33/3.49 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(26,plain,
% 3.33/3.49 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[25, 24])).
% 3.33/3.49 tff(27,plain,
% 3.33/3.49 (segmentP(nil, V!46) <=> (nil = V!46)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 3.33/3.49 tff(28,plain,
% 3.33/3.49 (^[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))))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(29,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[28])).
% 3.33/3.49 tff(30,plain,
% 3.33/3.49 (^[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))))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(31,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[30])).
% 3.33/3.49 tff(32,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(transitivity,[status(thm)],[31, 29])).
% 3.33/3.49 tff(33,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(34,plain,
% 3.33/3.49 (^[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)))))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(35,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[34])).
% 3.33/3.49 tff(36,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 3.33/3.49 tff(37,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 3.33/3.49 tff(38,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[37, 33])).
% 3.33/3.49 tff(39,plain,(
% 3.33/3.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.33/3.49 inference(skolemize,[status(sab)],[38])).
% 3.33/3.49 tff(40,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[39, 32])).
% 3.33/3.49 tff(41,plain,
% 3.33/3.49 (((~![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)))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(42,plain,
% 3.33/3.49 ((~![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)))))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(43,plain,
% 3.33/3.49 ((~![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))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[42, 41])).
% 3.33/3.49 tff(44,plain,
% 3.33/3.49 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[43, 40, 13])).
% 3.33/3.49 tff(45,plain,
% 3.33/3.49 (ssList(nil) <=> ssList(nil)),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(46,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.33/3.49 tff(47,plain,
% 3.33/3.49 (ssList(nil)),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.33/3.49 tff(48,plain,
% 3.33/3.49 (((~![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))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(49,plain,
% 3.33/3.49 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(50,plain,
% 3.33/3.49 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[49, 48])).
% 3.33/3.49 tff(51,plain,
% 3.33/3.49 (~((V!46 = nil) <=> neq(V!46, nil))),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[50, 47, 44])).
% 3.33/3.49 tff(52,plain,
% 3.33/3.49 (neq(V!46, nil)),
% 3.33/3.49 inference(and_elim,[status(thm)],[12])).
% 3.33/3.49 tff(53,plain,
% 3.33/3.49 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 3.33/3.49 inference(tautology,[status(thm)],[])).
% 3.33/3.49 tff(54,plain,
% 3.33/3.49 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[53, 52])).
% 3.33/3.49 tff(55,plain,
% 3.33/3.49 (~(V!46 = nil)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[54, 51])).
% 3.33/3.49 tff(56,plain,
% 3.33/3.49 (^[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)))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(57,plain,
% 3.33/3.49 (![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))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[56])).
% 3.33/3.49 tff(58,plain,
% 3.33/3.49 (^[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)))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(59,plain,
% 3.33/3.49 (![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))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[58])).
% 3.33/3.49 tff(60,plain,
% 3.33/3.49 (![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))))),
% 3.33/3.49 inference(transitivity,[status(thm)],[59, 57])).
% 3.33/3.49 tff(61,plain,
% 3.33/3.49 (^[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)))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(62,plain,
% 3.33/3.49 (![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))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[61])).
% 3.33/3.49 tff(63,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(64,plain,
% 3.33/3.49 (^[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)))))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(65,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[64])).
% 3.33/3.49 tff(66,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 3.33/3.49 tff(67,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.33/3.49 tff(68,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[67, 63])).
% 3.33/3.49 tff(69,plain,(
% 3.33/3.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 3.33/3.49 inference(skolemize,[status(sab)],[68])).
% 3.33/3.49 tff(70,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[69, 62])).
% 3.33/3.49 tff(71,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[70, 60])).
% 3.33/3.49 tff(72,plain,
% 3.33/3.49 (((~![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))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(73,plain,
% 3.33/3.49 (((~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))))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(74,plain,
% 3.33/3.49 (((~![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)))))),
% 3.33/3.49 inference(monotonicity,[status(thm)],[73])).
% 3.33/3.49 tff(75,plain,
% 3.33/3.49 (((~![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))))),
% 3.33/3.49 inference(transitivity,[status(thm)],[74, 72])).
% 3.33/3.49 tff(76,plain,
% 3.33/3.49 ((~![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))))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(77,plain,
% 3.33/3.49 ((~![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)))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.33/3.49 tff(78,plain,
% 3.33/3.49 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[77, 71, 13])).
% 3.33/3.49 tff(79,plain,
% 3.33/3.49 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(80,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[79])).
% 3.33/3.49 tff(81,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(82,plain,
% 3.33/3.49 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(83,plain,
% 3.33/3.49 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[82])).
% 3.33/3.49 tff(84,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 3.33/3.49 tff(85,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 3.33/3.49 tff(86,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[85, 81])).
% 3.33/3.49 tff(87,plain,(
% 3.33/3.49 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(skolemize,[status(sab)],[86])).
% 3.33/3.49 tff(88,plain,
% 3.33/3.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[87, 80])).
% 3.33/3.49 tff(89,plain,
% 3.33/3.49 (((~![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))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(90,plain,
% 3.33/3.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(91,plain,
% 3.33/3.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 3.33/3.49 tff(92,plain,
% 3.33/3.49 (segmentP(V!46, nil)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[91, 88, 13])).
% 3.33/3.49 tff(93,plain,
% 3.33/3.49 (((~![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)))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(94,plain,
% 3.33/3.49 (((~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)))),
% 3.33/3.49 inference(rewrite,[status(thm)],[])).
% 3.33/3.49 tff(95,plain,
% 3.33/3.49 (((~![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))))),
% 3.33/3.49 inference(monotonicity,[status(thm)],[94])).
% 3.33/3.49 tff(96,plain,
% 3.33/3.49 (((~![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)))),
% 3.33/3.49 inference(transitivity,[status(thm)],[95, 93])).
% 3.33/3.49 tff(97,plain,
% 3.33/3.49 ((~![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)))),
% 3.33/3.49 inference(quant_inst,[status(thm)],[])).
% 3.33/3.49 tff(98,plain,
% 3.33/3.49 ((~![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))),
% 3.33/3.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 3.33/3.49 tff(99,plain,
% 3.33/3.49 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[98, 47, 92, 78])).
% 3.33/3.49 tff(100,plain,
% 3.33/3.49 (~segmentP(nil, V!46)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[99, 55])).
% 3.33/3.49 tff(101,plain,
% 3.33/3.49 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 3.33/3.49 inference(tautology,[status(thm)],[])).
% 3.33/3.49 tff(102,plain,
% 3.33/3.49 (~(nil = V!46)),
% 3.33/3.49 inference(unit_resolution,[status(thm)],[101, 100, 27])).
% 3.33/3.49 tff(103,plain,
% 3.33/3.49 (^[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))))))),
% 3.33/3.49 inference(bind,[status(th)],[])).
% 3.33/3.49 tff(104,plain,
% 3.33/3.49 (![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)))))),
% 3.33/3.49 inference(quant_intro,[status(thm)],[103])).
% 3.33/3.49 tff(105,plain,
% 3.33/3.49 (^[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)))))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(106,plain,
% 3.33/3.50 (![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)))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[105])).
% 3.33/3.50 tff(107,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(108,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[107])).
% 3.33/3.50 tff(109,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(110,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(111,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[110])).
% 3.33/3.50 tff(112,axiom,(![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax20')).
% 3.33/3.50 tff(113,plain,
% 3.33/3.50 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.33/3.50 tff(114,plain,
% 3.33/3.50 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[113, 109])).
% 3.33/3.50 tff(115,plain,(
% 3.33/3.50 ![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)))),
% 3.33/3.50 inference(skolemize,[status(sab)],[114])).
% 3.33/3.50 tff(116,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[115, 108])).
% 3.33/3.50 tff(117,plain,
% 3.33/3.50 (![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)))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[116, 106])).
% 3.33/3.50 tff(118,plain,
% 3.33/3.50 (![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)))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[117, 104])).
% 3.33/3.50 tff(119,plain,
% 3.33/3.50 (((~![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)))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(120,plain,
% 3.33/3.50 (((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)))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(121,plain,
% 3.33/3.50 ((~((~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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(122,plain,
% 3.33/3.50 (((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)))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[121])).
% 3.33/3.50 tff(123,plain,
% 3.33/3.50 (((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)))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[122, 120])).
% 3.33/3.50 tff(124,plain,
% 3.33/3.50 (((~![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))))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[123])).
% 3.33/3.50 tff(125,plain,
% 3.33/3.50 (((~![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)))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[124, 119])).
% 3.33/3.50 tff(126,plain,
% 3.33/3.50 ((~![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)))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(127,plain,
% 3.33/3.50 ((~![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))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[126, 125])).
% 3.33/3.50 tff(128,plain,
% 3.33/3.50 ((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))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[127, 118, 13])).
% 3.33/3.50 tff(129,plain,
% 3.33/3.50 (~((~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)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[128, 102])).
% 3.33/3.50 tff(130,plain,
% 3.33/3.50 (((~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)),
% 3.33/3.50 inference(tautology,[status(thm)],[])).
% 3.33/3.50 tff(131,plain,
% 3.33/3.50 (cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)) = V!46),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[130, 129])).
% 3.33/3.50 tff(132,plain,
% 3.33/3.50 (((~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))),
% 3.33/3.50 inference(tautology,[status(thm)],[])).
% 3.33/3.50 tff(133,plain,
% 3.33/3.50 (ssList(tptp_fun_V_43(V!46))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[132, 129])).
% 3.33/3.50 tff(134,plain,
% 3.33/3.50 (^[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))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(135,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[134])).
% 3.33/3.50 tff(136,plain,
% 3.33/3.50 (^[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))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(137,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[136])).
% 3.33/3.50 tff(138,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(transitivity,[status(thm)],[137, 135])).
% 3.33/3.50 tff(139,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(140,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(141,plain,
% 3.33/3.50 (![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)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[140])).
% 3.33/3.50 tff(142,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax23')).
% 3.33/3.50 tff(143,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 3.33/3.50 tff(144,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[143, 139])).
% 3.33/3.50 tff(145,plain,(
% 3.33/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.33/3.50 inference(skolemize,[status(sab)],[144])).
% 3.33/3.50 tff(146,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[145, 138])).
% 3.33/3.50 tff(147,plain,
% 3.33/3.50 (((~![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)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(148,plain,
% 3.33/3.50 ((~![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)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(149,plain,
% 3.33/3.50 ((~![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))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 3.33/3.50 tff(150,plain,
% 3.33/3.50 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(V!46))) = V))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[149, 146, 133])).
% 3.33/3.50 tff(151,plain,
% 3.33/3.50 (((~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))),
% 3.33/3.50 inference(tautology,[status(thm)],[])).
% 3.33/3.50 tff(152,plain,
% 3.33/3.50 (ssItem(tptp_fun_W_44(V!46))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[151, 129])).
% 3.33/3.50 tff(153,plain,
% 3.33/3.50 (((~![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)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(154,plain,
% 3.33/3.50 ((~![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)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(155,plain,
% 3.33/3.50 ((~![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))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[154, 153])).
% 3.33/3.50 tff(156,plain,
% 3.33/3.50 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = tptp_fun_W_44(V!46)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[155, 152, 150])).
% 3.33/3.50 tff(157,plain,
% 3.33/3.50 (hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))) = hd(V!46)),
% 3.33/3.50 inference(monotonicity,[status(thm)],[131])).
% 3.33/3.50 tff(158,plain,
% 3.33/3.50 (hd(V!46) = hd(cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46)))),
% 3.33/3.50 inference(symmetry,[status(thm)],[157])).
% 3.33/3.50 tff(159,plain,
% 3.33/3.50 (hd(V!46) = tptp_fun_W_44(V!46)),
% 3.33/3.50 inference(transitivity,[status(thm)],[158, 156])).
% 3.33/3.50 tff(160,plain,
% 3.33/3.50 (cons(hd(V!46), tptp_fun_V_43(V!46)) = cons(tptp_fun_W_44(V!46), tptp_fun_V_43(V!46))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[159])).
% 3.33/3.50 tff(161,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(162,plain,
% 3.33/3.50 (![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))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[161])).
% 3.33/3.50 tff(163,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(164,plain,
% 3.33/3.50 (![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))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[163])).
% 3.33/3.50 tff(165,plain,
% 3.33/3.50 (![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))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[164, 162])).
% 3.33/3.50 tff(166,plain,
% 3.33/3.50 (![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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(167,plain,
% 3.33/3.50 (^[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))))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(168,plain,
% 3.33/3.50 (![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))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[167])).
% 3.33/3.50 tff(169,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax81')).
% 3.33/3.50 tff(170,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[169, 168])).
% 3.33/3.50 tff(171,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[170, 166])).
% 3.33/3.50 tff(172,plain,(
% 3.33/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.33/3.50 inference(skolemize,[status(sab)],[171])).
% 3.33/3.50 tff(173,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[172, 165])).
% 3.33/3.50 tff(174,plain,
% 3.33/3.50 (((~![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)))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(175,plain,
% 3.33/3.50 ((~![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)))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(176,plain,
% 3.33/3.50 ((~![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))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 3.33/3.50 tff(177,plain,
% 3.33/3.50 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_V_43(V!46)) = app(cons(V, nil), tptp_fun_V_43(V!46))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[176, 173, 133])).
% 3.33/3.50 tff(178,plain,
% 3.33/3.50 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(179,plain,
% 3.33/3.50 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[178])).
% 3.33/3.50 tff(180,plain,
% 3.33/3.50 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(181,plain,
% 3.33/3.50 (^[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)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(182,plain,
% 3.33/3.50 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[181])).
% 3.33/3.50 tff(183,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax22')).
% 3.33/3.50 tff(184,plain,
% 3.33/3.50 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 3.33/3.50 tff(185,plain,
% 3.33/3.50 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[184, 180])).
% 3.33/3.50 tff(186,plain,(
% 3.33/3.50 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(skolemize,[status(sab)],[185])).
% 3.33/3.50 tff(187,plain,
% 3.33/3.50 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[186, 179])).
% 3.33/3.50 tff(188,plain,
% 3.33/3.50 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(189,plain,
% 3.33/3.50 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(190,plain,
% 3.33/3.50 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46)))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[189])).
% 3.33/3.50 tff(191,plain,
% 3.33/3.50 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46))),
% 3.33/3.50 inference(transitivity,[status(thm)],[190, 188])).
% 3.33/3.50 tff(192,plain,
% 3.33/3.50 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(193,plain,
% 3.33/3.50 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ssItem(hd(V!46)) | (~ssList(V!46)) | (nil = V!46)),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[192, 191])).
% 3.33/3.50 tff(194,plain,
% 3.33/3.50 (ssItem(hd(V!46)) | (nil = V!46)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[193, 187, 13])).
% 3.33/3.50 tff(195,plain,
% 3.33/3.50 (ssItem(hd(V!46))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[194, 102])).
% 3.33/3.50 tff(196,plain,
% 3.33/3.50 (((~![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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(197,plain,
% 3.33/3.50 ((~![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))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(198,plain,
% 3.33/3.50 ((~![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)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[197, 196])).
% 3.33/3.50 tff(199,plain,
% 3.33/3.50 (cons(hd(V!46), tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[198, 195, 177])).
% 3.33/3.50 tff(200,plain,
% 3.33/3.50 (app(cons(hd(V!46), nil), tptp_fun_V_43(V!46)) = cons(hd(V!46), tptp_fun_V_43(V!46))),
% 3.33/3.50 inference(symmetry,[status(thm)],[199])).
% 3.33/3.50 tff(201,plain,
% 3.33/3.50 (((~![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)))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(202,plain,
% 3.33/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(203,plain,
% 3.33/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[202, 201])).
% 3.33/3.50 tff(204,plain,
% 3.33/3.50 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[203, 40, 47])).
% 3.33/3.50 tff(205,plain,
% 3.33/3.50 (((~![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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(206,plain,
% 3.33/3.50 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(207,plain,
% 3.33/3.50 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 3.33/3.50 tff(208,plain,
% 3.33/3.50 (~((nil = V!46) <=> neq(nil, V!46))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[207, 13, 204])).
% 3.33/3.50 tff(209,plain,
% 3.33/3.50 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 3.33/3.50 inference(tautology,[status(thm)],[])).
% 3.33/3.50 tff(210,plain,
% 3.33/3.50 (neq(nil, V!46)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[209, 102, 208])).
% 3.33/3.50 tff(211,plain,
% 3.33/3.50 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(212,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[211])).
% 3.33/3.50 tff(213,plain,
% 3.33/3.50 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(214,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[213])).
% 3.33/3.50 tff(215,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[214, 212])).
% 3.33/3.50 tff(216,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(217,plain,
% 3.33/3.50 (^[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))))))),
% 3.33/3.50 inference(bind,[status(th)],[])).
% 3.33/3.50 tff(218,plain,
% 3.33/3.50 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(quant_intro,[status(thm)],[217])).
% 3.33/3.50 tff(219,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax16')).
% 3.33/3.50 tff(220,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.33/3.50 tff(221,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[220, 216])).
% 3.33/3.50 tff(222,plain,(
% 3.33/3.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(skolemize,[status(sab)],[221])).
% 3.33/3.50 tff(223,plain,
% 3.33/3.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[222, 215])).
% 3.33/3.50 tff(224,plain,
% 3.33/3.50 (((~![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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(225,plain,
% 3.33/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(226,plain,
% 3.33/3.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[225, 224])).
% 3.33/3.50 tff(227,plain,
% 3.33/3.50 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[226, 223, 47])).
% 3.33/3.50 tff(228,plain,
% 3.33/3.50 (((~![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)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(229,plain,
% 3.33/3.50 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(230,plain,
% 3.33/3.50 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[229, 228])).
% 3.33/3.50 tff(231,plain,
% 3.33/3.50 (ssList(cons(hd(V!46), nil))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[230, 195, 227])).
% 3.33/3.50 tff(232,plain,
% 3.33/3.50 ((~(~((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))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(233,plain,
% 3.33/3.50 ((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)))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(234,plain,
% 3.33/3.50 ((~(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))))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[233])).
% 3.33/3.50 tff(235,plain,
% 3.33/3.50 ((~(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))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[234, 232])).
% 3.33/3.50 tff(236,plain,
% 3.33/3.50 (~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))),
% 3.33/3.50 inference(and_elim,[status(thm)],[12])).
% 3.33/3.50 tff(237,plain,
% 3.33/3.50 ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[236, 235])).
% 3.33/3.50 tff(238,plain,
% 3.33/3.50 (U!45 = cons(hd(V!46), nil)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[237, 231, 210, 195])).
% 3.33/3.51 tff(239,plain,
% 3.33/3.51 (app(U!45, tptp_fun_V_43(V!46)) = app(cons(hd(V!46), nil), tptp_fun_V_43(V!46))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[238])).
% 3.33/3.51 tff(240,plain,
% 3.33/3.51 (app(U!45, tptp_fun_V_43(V!46)) = V!46),
% 3.33/3.51 inference(transitivity,[status(thm)],[239, 200, 160, 131])).
% 3.33/3.51 tff(241,plain,
% 3.33/3.51 (frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45) <=> frontsegP(V!46, U!45)),
% 3.33/3.51 inference(monotonicity,[status(thm)],[240])).
% 3.33/3.51 tff(242,plain,
% 3.33/3.51 (frontsegP(V!46, U!45) <=> frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)),
% 3.33/3.51 inference(symmetry,[status(thm)],[241])).
% 3.33/3.51 tff(243,plain,
% 3.33/3.51 ((~frontsegP(V!46, U!45)) <=> (~frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[242])).
% 3.33/3.51 tff(244,plain,
% 3.33/3.51 (ssList(U!45)),
% 3.33/3.51 inference(and_elim,[status(thm)],[12])).
% 3.33/3.51 tff(245,plain,
% 3.33/3.51 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(246,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[245])).
% 3.33/3.51 tff(247,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(248,plain,
% 3.33/3.51 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(249,plain,
% 3.33/3.51 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[248])).
% 3.33/3.51 tff(250,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax42')).
% 3.33/3.51 tff(251,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[250, 249])).
% 3.33/3.51 tff(252,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[251, 247])).
% 3.33/3.51 tff(253,plain,(
% 3.33/3.51 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(skolemize,[status(sab)],[252])).
% 3.33/3.51 tff(254,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[253, 246])).
% 3.33/3.51 tff(255,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(256,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(257,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[256, 255])).
% 3.33/3.51 tff(258,plain,
% 3.33/3.51 (frontsegP(U!45, U!45)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[257, 254, 244])).
% 3.33/3.51 tff(259,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(260,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(261,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[260, 259])).
% 3.33/3.51 tff(262,plain,
% 3.33/3.51 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[261, 40, 244])).
% 3.33/3.51 tff(263,plain,
% 3.33/3.51 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(264,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(265,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[264, 263])).
% 3.33/3.51 tff(266,plain,
% 3.33/3.51 (~((U!45 = nil) <=> neq(U!45, nil))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[265, 47, 262])).
% 3.33/3.51 tff(267,plain,
% 3.33/3.51 ((U!45 = nil) <=> (nil = U!45)),
% 3.33/3.51 inference(commutativity,[status(thm)],[])).
% 3.33/3.51 tff(268,plain,
% 3.33/3.51 ((nil = U!45) <=> (U!45 = nil)),
% 3.33/3.51 inference(symmetry,[status(thm)],[267])).
% 3.33/3.51 tff(269,plain,
% 3.33/3.51 (cons(hd(V!46), nil) = U!45),
% 3.33/3.51 inference(symmetry,[status(thm)],[238])).
% 3.33/3.51 tff(270,plain,
% 3.33/3.51 ((cons(hd(V!46), nil) = nil) <=> (U!45 = nil)),
% 3.33/3.51 inference(monotonicity,[status(thm)],[269])).
% 3.33/3.51 tff(271,plain,
% 3.33/3.51 ((cons(hd(V!46), nil) = nil) <=> (nil = U!45)),
% 3.33/3.51 inference(transitivity,[status(thm)],[270, 267])).
% 3.33/3.51 tff(272,plain,
% 3.33/3.51 ((cons(hd(V!46), nil) = nil) <=> (U!45 = nil)),
% 3.33/3.51 inference(transitivity,[status(thm)],[271, 268])).
% 3.33/3.51 tff(273,plain,
% 3.33/3.51 ((~(cons(hd(V!46), nil) = nil)) <=> (~(U!45 = nil))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[272])).
% 3.33/3.51 tff(274,plain,
% 3.33/3.51 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(275,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[274])).
% 3.33/3.51 tff(276,plain,
% 3.33/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(277,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[276])).
% 3.33/3.51 tff(278,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[277, 275])).
% 3.33/3.51 tff(279,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(280,plain,
% 3.33/3.51 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(281,plain,
% 3.33/3.51 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[280])).
% 3.33/3.51 tff(282,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax18')).
% 3.33/3.51 tff(283,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[282, 281])).
% 3.33/3.51 tff(284,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[283, 279])).
% 3.33/3.51 tff(285,plain,(
% 3.33/3.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(skolemize,[status(sab)],[284])).
% 3.33/3.51 tff(286,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[285, 278])).
% 3.33/3.51 tff(287,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(288,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(289,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[288, 287])).
% 3.33/3.51 tff(290,plain,
% 3.33/3.51 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[289, 47, 286])).
% 3.33/3.51 tff(291,plain,
% 3.33/3.51 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = nil)))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(292,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = nil)))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(293,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(hd(V!46))) | (~(cons(hd(V!46), nil) = nil))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 3.33/3.51 tff(294,plain,
% 3.33/3.51 (~(cons(hd(V!46), nil) = nil)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[293, 195, 290])).
% 3.33/3.51 tff(295,plain,
% 3.33/3.51 (~(U!45 = nil)),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[294, 273])).
% 3.33/3.51 tff(296,plain,
% 3.33/3.51 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 3.33/3.51 inference(tautology,[status(thm)],[])).
% 3.33/3.51 tff(297,plain,
% 3.33/3.51 (neq(U!45, nil)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[296, 295, 266])).
% 3.33/3.51 tff(298,plain,
% 3.33/3.51 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(299,plain,
% 3.33/3.51 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[298])).
% 3.33/3.51 tff(300,plain,
% 3.33/3.51 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(301,plain,
% 3.33/3.51 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[300])).
% 3.33/3.51 tff(302,plain,
% 3.33/3.51 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(V!46, Y) & frontsegP(U!45, Y)))),
% 3.33/3.51 inference(and_elim,[status(thm)],[12])).
% 3.33/3.51 tff(303,plain,
% 3.33/3.51 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[302, 301])).
% 3.33/3.51 tff(304,plain,
% 3.33/3.51 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[303, 299])).
% 3.33/3.51 tff(305,plain,
% 3.33/3.51 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(306,plain,
% 3.33/3.51 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45)))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(307,plain,
% 3.33/3.51 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(V!46, Y)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[306, 305])).
% 3.33/3.51 tff(308,plain,
% 3.33/3.51 ((~neq(U!45, nil)) | (~frontsegP(V!46, U!45)) | (~frontsegP(U!45, U!45))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[307, 244, 304])).
% 3.33/3.51 tff(309,plain,
% 3.33/3.51 (~frontsegP(V!46, U!45)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[308, 297, 258])).
% 3.33/3.51 tff(310,plain,
% 3.33/3.51 (~frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[309, 243])).
% 3.33/3.51 tff(311,plain,
% 3.33/3.51 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(312,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[311])).
% 3.33/3.51 tff(313,plain,
% 3.33/3.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(314,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[313])).
% 3.33/3.51 tff(315,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[314, 312])).
% 3.33/3.51 tff(316,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(317,plain,
% 3.33/3.51 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((frontsegP(U, V) => frontsegP(app(U, W), V)) <=> ((~frontsegP(U, V)) | frontsegP(app(U, W), V))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))))), rewrite((ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), (![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> (ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))))),
% 3.33/3.51 inference(bind,[status(th)],[])).
% 3.33/3.51 tff(318,plain,
% 3.33/3.51 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(quant_intro,[status(thm)],[317])).
% 3.33/3.51 tff(319,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax43')).
% 3.33/3.51 tff(320,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[319, 318])).
% 3.33/3.51 tff(321,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[320, 316])).
% 3.33/3.51 tff(322,plain,(
% 3.33/3.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(skolemize,[status(sab)],[321])).
% 3.33/3.51 tff(323,plain,
% 3.33/3.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[322, 315])).
% 3.33/3.51 tff(324,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(325,plain,
% 3.33/3.51 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(326,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[325])).
% 3.33/3.51 tff(327,plain,
% 3.33/3.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[326, 324])).
% 3.33/3.51 tff(328,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(329,plain,
% 3.33/3.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[328, 327])).
% 3.33/3.51 tff(330,plain,
% 3.33/3.51 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[329, 323, 244])).
% 3.33/3.51 tff(331,plain,
% 3.33/3.51 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(332,plain,
% 3.33/3.51 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45)))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(333,plain,
% 3.33/3.51 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[332])).
% 3.33/3.51 tff(334,plain,
% 3.33/3.51 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 3.33/3.51 inference(transitivity,[status(thm)],[333, 331])).
% 3.33/3.51 tff(335,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(336,plain,
% 3.33/3.51 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[335, 334])).
% 3.33/3.51 tff(337,plain,
% 3.33/3.51 (![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[336, 244, 330])).
% 3.33/3.51 tff(338,plain,
% 3.33/3.51 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(339,plain,
% 3.33/3.51 (((~ssList(tptp_fun_V_43(V!46))) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)) <=> ((~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(340,plain,
% 3.33/3.51 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(tptp_fun_V_43(V!46))) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[339])).
% 3.33/3.51 tff(341,plain,
% 3.33/3.51 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(tptp_fun_V_43(V!46))) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))),
% 3.33/3.53 inference(transitivity,[status(thm)],[340, 338])).
% 3.33/3.53 tff(342,plain,
% 3.33/3.53 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(tptp_fun_V_43(V!46))) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(343,plain,
% 3.33/3.53 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~frontsegP(U!45, U!45)) | (~ssList(tptp_fun_V_43(V!46))) | frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[342, 341])).
% 3.33/3.53 tff(344,plain,
% 3.33/3.53 (frontsegP(app(U!45, tptp_fun_V_43(V!46)), U!45)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[343, 258, 133, 337])).
% 3.33/3.53 tff(345,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[344, 310])).
% 3.33/3.53 % SZS output end Proof
% 3.33/3.53 % E exiting
%------------------------------------------------------------------------------