%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC366+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:31:01 AM UTC 2025
% Result : Theorem 99.03s 99.20s
% Output : Proof 99.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC366+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:08:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 99.03/99.20 % SZS status Theorem
% 99.03/99.20 % SZS output start Proof
% 99.03/99.20 tff(tptp_fun_V_46_type, type, (
% 99.03/99.20 tptp_fun_V_46: $i)).
% 99.03/99.20 tff(app_type, type, (
% 99.03/99.20 app: ( $i * $i ) > $i)).
% 99.03/99.20 tff(tptp_fun_W_5_type, type, (
% 99.03/99.20 tptp_fun_W_5: ( $i * $i ) > $i)).
% 99.03/99.20 tff(tptp_fun_U_45_type, type, (
% 99.03/99.20 tptp_fun_U_45: $i)).
% 99.03/99.20 tff(nil_type, type, (
% 99.03/99.20 nil: $i)).
% 99.03/99.20 tff(cons_type, type, (
% 99.03/99.20 cons: ( $i * $i ) > $i)).
% 99.03/99.20 tff(hd_type, type, (
% 99.03/99.20 hd: $i > $i)).
% 99.03/99.20 tff(neq_type, type, (
% 99.03/99.20 neq: ( $i * $i ) > $o)).
% 99.03/99.20 tff(ssList_type, type, (
% 99.03/99.20 ssList: $i > $o)).
% 99.03/99.20 tff(ssItem_type, type, (
% 99.03/99.20 ssItem: $i > $o)).
% 99.03/99.20 tff(rearsegP_type, type, (
% 99.03/99.20 rearsegP: ( $i * $i ) > $o)).
% 99.03/99.20 tff(segmentP_type, type, (
% 99.03/99.20 segmentP: ( $i * $i ) > $o)).
% 99.03/99.20 tff(frontsegP_type, type, (
% 99.03/99.20 frontsegP: ( $i * $i ) > $o)).
% 99.03/99.20 tff(tptp_fun_W_6_type, type, (
% 99.03/99.20 tptp_fun_W_6: ( $i * $i ) > $i)).
% 99.03/99.20 tff(1,plain,
% 99.03/99.20 (ssList(nil) <=> ssList(nil)),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(2,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 99.03/99.20 tff(3,plain,
% 99.03/99.20 (ssList(nil)),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[2, 1])).
% 99.03/99.20 tff(4,plain,
% 99.03/99.20 (^[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))))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(5,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[4])).
% 99.03/99.20 tff(6,plain,
% 99.03/99.20 (^[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))))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(7,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[6])).
% 99.03/99.20 tff(8,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(transitivity,[status(thm)],[7, 5])).
% 99.03/99.20 tff(9,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(10,plain,
% 99.03/99.20 (^[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)))))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(11,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[10])).
% 99.03/99.20 tff(12,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 99.03/99.20 tff(13,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[12, 11])).
% 99.03/99.20 tff(14,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[13, 9])).
% 99.03/99.20 tff(15,plain,(
% 99.03/99.20 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 99.03/99.20 inference(skolemize,[status(sab)],[14])).
% 99.03/99.20 tff(16,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[15, 8])).
% 99.03/99.20 tff(17,plain,
% 99.03/99.20 (((~![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)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(18,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(19,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[18, 17])).
% 99.03/99.20 tff(20,plain,
% 99.03/99.20 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[19, 16, 3])).
% 99.03/99.20 tff(21,plain,
% 99.03/99.20 ((ssList(U!45) & (~(rearsegP(V!46, U!45) | (~ssList(V!46)) | (~ssList(U!45)) | (ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46)) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | rearsegP(V!46, U!45) | (~ssList(V!46)) | (ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46)) | (~neq(V!46, nil)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(22,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(23,plain,
% 99.03/99.20 ((~![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) & (~(X = Y))) & ?[Z: $i] : ((ssList(Z) & (app(Z, W) = Y)) & ?[X1: $i] : (((ssItem(X1) & (cons(X1, nil) = Z)) & (hd(X) = X1)) & neq(nil, X))))) | rearsegP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(24,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) & (~(X = Y))) & ?[Z: $i] : ((ssList(Z) & (app(Z, W) = Y)) & ?[X1: $i] : (((ssItem(X1) & (cons(X1, nil) = Z)) & (hd(X) = X1)) & neq(nil, X))))) | rearsegP(V, U)) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 99.03/99.20 tff(25,plain,
% 99.03/99.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[24, 23])).
% 99.03/99.20 tff(26,plain,
% 99.03/99.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[25, 22])).
% 99.03/99.20 tff(27,plain,
% 99.03/99.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[26, 22])).
% 99.03/99.20 tff(28,plain,
% 99.03/99.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (rearsegP(V, U) | (~ssList(V)) | (~ssList(U)) | (ssItem(hd(V)) & ssList(app(cons(hd(V), nil), U)) & (~(V = app(cons(hd(V), nil), U))) & ssList(cons(hd(V), nil)) & neq(nil, V)) | (~neq(V, nil))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[27, 22])).
% 99.03/99.20 tff(29,plain,
% 99.03/99.20 (ssList(U!45) & (~((~ssList(U!45)) | rearsegP(V!46, U!45) | (~ssList(V!46)) | (ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46)) | (~neq(V!46, nil))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[28, 21])).
% 99.03/99.20 tff(30,plain,
% 99.03/99.20 (~((~ssList(U!45)) | rearsegP(V!46, U!45) | (~ssList(V!46)) | (ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46)) | (~neq(V!46, nil)))),
% 99.03/99.20 inference(and_elim,[status(thm)],[29])).
% 99.03/99.20 tff(31,plain,
% 99.03/99.20 (ssList(V!46)),
% 99.03/99.20 inference(or_elim,[status(thm)],[30])).
% 99.03/99.20 tff(32,plain,
% 99.03/99.20 (((~![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))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(33,plain,
% 99.03/99.20 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(34,plain,
% 99.03/99.20 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[33, 32])).
% 99.03/99.20 tff(35,plain,
% 99.03/99.20 (~((nil = V!46) <=> neq(nil, V!46))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[34, 31, 20])).
% 99.03/99.20 tff(36,plain,
% 99.03/99.20 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(37,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[36])).
% 99.03/99.20 tff(38,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(39,plain,
% 99.03/99.20 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(40,plain,
% 99.03/99.20 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[39])).
% 99.03/99.20 tff(41,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 99.03/99.20 tff(42,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[41, 40])).
% 99.03/99.20 tff(43,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[42, 38])).
% 99.03/99.20 tff(44,plain,(
% 99.03/99.20 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(skolemize,[status(sab)],[43])).
% 99.03/99.20 tff(45,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[44, 37])).
% 99.03/99.20 tff(46,plain,
% 99.03/99.20 (((~![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)))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(47,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(48,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[47, 46])).
% 99.03/99.20 tff(49,plain,
% 99.03/99.20 (segmentP(nil, V!46) <=> (nil = V!46)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[48, 45, 31])).
% 99.03/99.20 tff(50,plain,
% 99.03/99.20 (((~![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)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(51,plain,
% 99.03/99.20 ((~![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)))))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(52,plain,
% 99.03/99.20 ((~![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))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[51, 50])).
% 99.03/99.20 tff(53,plain,
% 99.03/99.20 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[52, 16, 31])).
% 99.03/99.20 tff(54,plain,
% 99.03/99.20 (((~![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))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(55,plain,
% 99.03/99.20 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(56,plain,
% 99.03/99.20 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[55, 54])).
% 99.03/99.20 tff(57,plain,
% 99.03/99.20 (~((V!46 = nil) <=> neq(V!46, nil))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[56, 3, 53])).
% 99.03/99.20 tff(58,plain,
% 99.03/99.20 (neq(V!46, nil)),
% 99.03/99.20 inference(or_elim,[status(thm)],[30])).
% 99.03/99.20 tff(59,plain,
% 99.03/99.20 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 99.03/99.20 inference(tautology,[status(thm)],[])).
% 99.03/99.20 tff(60,plain,
% 99.03/99.20 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[59, 58])).
% 99.03/99.20 tff(61,plain,
% 99.03/99.20 (~(V!46 = nil)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[60, 57])).
% 99.03/99.20 tff(62,plain,
% 99.03/99.20 (^[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)))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(63,plain,
% 99.03/99.20 (![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))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[62])).
% 99.03/99.20 tff(64,plain,
% 99.03/99.20 (^[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)))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(65,plain,
% 99.03/99.20 (![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))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[64])).
% 99.03/99.20 tff(66,plain,
% 99.03/99.20 (![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))))),
% 99.03/99.20 inference(transitivity,[status(thm)],[65, 63])).
% 99.03/99.20 tff(67,plain,
% 99.03/99.20 (^[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)))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(68,plain,
% 99.03/99.20 (![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))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[67])).
% 99.03/99.20 tff(69,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(70,plain,
% 99.03/99.20 (^[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)))))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(71,plain,
% 99.03/99.20 (![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)))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[70])).
% 99.03/99.20 tff(72,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 99.03/99.20 tff(73,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[72, 71])).
% 99.03/99.20 tff(74,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[73, 69])).
% 99.03/99.20 tff(75,plain,(
% 99.03/99.20 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 99.03/99.20 inference(skolemize,[status(sab)],[74])).
% 99.03/99.20 tff(76,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[75, 68])).
% 99.03/99.20 tff(77,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[76, 66])).
% 99.03/99.20 tff(78,plain,
% 99.03/99.20 (((~![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))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(79,plain,
% 99.03/99.20 (((~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))))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(80,plain,
% 99.03/99.20 (((~![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)))))),
% 99.03/99.20 inference(monotonicity,[status(thm)],[79])).
% 99.03/99.20 tff(81,plain,
% 99.03/99.20 (((~![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))))),
% 99.03/99.20 inference(transitivity,[status(thm)],[80, 78])).
% 99.03/99.20 tff(82,plain,
% 99.03/99.20 ((~![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))))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(83,plain,
% 99.03/99.20 ((~![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)))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[82, 81])).
% 99.03/99.20 tff(84,plain,
% 99.03/99.20 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[83, 77, 31])).
% 99.03/99.20 tff(85,plain,
% 99.03/99.20 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(86,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[85])).
% 99.03/99.20 tff(87,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(88,plain,
% 99.03/99.20 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(89,plain,
% 99.03/99.20 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[88])).
% 99.03/99.20 tff(90,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 99.03/99.20 tff(91,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[90, 89])).
% 99.03/99.20 tff(92,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[91, 87])).
% 99.03/99.20 tff(93,plain,(
% 99.03/99.20 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(skolemize,[status(sab)],[92])).
% 99.03/99.20 tff(94,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[93, 86])).
% 99.03/99.20 tff(95,plain,
% 99.03/99.20 (((~![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))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(96,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(97,plain,
% 99.03/99.20 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[96, 95])).
% 99.03/99.20 tff(98,plain,
% 99.03/99.20 (segmentP(V!46, nil)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[97, 94, 31])).
% 99.03/99.20 tff(99,plain,
% 99.03/99.20 (((~![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)))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(100,plain,
% 99.03/99.20 (((~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)))),
% 99.03/99.20 inference(rewrite,[status(thm)],[])).
% 99.03/99.20 tff(101,plain,
% 99.03/99.20 (((~![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))))),
% 99.03/99.20 inference(monotonicity,[status(thm)],[100])).
% 99.03/99.20 tff(102,plain,
% 99.03/99.20 (((~![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)))),
% 99.03/99.20 inference(transitivity,[status(thm)],[101, 99])).
% 99.03/99.20 tff(103,plain,
% 99.03/99.20 ((~![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)))),
% 99.03/99.20 inference(quant_inst,[status(thm)],[])).
% 99.03/99.20 tff(104,plain,
% 99.03/99.20 ((~![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))),
% 99.03/99.20 inference(modus_ponens,[status(thm)],[103, 102])).
% 99.03/99.20 tff(105,plain,
% 99.03/99.20 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[104, 3, 98, 84])).
% 99.03/99.20 tff(106,plain,
% 99.03/99.20 (~segmentP(nil, V!46)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[105, 61])).
% 99.03/99.20 tff(107,plain,
% 99.03/99.20 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 99.03/99.20 inference(tautology,[status(thm)],[])).
% 99.03/99.20 tff(108,plain,
% 99.03/99.20 (~(nil = V!46)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[107, 106, 49])).
% 99.03/99.20 tff(109,plain,
% 99.03/99.20 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 99.03/99.20 inference(tautology,[status(thm)],[])).
% 99.03/99.20 tff(110,plain,
% 99.03/99.20 (neq(nil, V!46)),
% 99.03/99.20 inference(unit_resolution,[status(thm)],[109, 108, 35])).
% 99.03/99.20 tff(111,plain,
% 99.03/99.20 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(112,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[111])).
% 99.03/99.20 tff(113,plain,
% 99.03/99.20 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 99.03/99.20 inference(bind,[status(th)],[])).
% 99.03/99.20 tff(114,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.20 inference(quant_intro,[status(thm)],[113])).
% 99.03/99.20 tff(115,plain,
% 99.03/99.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.20 inference(transitivity,[status(thm)],[114, 112])).
% 99.03/99.21 tff(116,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(117,plain,
% 99.03/99.21 (^[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))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(118,plain,
% 99.03/99.21 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[117])).
% 99.03/99.21 tff(119,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 99.03/99.21 tff(120,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[119, 118])).
% 99.03/99.21 tff(121,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[120, 116])).
% 99.03/99.21 tff(122,plain,(
% 99.03/99.21 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(skolemize,[status(sab)],[121])).
% 99.03/99.21 tff(123,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[122, 115])).
% 99.03/99.21 tff(124,plain,
% 99.03/99.21 (((~![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))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(125,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(126,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[125, 124])).
% 99.03/99.21 tff(127,plain,
% 99.03/99.21 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[126, 123, 3])).
% 99.03/99.21 tff(128,plain,
% 99.03/99.21 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(129,plain,
% 99.03/99.21 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[128])).
% 99.03/99.21 tff(130,plain,
% 99.03/99.21 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(131,plain,
% 99.03/99.21 (^[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)))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(132,plain,
% 99.03/99.21 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[131])).
% 99.03/99.21 tff(133,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax22')).
% 99.03/99.21 tff(134,plain,
% 99.03/99.21 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[133, 132])).
% 99.03/99.21 tff(135,plain,
% 99.03/99.21 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[134, 130])).
% 99.03/99.21 tff(136,plain,(
% 99.03/99.21 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(skolemize,[status(sab)],[135])).
% 99.03/99.21 tff(137,plain,
% 99.03/99.21 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[136, 129])).
% 99.03/99.21 tff(138,plain,
% 99.03/99.21 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(139,plain,
% 99.03/99.21 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(140,plain,
% 99.03/99.21 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)))),
% 99.03/99.21 inference(monotonicity,[status(thm)],[139])).
% 99.03/99.21 tff(141,plain,
% 99.03/99.21 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 99.03/99.21 inference(transitivity,[status(thm)],[140, 138])).
% 99.03/99.21 tff(142,plain,
% 99.03/99.21 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(143,plain,
% 99.03/99.21 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[142, 141])).
% 99.03/99.21 tff(144,plain,
% 99.03/99.21 (ssItem(hd(V!46)) | (nil = V!46)),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[143, 137, 31])).
% 99.03/99.21 tff(145,plain,
% 99.03/99.21 (ssItem(hd(V!46))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[144, 108])).
% 99.03/99.21 tff(146,plain,
% 99.03/99.21 (((~![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)))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(147,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(148,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[147, 146])).
% 99.03/99.21 tff(149,plain,
% 99.03/99.21 (ssList(cons(hd(V!46), nil))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[148, 145, 127])).
% 99.03/99.21 tff(150,plain,
% 99.03/99.21 (ssList(U!45)),
% 99.03/99.21 inference(and_elim,[status(thm)],[29])).
% 99.03/99.21 tff(151,plain,
% 99.03/99.21 (^[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)))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(152,plain,
% 99.03/99.21 (![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))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[151])).
% 99.03/99.21 tff(153,plain,
% 99.03/99.21 (^[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)))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(154,plain,
% 99.03/99.21 (![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))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[153])).
% 99.03/99.21 tff(155,plain,
% 99.03/99.21 (![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))))),
% 99.03/99.21 inference(transitivity,[status(thm)],[154, 152])).
% 99.03/99.21 tff(156,plain,
% 99.03/99.21 (![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))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(157,plain,
% 99.03/99.21 (^[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))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(158,plain,
% 99.03/99.21 (![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))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[157])).
% 99.03/99.21 tff(159,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 99.03/99.21 tff(160,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[159, 158])).
% 99.03/99.21 tff(161,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[160, 156])).
% 99.03/99.21 tff(162,plain,(
% 99.03/99.21 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 99.03/99.21 inference(skolemize,[status(sab)],[161])).
% 99.03/99.21 tff(163,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[162, 155])).
% 99.03/99.21 tff(164,plain,
% 99.03/99.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(165,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45))))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(166,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[165, 164])).
% 99.03/99.21 tff(167,plain,
% 99.03/99.21 (![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[166, 163, 150])).
% 99.03/99.21 tff(168,plain,
% 99.03/99.21 (((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), U!45) = app(cons(hd(V!46), nil), U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), U!45) = app(cons(hd(V!46), nil), U!45)))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(169,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), U!45) = app(cons(hd(V!46), nil), U!45)))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(170,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | (cons(V, U!45) = app(cons(V, nil), U!45)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), U!45) = app(cons(hd(V!46), nil), U!45))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[169, 168])).
% 99.03/99.21 tff(171,plain,
% 99.03/99.21 (cons(hd(V!46), U!45) = app(cons(hd(V!46), nil), U!45)),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[170, 145, 167])).
% 99.03/99.21 tff(172,plain,
% 99.03/99.21 (ssList(cons(hd(V!46), U!45)) <=> ssList(app(cons(hd(V!46), nil), U!45))),
% 99.03/99.21 inference(monotonicity,[status(thm)],[171])).
% 99.03/99.21 tff(173,plain,
% 99.03/99.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(174,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45))))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(175,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(U!45)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[174, 173])).
% 99.03/99.21 tff(176,plain,
% 99.03/99.21 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[175, 123, 150])).
% 99.03/99.21 tff(177,plain,
% 99.03/99.21 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), U!45)))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(178,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), U!45)))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(179,plain,
% 99.03/99.21 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, U!45)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), U!45))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[178, 177])).
% 99.03/99.21 tff(180,plain,
% 99.03/99.21 (ssList(cons(hd(V!46), U!45))),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[179, 145, 176])).
% 99.03/99.21 tff(181,plain,
% 99.03/99.21 (ssList(app(cons(hd(V!46), nil), U!45))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[180, 172])).
% 99.03/99.21 tff(182,plain,
% 99.03/99.21 ((~(~((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46))))) <=> ((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(183,plain,
% 99.03/99.21 ((ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46)) <=> (~((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(184,plain,
% 99.03/99.21 ((~(ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46))) <=> (~(~((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)))))),
% 99.03/99.21 inference(monotonicity,[status(thm)],[183])).
% 99.03/99.21 tff(185,plain,
% 99.03/99.21 ((~(ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46))) <=> ((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)))),
% 99.03/99.21 inference(transitivity,[status(thm)],[184, 182])).
% 99.03/99.21 tff(186,plain,
% 99.03/99.21 (~(ssItem(hd(V!46)) & ssList(app(cons(hd(V!46), nil), U!45)) & (~(V!46 = app(cons(hd(V!46), nil), U!45))) & ssList(cons(hd(V!46), nil)) & neq(nil, V!46))),
% 99.03/99.21 inference(or_elim,[status(thm)],[30])).
% 99.03/99.21 tff(187,plain,
% 99.03/99.21 ((V!46 = app(cons(hd(V!46), nil), U!45)) | (~ssItem(hd(V!46))) | (~ssList(app(cons(hd(V!46), nil), U!45))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[186, 185])).
% 99.03/99.21 tff(188,plain,
% 99.03/99.21 (V!46 = app(cons(hd(V!46), nil), U!45)),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[187, 181, 145, 149, 110])).
% 99.03/99.21 tff(189,plain,
% 99.03/99.21 (app(cons(hd(V!46), nil), U!45) = V!46),
% 99.03/99.21 inference(symmetry,[status(thm)],[188])).
% 99.03/99.21 tff(190,plain,
% 99.03/99.21 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(191,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[190])).
% 99.03/99.21 tff(192,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(193,plain,
% 99.03/99.21 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(194,plain,
% 99.03/99.21 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[193])).
% 99.03/99.21 tff(195,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 99.03/99.21 tff(196,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[195, 194])).
% 99.03/99.21 tff(197,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[196, 192])).
% 99.03/99.21 tff(198,plain,(
% 99.03/99.21 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(skolemize,[status(sab)],[197])).
% 99.03/99.21 tff(199,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[198, 191])).
% 99.03/99.21 tff(200,plain,
% 99.03/99.21 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(201,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 99.03/99.21 inference(quant_inst,[status(thm)],[])).
% 99.03/99.21 tff(202,plain,
% 99.03/99.21 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[201, 200])).
% 99.03/99.21 tff(203,plain,
% 99.03/99.21 (app(nil, U!45) = U!45),
% 99.03/99.21 inference(unit_resolution,[status(thm)],[202, 199, 150])).
% 99.03/99.21 tff(204,plain,
% 99.03/99.21 (U!45 = app(nil, U!45)),
% 99.03/99.21 inference(symmetry,[status(thm)],[203])).
% 99.03/99.21 tff(205,plain,
% 99.03/99.21 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(206,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[205])).
% 99.03/99.21 tff(207,plain,
% 99.03/99.21 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(208,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[207])).
% 99.03/99.21 tff(209,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(transitivity,[status(thm)],[208, 206])).
% 99.03/99.21 tff(210,plain,
% 99.03/99.21 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(211,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[210])).
% 99.03/99.21 tff(212,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(213,plain,
% 99.03/99.21 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))) <=> (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), rewrite((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), (![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))))),
% 99.03/99.21 inference(bind,[status(th)],[])).
% 99.03/99.21 tff(214,plain,
% 99.03/99.21 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 99.03/99.21 inference(quant_intro,[status(thm)],[213])).
% 99.03/99.21 tff(215,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax5')).
% 99.03/99.21 tff(216,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[215, 214])).
% 99.03/99.21 tff(217,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[216, 212])).
% 99.03/99.21 tff(218,plain,(
% 99.03/99.21 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U)))))))),
% 99.03/99.21 inference(skolemize,[status(sab)],[217])).
% 99.03/99.21 tff(219,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[218, 211])).
% 99.03/99.21 tff(220,plain,
% 99.03/99.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 99.03/99.21 inference(modus_ponens,[status(thm)],[219, 209])).
% 99.03/99.21 tff(221,plain,
% 99.03/99.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(222,plain,
% 99.03/99.21 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 99.03/99.21 inference(rewrite,[status(thm)],[])).
% 99.03/99.21 tff(223,plain,
% 99.03/99.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))))),
% 99.03/99.22 inference(monotonicity,[status(thm)],[222])).
% 99.03/99.22 tff(224,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 99.03/99.22 inference(transitivity,[status(thm)],[223, 221])).
% 99.03/99.22 tff(225,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(226,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[225, 224])).
% 99.03/99.22 tff(227,plain,
% 99.03/99.22 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[226, 220, 150])).
% 99.03/99.22 tff(228,plain,
% 99.03/99.22 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(229,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(230,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(nil)) | (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[229, 228])).
% 99.03/99.22 tff(231,plain,
% 99.03/99.22 (~((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[230, 3, 227])).
% 99.03/99.22 tff(232,plain,
% 99.03/99.22 (((~(frontsegP(U!45, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = U!45))))) | (~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))))) | ((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))),
% 99.03/99.22 inference(tautology,[status(thm)],[])).
% 99.03/99.22 tff(233,plain,
% 99.03/99.22 ((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[232, 231])).
% 99.03/99.22 tff(234,plain,
% 99.03/99.22 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(235,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[234])).
% 99.03/99.22 tff(236,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(237,plain,
% 99.03/99.22 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(238,plain,
% 99.03/99.22 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[237])).
% 99.03/99.22 tff(239,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax45')).
% 99.03/99.22 tff(240,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[239, 238])).
% 99.03/99.22 tff(241,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[240, 236])).
% 99.03/99.22 tff(242,plain,(
% 99.03/99.22 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(skolemize,[status(sab)],[241])).
% 99.03/99.22 tff(243,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[242, 235])).
% 99.03/99.22 tff(244,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(U!45)) | frontsegP(U!45, nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(U!45)) | frontsegP(U!45, nil))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(245,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(U!45)) | frontsegP(U!45, nil))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(246,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(U!45)) | frontsegP(U!45, nil)),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[245, 244])).
% 99.03/99.22 tff(247,plain,
% 99.03/99.22 (frontsegP(U!45, nil)),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[246, 243, 150])).
% 99.03/99.22 tff(248,plain,
% 99.03/99.22 ((~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))) | (~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 99.03/99.22 inference(tautology,[status(thm)],[])).
% 99.03/99.22 tff(249,plain,
% 99.03/99.22 ((~((~frontsegP(U!45, nil)) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))))) | (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[248, 247])).
% 99.03/99.22 tff(250,plain,
% 99.03/99.22 (~((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45)))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[249, 233])).
% 99.03/99.22 tff(251,plain,
% 99.03/99.22 (((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))) | (app(nil, tptp_fun_W_5(nil, U!45)) = U!45)),
% 99.03/99.22 inference(tautology,[status(thm)],[])).
% 99.03/99.22 tff(252,plain,
% 99.03/99.22 (app(nil, tptp_fun_W_5(nil, U!45)) = U!45),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[251, 250])).
% 99.03/99.22 tff(253,plain,
% 99.03/99.22 (app(nil, tptp_fun_W_5(nil, U!45)) = app(nil, U!45)),
% 99.03/99.22 inference(transitivity,[status(thm)],[252, 204])).
% 99.03/99.22 tff(254,plain,
% 99.03/99.22 (((~ssList(tptp_fun_W_5(nil, U!45))) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = U!45))) | ssList(tptp_fun_W_5(nil, U!45))),
% 99.03/99.22 inference(tautology,[status(thm)],[])).
% 99.03/99.22 tff(255,plain,
% 99.03/99.22 (ssList(tptp_fun_W_5(nil, U!45))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[254, 250])).
% 99.03/99.22 tff(256,plain,
% 99.03/99.22 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(257,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[256])).
% 99.03/99.22 tff(258,plain,
% 99.03/99.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(259,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[258])).
% 99.03/99.22 tff(260,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(transitivity,[status(thm)],[259, 257])).
% 99.03/99.22 tff(261,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(262,plain,
% 99.03/99.22 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(V, W) = app(V, U)) => (W = U)) <=> ((~(app(V, W) = app(V, U))) | (W = U))), ((ssList(W) => ((app(V, W) = app(V, U)) => (W = U))) <=> (ssList(W) => ((~(app(V, W) = app(V, U))) | (W = U))))), rewrite((ssList(W) => ((~(app(V, W) = app(V, U))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))), ((ssList(W) => ((app(V, W) = app(V, U)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))), (![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(263,plain,
% 99.03/99.22 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[262])).
% 99.03/99.22 tff(264,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(V, W) = app(V, U)) => (W = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax80')).
% 99.03/99.22 tff(265,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[264, 263])).
% 99.03/99.22 tff(266,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[265, 261])).
% 99.03/99.22 tff(267,plain,(
% 99.03/99.22 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(skolemize,[status(sab)],[266])).
% 99.03/99.22 tff(268,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[267, 260])).
% 99.03/99.22 tff(269,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45))))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(270,plain,
% 99.03/99.22 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(V, W) = app(V, U!45)))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45))))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(271,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(V, W) = app(V, U!45))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))))),
% 99.03/99.22 inference(monotonicity,[status(thm)],[270])).
% 99.03/99.22 tff(272,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(V, W) = app(V, U!45))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45))))))),
% 99.03/99.22 inference(transitivity,[status(thm)],[271, 269])).
% 99.03/99.22 tff(273,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U!45) | (~ssList(W)) | (~(app(V, W) = app(V, U!45))))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(274,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(V, W) = app(V, U))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[273, 272])).
% 99.03/99.22 tff(275,plain,
% 99.03/99.22 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[274, 268, 150])).
% 99.03/99.22 tff(276,plain,
% 99.03/99.22 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45)))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(277,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45)))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(278,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(V, W) = app(V, U!45)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[277, 276])).
% 99.03/99.22 tff(279,plain,
% 99.03/99.22 (![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[278, 3, 275])).
% 99.03/99.22 tff(280,plain,
% 99.03/99.22 (((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (tptp_fun_W_5(nil, U!45) = U!45) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = app(nil, U!45))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (tptp_fun_W_5(nil, U!45) = U!45) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = app(nil, U!45))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(281,plain,
% 99.03/99.22 ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (tptp_fun_W_5(nil, U!45) = U!45) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = app(nil, U!45))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(282,plain,
% 99.03/99.22 ((~![W: $i] : ((~ssList(W)) | (W = U!45) | (~(app(nil, W) = app(nil, U!45))))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (tptp_fun_W_5(nil, U!45) = U!45) | (~(app(nil, tptp_fun_W_5(nil, U!45)) = app(nil, U!45)))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[281, 280])).
% 99.03/99.22 tff(283,plain,
% 99.03/99.22 (tptp_fun_W_5(nil, U!45) = U!45),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[282, 279, 255, 253])).
% 99.03/99.22 tff(284,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(285,plain,
% 99.03/99.22 (((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(286,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))))),
% 99.03/99.22 inference(monotonicity,[status(thm)],[285])).
% 99.03/99.22 tff(287,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 99.03/99.22 inference(transitivity,[status(thm)],[286, 284])).
% 99.03/99.22 tff(288,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(289,plain,
% 99.03/99.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[288, 287])).
% 99.03/99.22 tff(290,plain,
% 99.03/99.22 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[289, 3, 163])).
% 99.03/99.22 tff(291,plain,
% 99.03/99.22 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(292,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)))),
% 99.03/99.22 inference(quant_inst,[status(thm)],[])).
% 99.03/99.22 tff(293,plain,
% 99.03/99.22 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(hd(V!46))) | (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[292, 291])).
% 99.03/99.22 tff(294,plain,
% 99.03/99.22 (cons(hd(V!46), nil) = app(cons(hd(V!46), nil), nil)),
% 99.03/99.22 inference(unit_resolution,[status(thm)],[293, 145, 290])).
% 99.03/99.22 tff(295,plain,
% 99.03/99.22 (app(cons(hd(V!46), nil), nil) = cons(hd(V!46), nil)),
% 99.03/99.22 inference(symmetry,[status(thm)],[294])).
% 99.03/99.22 tff(296,plain,
% 99.03/99.22 (app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = app(cons(hd(V!46), nil), U!45)),
% 99.03/99.22 inference(monotonicity,[status(thm)],[295, 283])).
% 99.03/99.22 tff(297,plain,
% 99.03/99.22 (app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = V!46),
% 99.03/99.22 inference(transitivity,[status(thm)],[296, 189])).
% 99.03/99.22 tff(298,plain,
% 99.03/99.22 (ssList(app(cons(hd(V!46), nil), nil)) <=> ssList(cons(hd(V!46), nil))),
% 99.03/99.22 inference(monotonicity,[status(thm)],[295])).
% 99.03/99.22 tff(299,plain,
% 99.03/99.22 (ssList(cons(hd(V!46), nil)) <=> ssList(app(cons(hd(V!46), nil), nil))),
% 99.03/99.22 inference(symmetry,[status(thm)],[298])).
% 99.03/99.22 tff(300,plain,
% 99.03/99.22 (ssList(app(cons(hd(V!46), nil), nil))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[149, 299])).
% 99.03/99.22 tff(301,plain,
% 99.03/99.22 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(302,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[301])).
% 99.03/99.22 tff(303,plain,
% 99.03/99.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(304,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[303])).
% 99.03/99.22 tff(305,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(transitivity,[status(thm)],[304, 302])).
% 99.03/99.22 tff(306,plain,
% 99.03/99.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(307,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[306])).
% 99.03/99.22 tff(308,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(309,plain,
% 99.03/99.22 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 99.03/99.22 inference(bind,[status(th)],[])).
% 99.03/99.22 tff(310,plain,
% 99.03/99.22 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 99.03/99.22 inference(quant_intro,[status(thm)],[309])).
% 99.03/99.22 tff(311,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax6')).
% 99.03/99.22 tff(312,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[311, 310])).
% 99.03/99.22 tff(313,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[312, 308])).
% 99.03/99.22 tff(314,plain,(
% 99.03/99.22 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 99.03/99.22 inference(skolemize,[status(sab)],[313])).
% 99.03/99.22 tff(315,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[314, 307])).
% 99.03/99.22 tff(316,plain,
% 99.03/99.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 99.03/99.22 inference(modus_ponens,[status(thm)],[315, 305])).
% 99.03/99.22 tff(317,plain,
% 99.03/99.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 99.03/99.22 inference(rewrite,[status(thm)],[])).
% 99.03/99.22 tff(318,plain,
% 99.03/99.22 (((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))))))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 99.03/99.23 inference(rewrite,[status(thm)],[])).
% 99.03/99.23 tff(319,plain,
% 99.03/99.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))))),
% 99.03/99.23 inference(monotonicity,[status(thm)],[318])).
% 99.03/99.23 tff(320,plain,
% 99.03/99.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46))))))))))),
% 99.03/99.23 inference(transitivity,[status(thm)],[319, 317])).
% 99.03/99.23 tff(321,plain,
% 99.03/99.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))) | (~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46)))))))))),
% 99.03/99.23 inference(quant_inst,[status(thm)],[])).
% 99.03/99.23 tff(322,plain,
% 99.03/99.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))),
% 99.03/99.23 inference(modus_ponens,[status(thm)],[321, 320])).
% 99.03/99.23 tff(323,plain,
% 99.03/99.23 (![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))),
% 99.03/99.23 inference(unit_resolution,[status(thm)],[322, 316, 31])).
% 99.03/99.23 tff(324,plain,
% 99.03/99.23 (((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (~((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (~((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46)))))))))),
% 99.03/99.23 inference(rewrite,[status(thm)],[])).
% 99.03/99.23 tff(325,plain,
% 99.03/99.23 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | ((~ssList(tptp_fun_W_5(nil, U!45))) | (~((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46)))))))))),
% 99.03/99.23 inference(quant_inst,[status(thm)],[])).
% 99.03/99.23 tff(326,plain,
% 99.03/99.23 ((~![V: $i] : ((~ssList(V)) | (~((~(rearsegP(V!46, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = V!46))))) | (~((~rearsegP(V!46, V)) | (~((~ssList(tptp_fun_W_6(V, V!46))) | (~(app(tptp_fun_W_6(V, V!46), V) = V!46)))))))))) | (~ssList(tptp_fun_W_5(nil, U!45))) | (~((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46))))))))),
% 99.03/99.23 inference(modus_ponens,[status(thm)],[325, 324])).
% 99.03/99.23 tff(327,plain,
% 99.03/99.23 (~((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46)))))))),
% 99.03/99.23 inference(unit_resolution,[status(thm)],[326, 323, 255])).
% 99.03/99.23 tff(328,plain,
% 99.03/99.23 (((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | (~((~rearsegP(V!46, tptp_fun_W_5(nil, U!45))) | (~((~ssList(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46))) | (~(app(tptp_fun_W_6(tptp_fun_W_5(nil, U!45), V!46), tptp_fun_W_5(nil, U!45)) = V!46))))))) | (rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))),
% 99.03/99.23 inference(tautology,[status(thm)],[])).
% 99.03/99.23 tff(329,plain,
% 99.03/99.23 (rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))),
% 99.03/99.23 inference(unit_resolution,[status(thm)],[328, 327])).
% 99.03/99.23 tff(330,plain,
% 99.03/99.23 (rearsegP(V!46, tptp_fun_W_5(nil, U!45)) <=> rearsegP(V!46, U!45)),
% 99.03/99.23 inference(monotonicity,[status(thm)],[283])).
% 99.03/99.23 tff(331,plain,
% 99.03/99.23 (rearsegP(V!46, U!45) <=> rearsegP(V!46, tptp_fun_W_5(nil, U!45))),
% 99.03/99.23 inference(symmetry,[status(thm)],[330])).
% 99.03/99.23 tff(332,plain,
% 99.03/99.23 ((~rearsegP(V!46, U!45)) <=> (~rearsegP(V!46, tptp_fun_W_5(nil, U!45)))),
% 99.03/99.23 inference(monotonicity,[status(thm)],[331])).
% 99.03/99.23 tff(333,plain,
% 99.03/99.23 (~rearsegP(V!46, U!45)),
% 99.03/99.23 inference(or_elim,[status(thm)],[30])).
% 99.03/99.23 tff(334,plain,
% 99.03/99.23 (~rearsegP(V!46, tptp_fun_W_5(nil, U!45))),
% 99.03/99.23 inference(modus_ponens,[status(thm)],[333, 332])).
% 99.03/99.23 tff(335,plain,
% 99.03/99.23 ((~(rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46))))) | rearsegP(V!46, tptp_fun_W_5(nil, U!45)) | ![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))),
% 99.03/99.23 inference(tautology,[status(thm)],[])).
% 99.34/99.49 tff(336,plain,
% 99.34/99.49 (![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))),
% 99.34/99.49 inference(unit_resolution,[status(thm)],[335, 334, 329])).
% 99.34/99.49 tff(337,plain,
% 99.34/99.49 (((~![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))) | ((~ssList(app(cons(hd(V!46), nil), nil))) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = V!46)))) <=> ((~![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))) | (~ssList(app(cons(hd(V!46), nil), nil))) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = V!46)))),
% 99.34/99.49 inference(rewrite,[status(thm)],[])).
% 99.34/99.49 tff(338,plain,
% 99.34/99.49 ((~![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))) | ((~ssList(app(cons(hd(V!46), nil), nil))) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = V!46)))),
% 99.34/99.49 inference(quant_inst,[status(thm)],[])).
% 99.34/99.49 tff(339,plain,
% 99.34/99.49 ((~![W: $i] : ((~ssList(W)) | (~(app(W, tptp_fun_W_5(nil, U!45)) = V!46)))) | (~ssList(app(cons(hd(V!46), nil), nil))) | (~(app(app(cons(hd(V!46), nil), nil), tptp_fun_W_5(nil, U!45)) = V!46))),
% 99.34/99.49 inference(modus_ponens,[status(thm)],[338, 337])).
% 99.34/99.49 tff(340,plain,
% 99.34/99.49 ($false),
% 99.34/99.49 inference(unit_resolution,[status(thm)],[339, 336, 300, 297])).
% 99.34/99.49 % SZS output end Proof
% 99.34/99.49 % E exiting
%------------------------------------------------------------------------------