%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC126+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:14 AM UTC 2025
% Result : Theorem 194.74s 195.02s
% Output : Proof 195.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWC126+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 08:24:56 EDT 2025
% 0.14/0.35 % CPUTime :
% 194.74/195.02 % SZS status Theorem
% 194.74/195.02 % SZS output start Proof
% 194.74/195.02 tff(tptp_fun_V_46_type, type, (
% 194.74/195.02 tptp_fun_V_46: $i)).
% 194.74/195.02 tff(app_type, type, (
% 194.74/195.02 app: ( $i * $i ) > $i)).
% 194.74/195.02 tff(tptp_fun_X_3_type, type, (
% 194.74/195.02 tptp_fun_X_3: ( $i * $i ) > $i)).
% 194.74/195.02 tff(tptp_fun_Y_47_type, type, (
% 194.74/195.02 tptp_fun_Y_47: $i)).
% 194.74/195.02 tff(tptp_fun_U_45_type, type, (
% 194.74/195.02 tptp_fun_U_45: $i)).
% 194.74/195.02 tff(tptp_fun_W_2_type, type, (
% 194.74/195.02 tptp_fun_W_2: ( $i * $i ) > $i)).
% 194.74/195.02 tff(cons_type, type, (
% 194.74/195.02 cons: ( $i * $i ) > $i)).
% 194.74/195.02 tff(ssList_type, type, (
% 194.74/195.02 ssList: $i > $o)).
% 194.74/195.02 tff(memberP_type, type, (
% 194.74/195.02 memberP: ( $i * $i ) > $o)).
% 194.74/195.02 tff(ssItem_type, type, (
% 194.74/195.02 ssItem: $i > $o)).
% 194.74/195.02 tff(neq_type, type, (
% 194.74/195.02 neq: ( $i * $i ) > $o)).
% 194.74/195.02 tff(nil_type, type, (
% 194.74/195.02 nil: $i)).
% 194.74/195.02 tff(segmentP_type, type, (
% 194.74/195.02 segmentP: ( $i * $i ) > $o)).
% 194.74/195.02 tff(tptp_fun_X_8_type, type, (
% 194.74/195.02 tptp_fun_X_8: ( $i * $i ) > $i)).
% 194.74/195.02 tff(tptp_fun_W_7_type, type, (
% 194.74/195.02 tptp_fun_W_7: ( $i * $i ) > $i)).
% 194.74/195.02 tff(1,plain,
% 194.74/195.02 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(2,plain,
% 194.74/195.02 ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) <=> (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(3,plain,
% 194.74/195.02 ((ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)) <=> (ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 194.74/195.02 inference(monotonicity,[status(thm)],[2])).
% 194.74/195.02 tff(4,plain,
% 194.74/195.02 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)))),
% 194.74/195.02 inference(monotonicity,[status(thm)],[3])).
% 194.74/195.02 tff(5,plain,
% 194.74/195.02 ((ssList(U!45) & (ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 194.74/195.02 inference(transitivity,[status(thm)],[4, 1])).
% 194.74/195.02 tff(6,plain,
% 194.74/195.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)))))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(7,plain,
% 194.74/195.02 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y))))) | (neq(U, nil) & segmentP(V, U))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)))))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(8,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y))))) | (neq(U, nil) & segmentP(V, U))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 194.74/195.02 tff(9,plain,
% 194.74/195.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[8, 7])).
% 194.74/195.02 tff(10,plain,
% 194.74/195.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[9, 6])).
% 194.74/195.02 tff(11,plain,
% 194.74/195.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[10, 6])).
% 194.74/195.02 tff(12,plain,
% 194.74/195.02 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[11, 6])).
% 194.74/195.02 tff(13,plain,
% 194.74/195.02 (ssList(U!45) & ssList(V!46) & (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[12, 5])).
% 194.74/195.02 tff(14,plain,
% 194.74/195.02 (ssList(V!46)),
% 194.74/195.02 inference(and_elim,[status(thm)],[13])).
% 194.74/195.02 tff(15,plain,
% 194.74/195.02 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 194.74/195.02 inference(bind,[status(th)],[])).
% 194.74/195.02 tff(16,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(quant_intro,[status(thm)],[15])).
% 194.74/195.02 tff(17,plain,
% 194.74/195.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 194.74/195.02 inference(bind,[status(th)],[])).
% 194.74/195.02 tff(18,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(quant_intro,[status(thm)],[17])).
% 194.74/195.02 tff(19,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(transitivity,[status(thm)],[18, 16])).
% 194.74/195.02 tff(20,plain,
% 194.74/195.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 194.74/195.02 inference(bind,[status(th)],[])).
% 194.74/195.02 tff(21,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(quant_intro,[status(thm)],[20])).
% 194.74/195.02 tff(22,plain,
% 194.74/195.02 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))))),
% 194.74/195.02 inference(bind,[status(th)],[])).
% 194.74/195.02 tff(23,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 194.74/195.02 inference(quant_intro,[status(thm)],[22])).
% 194.74/195.02 tff(24,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(25,plain,
% 194.74/195.02 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))) <=> (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))), ((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), rewrite((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))), ((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))))), (![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 194.74/195.02 inference(bind,[status(th)],[])).
% 194.74/195.02 tff(26,plain,
% 194.74/195.02 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 194.74/195.02 inference(quant_intro,[status(thm)],[25])).
% 194.74/195.02 tff(27,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax3')).
% 194.74/195.02 tff(28,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[27, 26])).
% 194.74/195.02 tff(29,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[28, 24])).
% 194.74/195.02 tff(30,plain,(
% 194.74/195.02 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 194.74/195.02 inference(skolemize,[status(sab)],[29])).
% 194.74/195.02 tff(31,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[30, 23])).
% 194.74/195.02 tff(32,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[31, 21])).
% 194.74/195.02 tff(33,plain,
% 194.74/195.02 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[32, 19])).
% 194.74/195.02 tff(34,plain,
% 194.74/195.02 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46))))))))))),
% 194.74/195.02 inference(rewrite,[status(thm)],[])).
% 194.74/195.02 tff(35,plain,
% 194.74/195.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46))))))))))),
% 194.74/195.02 inference(quant_inst,[status(thm)],[])).
% 194.74/195.02 tff(36,plain,
% 194.74/195.02 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))),
% 194.74/195.02 inference(modus_ponens,[status(thm)],[35, 34])).
% 194.74/195.02 tff(37,plain,
% 194.74/195.02 (![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))),
% 194.74/195.02 inference(unit_resolution,[status(thm)],[36, 33, 14])).
% 194.74/195.02 tff(38,plain,
% 194.74/195.02 (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))),
% 194.74/195.02 inference(and_elim,[status(thm)],[13])).
% 194.74/195.02 tff(39,plain,
% 194.74/195.02 (ssItem(Y!47)),
% 194.74/195.02 inference(or_elim,[status(thm)],[38])).
% 194.74/195.02 tff(40,plain,
% 194.74/195.02 (((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))) | ((~ssItem(Y!47)) | (~((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46)))))))))) <=> ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))) | (~ssItem(Y!47)) | (~((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46)))))))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(41,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))) | ((~ssItem(Y!47)) | (~((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46)))))))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(42,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(V!46, V)) | (~((~ssList(tptp_fun_W_2(V, V!46))) | (~ssList(tptp_fun_X_3(V, V!46))) | (~(app(tptp_fun_W_2(V, V!46), cons(V, tptp_fun_X_3(V, V!46))) = V!46)))))) | (~(memberP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = V!46)))))))))) | (~ssItem(Y!47)) | (~((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46))))))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[41, 40])).
% 194.74/195.03 tff(43,plain,
% 194.74/195.03 (~((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46)))))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[42, 39, 37])).
% 194.74/195.03 tff(44,plain,
% 194.74/195.03 (((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~(memberP(V!46, Y!47) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!47, X)) = V!46))))))) | ((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))),
% 194.74/195.03 inference(tautology,[status(thm)],[])).
% 194.74/195.03 tff(45,plain,
% 194.74/195.03 ((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[44, 43])).
% 194.74/195.03 tff(46,plain,
% 194.74/195.03 (memberP(V!46, Y!47)),
% 194.74/195.03 inference(or_elim,[status(thm)],[38])).
% 194.74/195.03 tff(47,plain,
% 194.74/195.03 ((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))))),
% 194.74/195.03 inference(tautology,[status(thm)],[])).
% 194.74/195.03 tff(48,plain,
% 194.74/195.03 ((~((~memberP(V!46, Y!47)) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))))) | (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[47, 46])).
% 194.74/195.03 tff(49,plain,
% 194.74/195.03 (~((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[48, 45])).
% 194.74/195.03 tff(50,plain,
% 194.74/195.03 (((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))) | (app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46)),
% 194.74/195.03 inference(tautology,[status(thm)],[])).
% 194.74/195.03 tff(51,plain,
% 194.74/195.03 (app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[50, 49])).
% 194.74/195.03 tff(52,plain,
% 194.74/195.03 (((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))) | ssList(tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(tautology,[status(thm)],[])).
% 194.74/195.03 tff(53,plain,
% 194.74/195.03 (ssList(tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[52, 49])).
% 194.74/195.03 tff(54,plain,
% 194.74/195.03 (^[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)))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(55,plain,
% 194.74/195.03 (![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))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[54])).
% 194.74/195.03 tff(56,plain,
% 194.74/195.03 (^[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)))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(57,plain,
% 194.74/195.03 (![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))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[56])).
% 194.74/195.03 tff(58,plain,
% 194.74/195.03 (![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))))),
% 194.74/195.03 inference(transitivity,[status(thm)],[57, 55])).
% 194.74/195.03 tff(59,plain,
% 194.74/195.03 (![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))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(60,plain,
% 194.74/195.03 (^[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))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(61,plain,
% 194.74/195.03 (![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))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[60])).
% 194.74/195.03 tff(62,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')).
% 194.74/195.03 tff(63,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[62, 61])).
% 194.74/195.03 tff(64,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[63, 59])).
% 194.74/195.03 tff(65,plain,(
% 194.74/195.03 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 194.74/195.03 inference(skolemize,[status(sab)],[64])).
% 194.74/195.03 tff(66,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[65, 58])).
% 194.74/195.03 tff(67,plain,
% 194.74/195.03 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46)))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(68,plain,
% 194.74/195.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46)))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(69,plain,
% 194.74/195.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[68, 67])).
% 194.74/195.03 tff(70,plain,
% 194.74/195.03 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[69, 66, 53])).
% 194.74/195.03 tff(71,plain,
% 194.74/195.03 (((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))) | ((~ssItem(Y!47)) | (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))) | (~ssItem(Y!47)) | (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(72,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))) | ((~ssItem(Y!47)) | (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(73,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!47, V!46)) = app(cons(V, nil), tptp_fun_X_3(Y!47, V!46))))) | (~ssItem(Y!47)) | (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46)))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[72, 71])).
% 194.74/195.03 tff(74,plain,
% 194.74/195.03 (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[73, 39, 70])).
% 194.74/195.03 tff(75,plain,
% 194.74/195.03 (app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46)) = cons(Y!47, tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(symmetry,[status(thm)],[74])).
% 194.74/195.03 tff(76,plain,
% 194.74/195.03 (cons(Y!47, nil) = U!45),
% 194.74/195.03 inference(or_elim,[status(thm)],[38])).
% 194.74/195.03 tff(77,plain,
% 194.74/195.03 (app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46)) = app(U!45, tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(monotonicity,[status(thm)],[76])).
% 194.74/195.03 tff(78,plain,
% 194.74/195.03 (app(U!45, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(symmetry,[status(thm)],[77])).
% 194.74/195.03 tff(79,plain,
% 194.74/195.03 (app(U!45, tptp_fun_X_3(Y!47, V!46)) = cons(Y!47, tptp_fun_X_3(Y!47, V!46))),
% 194.74/195.03 inference(transitivity,[status(thm)],[78, 75])).
% 194.74/195.03 tff(80,plain,
% 194.74/195.03 (app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46))) = app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46)))),
% 194.74/195.03 inference(monotonicity,[status(thm)],[79])).
% 194.74/195.03 tff(81,plain,
% 194.74/195.03 (((~ssList(tptp_fun_W_2(Y!47, V!46))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46))) | ssList(tptp_fun_W_2(Y!47, V!46))),
% 194.74/195.03 inference(tautology,[status(thm)],[])).
% 194.74/195.03 tff(82,plain,
% 194.74/195.03 (ssList(tptp_fun_W_2(Y!47, V!46))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[81, 49])).
% 194.74/195.03 tff(83,plain,
% 194.74/195.03 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(84,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[83])).
% 194.74/195.03 tff(85,plain,
% 194.74/195.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(86,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[85])).
% 194.74/195.03 tff(87,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(transitivity,[status(thm)],[86, 84])).
% 194.74/195.03 tff(88,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(89,plain,
% 194.74/195.03 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(90,plain,
% 194.74/195.03 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[89])).
% 194.74/195.03 tff(91,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax82')).
% 194.74/195.03 tff(92,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[91, 90])).
% 194.74/195.03 tff(93,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[92, 88])).
% 194.74/195.03 tff(94,plain,(
% 194.74/195.03 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(skolemize,[status(sab)],[93])).
% 194.74/195.03 tff(95,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[94, 87])).
% 194.74/195.03 tff(96,plain,
% 194.74/195.03 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(tptp_fun_W_2(Y!47, V!46))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(tptp_fun_W_2(Y!47, V!46))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W))))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(97,plain,
% 194.74/195.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(tptp_fun_W_2(Y!47, V!46))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W))))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(98,plain,
% 194.74/195.03 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(tptp_fun_W_2(Y!47, V!46))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[97, 96])).
% 194.74/195.03 tff(99,plain,
% 194.74/195.03 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[98, 95, 82])).
% 194.74/195.03 tff(100,plain,
% 194.74/195.03 (ssList(U!45)),
% 194.74/195.03 inference(and_elim,[status(thm)],[13])).
% 194.74/195.03 tff(101,plain,
% 194.74/195.03 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W)))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(102,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W)))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(103,plain,
% 194.74/195.03 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), V), W) = app(tptp_fun_W_2(Y!47, V!46), app(V, W)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[102, 101])).
% 194.74/195.03 tff(104,plain,
% 194.74/195.03 (![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[103, 100, 99])).
% 194.74/195.03 tff(105,plain,
% 194.74/195.03 (((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46)))))),
% 194.74/195.03 inference(rewrite,[status(thm)],[])).
% 194.74/195.03 tff(106,plain,
% 194.74/195.03 ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46)))))),
% 194.74/195.03 inference(quant_inst,[status(thm)],[])).
% 194.74/195.03 tff(107,plain,
% 194.74/195.03 ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), W) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, W))))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46))))),
% 194.74/195.03 inference(modus_ponens,[status(thm)],[106, 105])).
% 194.74/195.03 tff(108,plain,
% 194.74/195.03 (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = app(tptp_fun_W_2(Y!47, V!46), app(U!45, tptp_fun_X_3(Y!47, V!46)))),
% 194.74/195.03 inference(unit_resolution,[status(thm)],[107, 53, 104])).
% 194.74/195.03 tff(109,plain,
% 194.74/195.03 (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46),
% 194.74/195.03 inference(transitivity,[status(thm)],[108, 80, 51])).
% 194.74/195.03 tff(110,plain,
% 194.74/195.03 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(111,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[110])).
% 194.74/195.03 tff(112,plain,
% 194.74/195.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(113,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[112])).
% 194.74/195.03 tff(114,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.03 inference(transitivity,[status(thm)],[113, 111])).
% 194.74/195.03 tff(115,plain,
% 194.74/195.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 194.74/195.03 inference(bind,[status(th)],[])).
% 194.74/195.03 tff(116,plain,
% 194.74/195.03 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.03 inference(quant_intro,[status(thm)],[115])).
% 194.74/195.03 tff(117,plain,
% 194.74/195.03 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(118,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[117])).
% 194.74/195.04 tff(119,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(120,plain,
% 194.74/195.04 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(121,plain,
% 194.74/195.04 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[120])).
% 194.74/195.04 tff(122,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 194.74/195.04 tff(123,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[122, 121])).
% 194.74/195.04 tff(124,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[123, 119])).
% 194.74/195.04 tff(125,plain,(
% 194.74/195.04 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 194.74/195.04 inference(skolemize,[status(sab)],[124])).
% 194.74/195.04 tff(126,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[125, 118])).
% 194.74/195.04 tff(127,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[126, 116])).
% 194.74/195.04 tff(128,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[127, 114])).
% 194.74/195.04 tff(129,plain,
% 194.74/195.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(130,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(131,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[130, 129])).
% 194.74/195.04 tff(132,plain,
% 194.74/195.04 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[131, 128, 14])).
% 194.74/195.04 tff(133,plain,
% 194.74/195.04 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(134,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(135,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[134, 133])).
% 194.74/195.04 tff(136,plain,
% 194.74/195.04 (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[135, 100, 132])).
% 194.74/195.04 tff(137,plain,
% 194.74/195.04 (((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))) | (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))),
% 194.74/195.04 inference(tautology,[status(thm)],[])).
% 194.74/195.04 tff(138,plain,
% 194.74/195.04 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[137, 136])).
% 194.74/195.04 tff(139,plain,
% 194.74/195.04 (^[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))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(140,plain,
% 194.74/195.04 (![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)))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[139])).
% 194.74/195.04 tff(141,plain,
% 194.74/195.04 (^[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))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(142,plain,
% 194.74/195.04 (![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)))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[141])).
% 194.74/195.04 tff(143,plain,
% 194.74/195.04 (![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)))))),
% 194.74/195.04 inference(transitivity,[status(thm)],[142, 140])).
% 194.74/195.04 tff(144,plain,
% 194.74/195.04 (![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)))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(145,plain,
% 194.74/195.04 (^[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)))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(146,plain,
% 194.74/195.04 (![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)))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[145])).
% 194.74/195.04 tff(147,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 194.74/195.04 tff(148,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[147, 146])).
% 194.74/195.04 tff(149,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[148, 144])).
% 194.74/195.04 tff(150,plain,(
% 194.74/195.04 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 194.74/195.04 inference(skolemize,[status(sab)],[149])).
% 194.74/195.04 tff(151,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[150, 143])).
% 194.74/195.04 tff(152,plain,
% 194.74/195.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(153,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(154,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[153, 152])).
% 194.74/195.04 tff(155,plain,
% 194.74/195.04 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[154, 151, 100])).
% 194.74/195.04 tff(156,plain,
% 194.74/195.04 (ssList(nil) <=> ssList(nil)),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(157,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 194.74/195.04 tff(158,plain,
% 194.74/195.04 (ssList(nil)),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[157, 156])).
% 194.74/195.04 tff(159,plain,
% 194.74/195.04 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(160,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(161,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[160, 159])).
% 194.74/195.04 tff(162,plain,
% 194.74/195.04 (~((U!45 = nil) <=> neq(U!45, nil))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[161, 158, 155])).
% 194.74/195.04 tff(163,plain,
% 194.74/195.04 ((U!45 = nil) <=> (nil = U!45)),
% 194.74/195.04 inference(commutativity,[status(thm)],[])).
% 194.74/195.04 tff(164,plain,
% 194.74/195.04 ((nil = U!45) <=> (U!45 = nil)),
% 194.74/195.04 inference(symmetry,[status(thm)],[163])).
% 194.74/195.04 tff(165,plain,
% 194.74/195.04 ((cons(Y!47, nil) = nil) <=> (U!45 = nil)),
% 194.74/195.04 inference(monotonicity,[status(thm)],[76])).
% 194.74/195.04 tff(166,plain,
% 194.74/195.04 ((cons(Y!47, nil) = nil) <=> (nil = U!45)),
% 194.74/195.04 inference(transitivity,[status(thm)],[165, 163])).
% 194.74/195.04 tff(167,plain,
% 194.74/195.04 ((cons(Y!47, nil) = nil) <=> (U!45 = nil)),
% 194.74/195.04 inference(transitivity,[status(thm)],[166, 164])).
% 194.74/195.04 tff(168,plain,
% 194.74/195.04 ((~(cons(Y!47, nil) = nil)) <=> (~(U!45 = nil))),
% 194.74/195.04 inference(monotonicity,[status(thm)],[167])).
% 194.74/195.04 tff(169,plain,
% 194.74/195.04 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(170,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[169])).
% 194.74/195.04 tff(171,plain,
% 194.74/195.04 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(172,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[171])).
% 194.74/195.04 tff(173,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(transitivity,[status(thm)],[172, 170])).
% 194.74/195.04 tff(174,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(175,plain,
% 194.74/195.04 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 194.74/195.04 inference(bind,[status(th)],[])).
% 194.74/195.04 tff(176,plain,
% 194.74/195.04 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(quant_intro,[status(thm)],[175])).
% 194.74/195.04 tff(177,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 194.74/195.04 tff(178,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[177, 176])).
% 194.74/195.04 tff(179,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[178, 174])).
% 194.74/195.04 tff(180,plain,(
% 194.74/195.04 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(skolemize,[status(sab)],[179])).
% 194.74/195.04 tff(181,plain,
% 194.74/195.04 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[180, 173])).
% 194.74/195.04 tff(182,plain,
% 194.74/195.04 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(183,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(184,plain,
% 194.74/195.04 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[183, 182])).
% 194.74/195.04 tff(185,plain,
% 194.74/195.04 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[184, 158, 181])).
% 194.74/195.04 tff(186,plain,
% 194.74/195.04 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(187,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(188,plain,
% 194.74/195.04 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[187, 186])).
% 194.74/195.04 tff(189,plain,
% 194.74/195.04 (~(cons(Y!47, nil) = nil)),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[188, 39, 185])).
% 194.74/195.04 tff(190,plain,
% 194.74/195.04 (~(U!45 = nil)),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[189, 168])).
% 194.74/195.04 tff(191,plain,
% 194.74/195.04 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 194.74/195.04 inference(tautology,[status(thm)],[])).
% 194.74/195.04 tff(192,plain,
% 194.74/195.04 (neq(U!45, nil)),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[191, 190, 162])).
% 194.74/195.04 tff(193,plain,
% 194.74/195.04 ((~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(194,plain,
% 194.74/195.04 ((neq(U!45, nil) & segmentP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(195,plain,
% 194.74/195.04 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 194.74/195.04 inference(monotonicity,[status(thm)],[194])).
% 194.74/195.04 tff(196,plain,
% 194.74/195.04 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 194.74/195.04 inference(transitivity,[status(thm)],[195, 193])).
% 194.74/195.04 tff(197,plain,
% 194.74/195.04 (~(neq(U!45, nil) & segmentP(V!46, U!45))),
% 194.74/195.04 inference(and_elim,[status(thm)],[13])).
% 194.74/195.04 tff(198,plain,
% 194.74/195.04 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[197, 196])).
% 194.74/195.04 tff(199,plain,
% 194.74/195.04 (~segmentP(V!46, U!45)),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[198, 192])).
% 194.74/195.04 tff(200,plain,
% 194.74/195.04 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 194.74/195.04 inference(tautology,[status(thm)],[])).
% 194.74/195.04 tff(201,plain,
% 194.74/195.04 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[200, 199, 138])).
% 194.74/195.04 tff(202,plain,
% 194.74/195.04 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_2(Y!47, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_2(Y!47, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46))))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(203,plain,
% 194.74/195.04 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(tptp_fun_W_2(Y!47, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46))))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(204,plain,
% 194.74/195.04 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(tptp_fun_W_2(Y!47, V!46))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))),
% 194.74/195.04 inference(modus_ponens,[status(thm)],[203, 202])).
% 194.74/195.04 tff(205,plain,
% 194.74/195.04 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))),
% 194.74/195.04 inference(unit_resolution,[status(thm)],[204, 82, 201])).
% 194.74/195.04 tff(206,plain,
% 194.74/195.04 (((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46)))),
% 194.74/195.04 inference(rewrite,[status(thm)],[])).
% 194.74/195.04 tff(207,plain,
% 194.74/195.04 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))) | ((~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46)))),
% 194.74/195.04 inference(quant_inst,[status(thm)],[])).
% 194.74/195.04 tff(208,plain,
% 194.74/195.04 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46))),
% 195.21/195.49 inference(modus_ponens,[status(thm)],[207, 206])).
% 195.21/195.49 tff(209,plain,
% 195.21/195.49 (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46)),
% 195.21/195.49 inference(unit_resolution,[status(thm)],[208, 53, 205])).
% 195.21/195.49 tff(210,plain,
% 195.21/195.49 ($false),
% 195.21/195.49 inference(unit_resolution,[status(thm)],[209, 109])).
% 195.21/195.49 % SZS output end Proof
% 195.21/195.50 % E exiting
%------------------------------------------------------------------------------