%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC363+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 198.24s 198.57s
% Output : Proof 198.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC363+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:08:10 EDT 2025
% 0.13/0.35 % CPUTime :
% 198.24/198.57 % SZS status Theorem
% 198.24/198.57 % SZS output start Proof
% 198.24/198.57 tff(tptp_fun_V_46_type, type, (
% 198.24/198.57 tptp_fun_V_46: $i)).
% 198.24/198.57 tff(app_type, type, (
% 198.24/198.57 app: ( $i * $i ) > $i)).
% 198.24/198.57 tff(tptp_fun_X_3_type, type, (
% 198.24/198.57 tptp_fun_X_3: ( $i * $i ) > $i)).
% 198.24/198.57 tff(tptp_fun_Y_47_type, type, (
% 198.24/198.57 tptp_fun_Y_47: $i)).
% 198.24/198.57 tff(tptp_fun_U_45_type, type, (
% 198.24/198.57 tptp_fun_U_45: $i)).
% 198.24/198.57 tff(tptp_fun_W_2_type, type, (
% 198.24/198.57 tptp_fun_W_2: ( $i * $i ) > $i)).
% 198.24/198.57 tff(cons_type, type, (
% 198.24/198.57 cons: ( $i * $i ) > $i)).
% 198.24/198.57 tff(ssList_type, type, (
% 198.24/198.57 ssList: $i > $o)).
% 198.24/198.57 tff(memberP_type, type, (
% 198.24/198.57 memberP: ( $i * $i ) > $o)).
% 198.24/198.57 tff(ssItem_type, type, (
% 198.24/198.57 ssItem: $i > $o)).
% 198.24/198.57 tff(neq_type, type, (
% 198.24/198.57 neq: ( $i * $i ) > $o)).
% 198.24/198.57 tff(nil_type, type, (
% 198.24/198.57 nil: $i)).
% 198.24/198.57 tff(segmentP_type, type, (
% 198.24/198.57 segmentP: ( $i * $i ) > $o)).
% 198.24/198.57 tff(tptp_fun_X_8_type, type, (
% 198.24/198.57 tptp_fun_X_8: ( $i * $i ) > $i)).
% 198.24/198.57 tff(tptp_fun_W_7_type, type, (
% 198.24/198.57 tptp_fun_W_7: ( $i * $i ) > $i)).
% 198.24/198.57 tff(1,plain,
% 198.24/198.57 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & neq(V!46, nil))),
% 198.24/198.57 inference(rewrite,[status(thm)],[])).
% 198.24/198.57 tff(2,plain,
% 198.24/198.57 (((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil)) <=> ((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & neq(V!46, nil))),
% 198.24/198.57 inference(rewrite,[status(thm)],[])).
% 198.24/198.57 tff(3,plain,
% 198.24/198.57 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & neq(V!46, nil)))),
% 198.24/198.57 inference(monotonicity,[status(thm)],[2])).
% 198.24/198.57 tff(4,plain,
% 198.24/198.57 ((ssList(U!45) & ((~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & neq(V!46, nil))) <=> (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & neq(V!46, nil))),
% 198.24/198.57 inference(transitivity,[status(thm)],[3, 1])).
% 198.24/198.57 tff(5,plain,
% 198.24/198.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil)))))),
% 198.24/198.57 inference(rewrite,[status(thm)],[])).
% 198.24/198.57 tff(6,plain,
% 198.24/198.57 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil)))))),
% 198.24/198.57 inference(rewrite,[status(thm)],[])).
% 198.24/198.57 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 198.24/198.58 tff(8,plain,
% 198.24/198.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[7, 6])).
% 198.24/198.58 tff(9,plain,
% 198.24/198.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[8, 5])).
% 198.24/198.58 tff(10,plain,
% 198.24/198.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[9, 5])).
% 198.24/198.58 tff(11,plain,
% 198.24/198.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | ((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | (~neq(V, nil))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[10, 5])).
% 198.24/198.58 tff(12,plain,
% 198.24/198.58 (ssList(U!45) & (~segmentP(V!46, U!45)) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & neq(V!46, nil)),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[11, 4])).
% 198.24/198.58 tff(13,plain,
% 198.24/198.58 (ssList(V!46)),
% 198.24/198.58 inference(and_elim,[status(thm)],[12])).
% 198.24/198.58 tff(14,plain,
% 198.24/198.58 (^[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)))))))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(15,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[14])).
% 198.24/198.58 tff(16,plain,
% 198.24/198.58 (^[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)))))))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(17,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[16])).
% 198.24/198.58 tff(18,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(transitivity,[status(thm)],[17, 15])).
% 198.24/198.58 tff(19,plain,
% 198.24/198.58 (^[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)))))))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(20,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[19])).
% 198.24/198.58 tff(21,plain,
% 198.24/198.58 (^[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)))))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(22,plain,
% 198.24/198.58 (![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))))))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[21])).
% 198.24/198.58 tff(23,plain,
% 198.24/198.58 (![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))))))),
% 198.24/198.58 inference(rewrite,[status(thm)],[])).
% 198.24/198.58 tff(24,plain,
% 198.24/198.58 (^[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))))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(25,plain,
% 198.24/198.58 (![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))))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[24])).
% 198.24/198.58 tff(26,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/sandbox2/benchmark/Axioms/SWC001+0.ax','ax3')).
% 198.24/198.58 tff(27,plain,
% 198.24/198.58 (![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))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[26, 25])).
% 198.24/198.58 tff(28,plain,
% 198.24/198.58 (![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))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[27, 23])).
% 198.24/198.58 tff(29,plain,(
% 198.24/198.58 ![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))))))))),
% 198.24/198.58 inference(skolemize,[status(sab)],[28])).
% 198.24/198.58 tff(30,plain,
% 198.24/198.58 (![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))))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[29, 22])).
% 198.24/198.58 tff(31,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[30, 20])).
% 198.24/198.58 tff(32,plain,
% 198.24/198.58 (![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))))))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[31, 18])).
% 198.24/198.58 tff(33,plain,
% 198.24/198.58 (((~![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))))))))))),
% 198.24/198.58 inference(rewrite,[status(thm)],[])).
% 198.24/198.58 tff(34,plain,
% 198.24/198.58 ((~![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))))))))))),
% 198.24/198.58 inference(quant_inst,[status(thm)],[])).
% 198.24/198.58 tff(35,plain,
% 198.24/198.58 ((~![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)))))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[34, 33])).
% 198.24/198.58 tff(36,plain,
% 198.24/198.58 (![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)))))))))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[35, 32, 13])).
% 198.24/198.58 tff(37,plain,
% 198.24/198.58 (neq(V!46, nil)),
% 198.24/198.58 inference(and_elim,[status(thm)],[12])).
% 198.24/198.58 tff(38,plain,
% 198.24/198.58 ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))),
% 198.24/198.58 inference(and_elim,[status(thm)],[12])).
% 198.24/198.58 tff(39,plain,
% 198.24/198.58 (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[38, 37])).
% 198.24/198.58 tff(40,plain,
% 198.24/198.58 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | ssItem(Y!47)),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(41,plain,
% 198.24/198.58 (ssItem(Y!47)),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[40, 39])).
% 198.24/198.58 tff(42,plain,
% 198.24/198.58 (((~![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)))))))))),
% 198.24/198.58 inference(rewrite,[status(thm)],[])).
% 198.24/198.58 tff(43,plain,
% 198.24/198.58 ((~![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)))))))))),
% 198.24/198.58 inference(quant_inst,[status(thm)],[])).
% 198.24/198.58 tff(44,plain,
% 198.24/198.58 ((~![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))))))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 198.24/198.58 tff(45,plain,
% 198.24/198.58 (~((~((~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)))))))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[44, 41, 36])).
% 198.24/198.58 tff(46,plain,
% 198.24/198.58 (((~((~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)))))),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(47,plain,
% 198.24/198.58 ((~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))))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[46, 45])).
% 198.24/198.58 tff(48,plain,
% 198.24/198.58 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | memberP(V!46, Y!47)),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(49,plain,
% 198.24/198.58 (memberP(V!46, Y!47)),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[48, 39])).
% 198.24/198.58 tff(50,plain,
% 198.24/198.58 ((~((~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))))),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(51,plain,
% 198.24/198.58 ((~((~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))))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[50, 49])).
% 198.24/198.58 tff(52,plain,
% 198.24/198.58 (~((~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)))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[51, 47])).
% 198.24/198.58 tff(53,plain,
% 198.24/198.58 (((~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)),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(54,plain,
% 198.24/198.58 (app(tptp_fun_W_2(Y!47, V!46), cons(Y!47, tptp_fun_X_3(Y!47, V!46))) = V!46),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[53, 52])).
% 198.24/198.58 tff(55,plain,
% 198.24/198.58 (((~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))),
% 198.24/198.58 inference(tautology,[status(thm)],[])).
% 198.24/198.58 tff(56,plain,
% 198.24/198.58 (ssList(tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[55, 52])).
% 198.24/198.58 tff(57,plain,
% 198.24/198.58 (^[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)))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(58,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[57])).
% 198.24/198.58 tff(59,plain,
% 198.24/198.58 (^[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)))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(60,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[59])).
% 198.24/198.58 tff(61,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(transitivity,[status(thm)],[60, 58])).
% 198.24/198.58 tff(62,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(rewrite,[status(thm)],[])).
% 198.24/198.58 tff(63,plain,
% 198.24/198.58 (^[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))))))),
% 198.24/198.58 inference(bind,[status(th)],[])).
% 198.24/198.58 tff(64,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(quant_intro,[status(thm)],[63])).
% 198.24/198.58 tff(65,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax81')).
% 198.24/198.58 tff(66,plain,
% 198.24/198.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[65, 64])).
% 198.24/198.58 tff(67,plain,
% 198.24/198.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[66, 62])).
% 198.24/198.58 tff(68,plain,(
% 198.24/198.58 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 198.24/198.58 inference(skolemize,[status(sab)],[67])).
% 198.24/198.58 tff(69,plain,
% 198.24/198.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[68, 61])).
% 198.24/198.58 tff(70,plain,
% 198.24/198.58 (((~![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)))))),
% 198.24/198.58 inference(rewrite,[status(thm)],[])).
% 198.24/198.58 tff(71,plain,
% 198.24/198.58 ((~![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)))))),
% 198.24/198.58 inference(quant_inst,[status(thm)],[])).
% 198.24/198.58 tff(72,plain,
% 198.24/198.58 ((~![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))))),
% 198.24/198.58 inference(modus_ponens,[status(thm)],[71, 70])).
% 198.24/198.58 tff(73,plain,
% 198.24/198.58 (![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))))),
% 198.24/198.58 inference(unit_resolution,[status(thm)],[72, 69, 56])).
% 198.24/198.58 tff(74,plain,
% 198.24/198.58 (((~![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))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(75,plain,
% 198.24/198.59 ((~![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))))),
% 198.24/198.59 inference(quant_inst,[status(thm)],[])).
% 198.24/198.59 tff(76,plain,
% 198.24/198.59 ((~![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)))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[75, 74])).
% 198.24/198.59 tff(77,plain,
% 198.24/198.59 (cons(Y!47, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[76, 41, 73])).
% 198.24/198.59 tff(78,plain,
% 198.24/198.59 (app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46)) = cons(Y!47, tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.59 inference(symmetry,[status(thm)],[77])).
% 198.24/198.59 tff(79,plain,
% 198.24/198.59 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | (cons(Y!47, nil) = U!45)),
% 198.24/198.59 inference(tautology,[status(thm)],[])).
% 198.24/198.59 tff(80,plain,
% 198.24/198.59 (cons(Y!47, nil) = U!45),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[79, 39])).
% 198.24/198.59 tff(81,plain,
% 198.24/198.59 (app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46)) = app(U!45, tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.59 inference(monotonicity,[status(thm)],[80])).
% 198.24/198.59 tff(82,plain,
% 198.24/198.59 (app(U!45, tptp_fun_X_3(Y!47, V!46)) = app(cons(Y!47, nil), tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.59 inference(symmetry,[status(thm)],[81])).
% 198.24/198.59 tff(83,plain,
% 198.24/198.59 (app(U!45, tptp_fun_X_3(Y!47, V!46)) = cons(Y!47, tptp_fun_X_3(Y!47, V!46))),
% 198.24/198.59 inference(transitivity,[status(thm)],[82, 78])).
% 198.24/198.59 tff(84,plain,
% 198.24/198.59 (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)))),
% 198.24/198.59 inference(monotonicity,[status(thm)],[83])).
% 198.24/198.59 tff(85,plain,
% 198.24/198.59 (((~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))),
% 198.24/198.59 inference(tautology,[status(thm)],[])).
% 198.24/198.59 tff(86,plain,
% 198.24/198.59 (ssList(tptp_fun_W_2(Y!47, V!46))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[85, 52])).
% 198.24/198.59 tff(87,plain,
% 198.24/198.59 (^[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)))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(88,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[87])).
% 198.24/198.59 tff(89,plain,
% 198.24/198.59 (^[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)))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(90,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[89])).
% 198.24/198.59 tff(91,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(transitivity,[status(thm)],[90, 88])).
% 198.24/198.59 tff(92,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(93,plain,
% 198.24/198.59 (^[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))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(94,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[93])).
% 198.24/198.59 tff(95,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax82')).
% 198.24/198.59 tff(96,plain,
% 198.24/198.59 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[95, 94])).
% 198.24/198.59 tff(97,plain,
% 198.24/198.59 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[96, 92])).
% 198.24/198.59 tff(98,plain,(
% 198.24/198.59 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 198.24/198.59 inference(skolemize,[status(sab)],[97])).
% 198.24/198.59 tff(99,plain,
% 198.24/198.59 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[98, 91])).
% 198.24/198.59 tff(100,plain,
% 198.24/198.59 (((~![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))))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(101,plain,
% 198.24/198.59 ((~![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))))))),
% 198.24/198.59 inference(quant_inst,[status(thm)],[])).
% 198.24/198.59 tff(102,plain,
% 198.24/198.59 ((~![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)))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[101, 100])).
% 198.24/198.59 tff(103,plain,
% 198.24/198.59 (![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)))))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[102, 99, 86])).
% 198.24/198.59 tff(104,plain,
% 198.24/198.59 (ssList(U!45)),
% 198.24/198.59 inference(and_elim,[status(thm)],[12])).
% 198.24/198.59 tff(105,plain,
% 198.24/198.59 (((~![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)))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(106,plain,
% 198.24/198.59 ((~![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)))))),
% 198.24/198.59 inference(quant_inst,[status(thm)],[])).
% 198.24/198.59 tff(107,plain,
% 198.24/198.59 ((~![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))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[106, 105])).
% 198.24/198.59 tff(108,plain,
% 198.24/198.59 (![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))))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[107, 104, 103])).
% 198.24/198.59 tff(109,plain,
% 198.24/198.59 (((~![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)))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(110,plain,
% 198.24/198.59 ((~![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)))))),
% 198.24/198.59 inference(quant_inst,[status(thm)],[])).
% 198.24/198.59 tff(111,plain,
% 198.24/198.59 ((~![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))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[110, 109])).
% 198.24/198.59 tff(112,plain,
% 198.24/198.59 (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)))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[111, 56, 108])).
% 198.24/198.59 tff(113,plain,
% 198.24/198.59 (app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46),
% 198.24/198.59 inference(transitivity,[status(thm)],[112, 84, 54])).
% 198.24/198.59 tff(114,plain,
% 198.24/198.59 (^[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)))))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(115,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[114])).
% 198.24/198.59 tff(116,plain,
% 198.24/198.59 (^[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)))))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(117,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[116])).
% 198.24/198.59 tff(118,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(transitivity,[status(thm)],[117, 115])).
% 198.24/198.59 tff(119,plain,
% 198.24/198.59 (^[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)))))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(120,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[119])).
% 198.24/198.59 tff(121,plain,
% 198.24/198.59 (^[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)))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(122,plain,
% 198.24/198.59 (![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))))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[121])).
% 198.24/198.59 tff(123,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(124,plain,
% 198.24/198.59 (^[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))))))))),
% 198.24/198.59 inference(bind,[status(th)],[])).
% 198.24/198.59 tff(125,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(quant_intro,[status(thm)],[124])).
% 198.24/198.59 tff(126,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/sandbox2/benchmark/Axioms/SWC001+0.ax','ax7')).
% 198.24/198.59 tff(127,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[126, 125])).
% 198.24/198.59 tff(128,plain,
% 198.24/198.59 (![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))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[127, 123])).
% 198.24/198.59 tff(129,plain,(
% 198.24/198.59 ![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))))))))),
% 198.24/198.59 inference(skolemize,[status(sab)],[128])).
% 198.24/198.59 tff(130,plain,
% 198.24/198.59 (![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))))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[129, 122])).
% 198.24/198.59 tff(131,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[130, 120])).
% 198.24/198.59 tff(132,plain,
% 198.24/198.59 (![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))))))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[131, 118])).
% 198.24/198.59 tff(133,plain,
% 198.24/198.59 (((~![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))))))))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(134,plain,
% 198.24/198.59 ((~![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))))))))))),
% 198.24/198.59 inference(quant_inst,[status(thm)],[])).
% 198.24/198.59 tff(135,plain,
% 198.24/198.59 ((~![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)))))))))),
% 198.24/198.59 inference(modus_ponens,[status(thm)],[134, 133])).
% 198.24/198.59 tff(136,plain,
% 198.24/198.59 (![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)))))))))),
% 198.24/198.59 inference(unit_resolution,[status(thm)],[135, 132, 13])).
% 198.24/198.59 tff(137,plain,
% 198.24/198.59 (((~![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)))))))))),
% 198.24/198.59 inference(rewrite,[status(thm)],[])).
% 198.24/198.59 tff(138,plain,
% 198.24/198.59 ((~![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)))))))))),
% 198.24/198.60 inference(quant_inst,[status(thm)],[])).
% 198.24/198.60 tff(139,plain,
% 198.24/198.60 ((~![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))))))))),
% 198.24/198.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 198.24/198.60 tff(140,plain,
% 198.24/198.60 (~((~((~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)))))))),
% 198.24/198.60 inference(unit_resolution,[status(thm)],[139, 104, 136])).
% 198.24/198.60 tff(141,plain,
% 198.24/198.60 (((~((~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)))))),
% 198.24/198.60 inference(tautology,[status(thm)],[])).
% 198.24/198.60 tff(142,plain,
% 198.24/198.60 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 198.24/198.60 inference(unit_resolution,[status(thm)],[141, 140])).
% 198.24/198.60 tff(143,plain,
% 198.24/198.60 (~segmentP(V!46, U!45)),
% 198.24/198.60 inference(and_elim,[status(thm)],[12])).
% 198.24/198.60 tff(144,plain,
% 198.24/198.60 ((~(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))))),
% 198.24/198.60 inference(tautology,[status(thm)],[])).
% 198.24/198.60 tff(145,plain,
% 198.24/198.60 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 198.24/198.60 inference(unit_resolution,[status(thm)],[144, 143])).
% 198.24/198.60 tff(146,plain,
% 198.24/198.60 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 198.24/198.60 inference(unit_resolution,[status(thm)],[145, 142])).
% 198.24/198.60 tff(147,plain,
% 198.24/198.60 (((~![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))))),
% 198.24/198.60 inference(rewrite,[status(thm)],[])).
% 198.24/198.60 tff(148,plain,
% 198.24/198.60 ((~![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))))),
% 198.24/198.60 inference(quant_inst,[status(thm)],[])).
% 198.24/198.60 tff(149,plain,
% 198.24/198.60 ((~![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)))),
% 198.80/199.15 inference(modus_ponens,[status(thm)],[148, 147])).
% 198.80/199.15 tff(150,plain,
% 198.80/199.15 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))),
% 198.80/199.15 inference(unit_resolution,[status(thm)],[149, 86, 146])).
% 198.80/199.15 tff(151,plain,
% 198.80/199.15 (((~![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)))),
% 198.80/199.15 inference(rewrite,[status(thm)],[])).
% 198.80/199.15 tff(152,plain,
% 198.80/199.15 ((~![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)))),
% 198.80/199.15 inference(quant_inst,[status(thm)],[])).
% 198.80/199.15 tff(153,plain,
% 198.80/199.15 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), X) = V!46)))) | (~ssList(tptp_fun_X_3(Y!47, V!46))) | (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46))),
% 198.80/199.15 inference(modus_ponens,[status(thm)],[152, 151])).
% 198.80/199.15 tff(154,plain,
% 198.80/199.15 (~(app(app(tptp_fun_W_2(Y!47, V!46), U!45), tptp_fun_X_3(Y!47, V!46)) = V!46)),
% 198.80/199.15 inference(unit_resolution,[status(thm)],[153, 56, 150])).
% 198.80/199.15 tff(155,plain,
% 198.80/199.15 ($false),
% 198.80/199.15 inference(unit_resolution,[status(thm)],[154, 113])).
% 198.80/199.15 % SZS output end Proof
% 198.80/199.16 % E exiting
%------------------------------------------------------------------------------