%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET793+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:26:21 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET793+4 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:42:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(apply_type, type, (
% 0.11/0.37 apply: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_8_type, type, (
% 0.11/0.37 tptp_fun_X_8: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_R_16_type, type, (
% 0.11/0.37 tptp_fun_R_16: $i)).
% 0.11/0.37 tff(tptp_fun_E_15_type, type, (
% 0.11/0.37 tptp_fun_E_15: $i)).
% 0.11/0.37 tff(tptp_fun_M_14_type, type, (
% 0.11/0.37 tptp_fun_M_14: $i)).
% 0.11/0.37 tff(member_type, type, (
% 0.11/0.37 member: ( $i * $i ) > $o)).
% 0.11/0.37 tff(greatest_type, type, (
% 0.11/0.37 greatest: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(max_type, type, (
% 0.11/0.37 max: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_10_type, type, (
% 0.11/0.37 tptp_fun_X_10: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(total_order_type, type, (
% 0.11/0.37 total_order: ( $i * $i ) > $o)).
% 0.11/0.37 tff(order_type, type, (
% 0.11/0.37 order: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_7_type, type, (
% 0.11/0.37 tptp_fun_X_7: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_Y_6_type, type, (
% 0.11/0.37 tptp_fun_Y_6: ( $i * $i ) > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : refl((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[6, 4])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))), rewrite((greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))) <=> (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))), rewrite((((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : rewrite((greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.38 tff(15,axiom,(![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','greatest')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.38 tff(18,plain,(
% 0.11/0.38 ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((~![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))) | (~((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (~((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))))) | (greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : refl((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[32, 30])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) <=> ((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))) <=> (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))), ((max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))), rewrite((max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))), ((max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))), ((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> (((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))) & (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))), rewrite((((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))) & (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))), ((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : rewrite((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))) <=> (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))) <=> ![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) <=> ![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (^[R: $i, E: $i, M: $i] : rewrite((max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X)))) <=> (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X)))) <=> ![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.38 tff(41,axiom,(![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','max')).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.11/0.38 tff(44,plain,(
% 0.11/0.38 ![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[46, 33])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[47, 28])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 ((~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((M!14 = tptp_fun_X_10(M!14, E!15, R!16)) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((M!14 = X) | (~member(X, E!15)) | (~apply(R!16, M!14, X)))))))))) <=> (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((M!14 = tptp_fun_X_10(M!14, E!15, R!16)) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((M!14 = X) | (~member(X, E!15)) | (~apply(R!16, M!14, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((M!14 = tptp_fun_X_10(M!14, E!15, R!16)) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((M!14 = X) | (~member(X, E!15)) | (~apply(R!16, M!14, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((M!14 = tptp_fun_X_10(M!14, E!15, R!16)) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((M!14 = X) | (~member(X, E!15)) | (~apply(R!16, M!14, X))))))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (~((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (((~(max(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~apply(R!16, M!14, tptp_fun_X_10(M!14, E!15, R!16))) | (~member(tptp_fun_X_10(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_10(M!14, E!15, R!16)))))) | (~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))))) | ((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 ((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 ((~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E))) <=> (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 ((~![R: $i, E: $i, M: $i] : ((total_order(R, E) & max(M, R, E)) => greatest(M, R, E))) <=> (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(60,axiom,(~![R: $i, E: $i, M: $i] : ((total_order(R, E) & max(M, R, E)) => greatest(M, R, E))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIV5')).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (~![R: $i, E: $i, M: $i] : ((~(total_order(R, E) & max(M, R, E))) | greatest(M, R, E))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.11/0.39 tff(65,plain,(
% 0.11/0.39 ~((~(total_order(R!16, E!15) & max(M!14, R!16, E!15))) | greatest(M!14, R!16, E!15))),
% 0.11/0.39 inference(skolemize,[status(sab)],[64])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (total_order(R!16, E!15) & max(M!14, R!16, E!15)),
% 0.11/0.39 inference(or_elim,[status(thm)],[65])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (max(M!14, R!16, E!15)),
% 0.11/0.39 inference(and_elim,[status(thm)],[66])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 ((~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))) | (~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 ((~((~max(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))))) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[69, 57])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))) | member(M!14, E!15)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (member(M!14, E!15)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (~greatest(M!14, R!16, E!15)),
% 0.11/0.39 inference(or_elim,[status(thm)],[65])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 ((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(75,plain,
% 0.11/0.39 ((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[75, 72, 26])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)) | (~apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(78,plain,
% 0.11/0.39 (~apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)) | member(tptp_fun_X_8(M!14, E!15, R!16), E!15)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 (member(tptp_fun_X_8(M!14, E!15, R!16), E!15)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 (^[R: $i, E: $i] : rewrite((~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (^[R: $i, E: $i] : refl((~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 (^[R: $i, E: $i] : rewrite((~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.11/0.40 tff(87,plain,
% 0.11/0.40 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[86, 84])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) <=> ((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))) <=> (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))), ((total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))) <=> (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))), rewrite((total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))) <=> (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))), ((total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))) <=> (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))), ((((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))))) <=> (((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))))), rewrite((((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) <=> (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))), ((((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))))) <=> (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (![R: $i, E: $i] : (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 (^[R: $i, E: $i] : rewrite((((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | ((~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))))) <=> (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 (![R: $i, E: $i] : (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | ((~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 (![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) <=> ![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 (^[R: $i, E: $i] : rewrite((total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (apply(R, X, Y) | apply(R, Y, X))))) <=> (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(94,plain,
% 0.11/0.40 (![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (apply(R, X, Y) | apply(R, Y, X))))) <=> ![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.11/0.40 tff(95,axiom,(![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (apply(R, X, Y) | apply(R, Y, X)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','total_order')).
% 0.11/0.40 tff(96,plain,
% 0.11/0.40 (![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (![R: $i, E: $i] : (total_order(R, E) <=> (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.11/0.40 tff(98,plain,(
% 0.11/0.40 ![R: $i, E: $i] : (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | ((~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[97])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (![R: $i, E: $i] : (((~total_order(R, E)) | (order(R, E) & ![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~(member(X, E) & member(Y, E)))))) & (total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~(member(tptp_fun_X_7(E, R), E) & member(tptp_fun_Y_6(E, R), E)))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.11/0.40 tff(100,plain,
% 0.11/0.40 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.11/0.40 tff(101,plain,
% 0.11/0.40 (![R: $i, E: $i] : (~((~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E)))))))) | (~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.11/0.40 tff(102,plain,
% 0.11/0.40 (![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[101, 82])).
% 0.11/0.40 tff(103,plain,
% 0.11/0.40 (((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(104,plain,
% 0.11/0.40 ((~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~(apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | (~member(tptp_fun_Y_6(E!15, R!16), E!15)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))))) <=> (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(105,plain,
% 0.11/0.40 (((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~(apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | (~member(tptp_fun_Y_6(E!15, R!16), E!15)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))))))),
% 0.11/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.11/0.41 tff(106,plain,
% 0.11/0.41 (((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~(apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | (~member(tptp_fun_Y_6(E!15, R!16), E!15)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))))))),
% 0.11/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.11/0.41 tff(107,plain,
% 0.11/0.41 ((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~(apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | (~member(tptp_fun_Y_6(E!15, R!16), E!15)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(108,plain,
% 0.11/0.41 ((~![R: $i, E: $i] : (~((~(total_order(R, E) | (~order(R, E)) | (~(apply(R, tptp_fun_Y_6(E, R), tptp_fun_X_7(E, R)) | apply(R, tptp_fun_X_7(E, R), tptp_fun_Y_6(E, R)) | (~member(tptp_fun_X_7(E, R), E)) | (~member(tptp_fun_Y_6(E, R), E)))))) | (~((~total_order(R, E)) | (~((~order(R, E)) | (~![X: $i, Y: $i] : (apply(R, Y, X) | apply(R, X, Y) | (~member(Y, E)) | (~member(X, E))))))))))) | (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (~((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 102])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (((~(total_order(R!16, E!15) | (~order(R!16, E!15)) | (~((~member(tptp_fun_Y_6(E!15, R!16), E!15)) | (~member(tptp_fun_X_7(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_7(E!15, R!16), tptp_fun_Y_6(E!15, R!16)) | apply(R!16, tptp_fun_Y_6(E!15, R!16), tptp_fun_X_7(E!15, R!16)))))) | (~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))))) | ((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (total_order(R!16, E!15)),
% 0.20/0.41 inference(and_elim,[status(thm)],[66])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))) | (~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((~((~total_order(R!16, E!15)) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))))) | (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (~((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~order(R!16, E!15)) | (~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15))))) | ![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | ((~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))) <=> ((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (~member(M!14, E!15))) <=> ((~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (~member(M!14, E!15)))) <=> ((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | ((~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (~member(M!14, E!15)))) <=> ((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (~member(M!14, E!15)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (apply(R!16, Y, X) | apply(R!16, X, Y) | (~member(Y, E!15)) | (~member(X, E!15)))) | (~member(M!14, E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 117, 72, 80, 78])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X))))) | ![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[125, 70])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))) | ((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_8(M!14, E!15, R!16)) | (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))))) <=> ((~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_8(M!14, E!15, R!16)) | (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))) | ((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_8(M!14, E!15, R!16)) | (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.42 ((~![X: $i] : ((~member(X, E!15)) | (M!14 = X) | (~apply(R!16, M!14, X)))) | (~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | (M!14 = tptp_fun_X_8(M!14, E!15, R!16)) | (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (M!14 = tptp_fun_X_8(M!14, E!15, R!16)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[129, 80, 126, 124])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (tptp_fun_X_8(M!14, E!15, R!16) = M!14),
% 0.20/0.42 inference(symmetry,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)) <=> apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[130, 131])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14) <=> apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))),
% 0.20/0.42 inference(symmetry,[status(thm)],[132])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14)) <=> (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (~apply(R!16, M!14, tptp_fun_X_8(M!14, E!15, R!16))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 134])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 135])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------