%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET790+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.21s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET790+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:44:16 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(apply_type, type, (
% 0.21/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_X_17_type, type, (
% 0.21/0.39 tptp_fun_X_17: $i)).
% 0.21/0.39 tff(tptp_fun_M_14_type, type, (
% 0.21/0.39 tptp_fun_M_14: $i)).
% 0.21/0.39 tff(tptp_fun_R_16_type, type, (
% 0.21/0.39 tptp_fun_R_16: $i)).
% 0.21/0.39 tff(member_type, type, (
% 0.21/0.39 member: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_E_15_type, type, (
% 0.21/0.39 tptp_fun_E_15: $i)).
% 0.21/0.39 tff(least_type, type, (
% 0.21/0.39 least: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_X_9_type, type, (
% 0.21/0.39 tptp_fun_X_9: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(order_type, type, (
% 0.21/0.39 order: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_Z_3_type, type, (
% 0.21/0.39 tptp_fun_Z_3: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X_5_type, type, (
% 0.21/0.39 tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_Y_4_type, type, (
% 0.21/0.39 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.39 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X_0_type, type, (
% 0.21/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> (~((~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) | (~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) | (~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[R: $i, E: $i, M: $i] : refl((~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) <=> ((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))), rewrite((least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))) <=> (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))), ((((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) <=> (((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))), rewrite((((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) <=> (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))), ((((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) <=> (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (^[R: $i, E: $i, M: $i] : rewrite((((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))) <=> (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))) <=> ![R: $i, E: $i, M: $i] : (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) <=> ![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (^[R: $i, E: $i, M: $i] : rewrite((least(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, M, X)))) <=> (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, M, X)))) <=> ![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.40 tff(15,axiom,(![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, M, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','least')).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (least(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.40 tff(18,plain,(
% 0.21/0.40 ![R: $i, E: $i, M: $i] : (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (((~least(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, M, X)))) & (least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (~((~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X))))))) | (~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![R: $i, E: $i, M: $i] : (~((~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) | (~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![R: $i, E: $i, M: $i] : (~((~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) | (~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))))))) | (~((~(least(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_9(X!17, E!15, R!16), E!15)) | apply(R!16, X!17, tptp_fun_X_9(X!17, E!15, R!16)))))) | (~((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (~((~(least(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_9(X!17, E!15, R!16), E!15)) | apply(R!16, X!17, tptp_fun_X_9(X!17, E!15, R!16)))))) | (~((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (((~(least(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_9(X!17, E!15, R!16), E!15)) | apply(R!16, X!17, tptp_fun_X_9(X!17, E!15, R!16)))))) | (~((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))))))) | ((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 ((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (((order(R!16, E!15) & least(M!14, R!16, E!15)) & (~((~least(X!17, R!16, E!15)) | (M!14 = X!17)))) <=> (order(R!16, E!15) & least(M!14, R!16, E!15) & (~((~least(X!17, R!16, E!15)) | (M!14 = X!17))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X)))) <=> (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~![R: $i, E: $i, M: $i] : ((order(R, E) & least(M, R, E)) => ![X: $i] : (least(X, R, E) => (M = X)))) <=> (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(30,axiom,(~![R: $i, E: $i, M: $i] : ((order(R, E) & least(M, R, E)) => ![X: $i] : (least(X, R, E) => (M = X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIV2')).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & least(M, R, E))) | ![X: $i] : ((~least(X, R, E)) | (M = X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (order(R!16, E!15) & least(M!14, R!16, E!15) & (~((~least(X!17, R!16, E!15)) | (M!14 = X!17)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (~((~least(X!17, R!16, E!15)) | (M!14 = X!17))),
% 0.21/0.40 inference(and_elim,[status(thm)],[35])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (least(X!17, R!16, E!15)),
% 0.21/0.40 inference(or_elim,[status(thm)],[36])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))))))) | (~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~((~least(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))))))) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[39, 26])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))) | member(X!17, E!15)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (member(X!17, E!15)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((~![R: $i, E: $i, M: $i] : (~((~(least(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_9(M, E, R), E)) | apply(R, M, tptp_fun_X_9(M, E, R)))))) | (~((~least(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, M, X)))))))))) | (~((~(least(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_9(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_9(M!14, E!15, R!16)))))) | (~((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (~((~(least(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_9(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_9(M!14, E!15, R!16)))))) | (~((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 22])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (((~(least(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_9(M!14, E!15, R!16), E!15)) | apply(R!16, M!14, tptp_fun_X_9(M!14, E!15, R!16)))))) | (~((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))))))) | ((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (least(M!14, R!16, E!15)),
% 0.21/0.41 inference(and_elim,[status(thm)],[35])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((~((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))))))) | (~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~((~least(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))))))) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))) | ![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))) | ((~member(X!17, E!15)) | apply(R!16, M!14, X!17))) <=> ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))) | (~member(X!17, E!15)) | apply(R!16, M!14, X!17))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))) | ((~member(X!17, E!15)) | apply(R!16, M!14, X!17))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X))) | (~member(X!17, E!15)) | apply(R!16, M!14, X!17)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (apply(R!16, M!14, X!17)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X)))) | ![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[57, 40])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, M!14, X)))) | member(M!14, E!15)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (member(M!14, E!15)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[59, 50])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))) | ((~member(M!14, E!15)) | apply(R!16, X!17, M!14))) <=> ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))) | (~member(M!14, E!15)) | apply(R!16, X!17, M!14))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))) | ((~member(M!14, E!15)) | apply(R!16, X!17, M!14))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X!17, X))) | (~member(M!14, E!15)) | apply(R!16, X!17, M!14)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (apply(R!16, X!17, M!14)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[63, 60, 58])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (^[R: $i, E: $i] : rewrite((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (^[R: $i, E: $i] : refl((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (^[R: $i, E: $i] : rewrite((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))), trans(monotonicity(rewrite((~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) <=> (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E))))), rewrite((~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))) <=> (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))), ((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))), rewrite((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))), ((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))), ((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> (((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))), rewrite((((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))), ((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (^[R: $i, E: $i] : rewrite((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))) <=> (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (^[R: $i, E: $i] : rewrite((order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![R: $i, E: $i] : (order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.42 tff(79,axiom,(![R: $i, E: $i] : (order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','order')).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.42 tff(82,plain,(
% 0.21/0.42 ![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[81])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[85, 66])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))) <=> (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[89, 87])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[92, 86])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 (((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((~member(tptp_fun_Y_1(E!15, R!16), E!15)) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)))) | (~((~member(tptp_fun_Z_3(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))) | ((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(95,plain,
% 0.22/0.45 ((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.22/0.45 tff(96,plain,
% 0.22/0.45 (order(R!16, E!15)),
% 0.22/0.45 inference(and_elim,[status(thm)],[35])).
% 0.22/0.45 tff(97,plain,
% 0.22/0.45 ((~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))) | (~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(98,plain,
% 0.22/0.45 ((~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.22/0.45 tff(99,plain,
% 0.22/0.45 (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.22/0.45 tff(100,plain,
% 0.22/0.45 (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))) | ![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(101,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.22/0.45 tff(102,plain,
% 0.22/0.45 (~(M!14 = X!17)),
% 0.22/0.45 inference(or_elim,[status(thm)],[36])).
% 0.22/0.45 tff(103,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(104,plain,
% 0.22/0.45 (((M!14 = X!17) | (~apply(R!16, M!14, X!17)) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14))) <=> ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(105,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | ((M!14 = X!17) | (~apply(R!16, M!14, X!17)) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[104])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | ((M!14 = X!17) | (~apply(R!16, M!14, X!17)) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[105, 103])).
% 0.22/0.45 tff(107,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | ((M!14 = X!17) | (~apply(R!16, M!14, X!17)) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!16, X, Y)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~apply(R!16, Y, X)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[108, 102, 101, 60, 42, 64, 56])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------