%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET803+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:23 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET803+4 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:43:26 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(tptp_fun_M_18_type, type, (
% 0.11/0.37 tptp_fun_M_18: $i)).
% 0.11/0.37 tff(tptp_fun_M2_16_type, type, (
% 0.11/0.37 tptp_fun_M2_16: $i)).
% 0.11/0.37 tff(tptp_fun_M1_17_type, type, (
% 0.11/0.37 tptp_fun_M1_17: $i)).
% 0.11/0.37 tff(apply_type, type, (
% 0.11/0.37 apply: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_R_15_type, type, (
% 0.11/0.37 tptp_fun_R_15: $i)).
% 0.11/0.37 tff(member_type, type, (
% 0.11/0.37 member: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_E_14_type, type, (
% 0.11/0.37 tptp_fun_E_14: $i)).
% 0.11/0.37 tff(max_type, type, (
% 0.11/0.37 max: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_10_type, type, (
% 0.11/0.37 tptp_fun_X_10: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(greatest_type, type, (
% 0.11/0.37 greatest: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(order_type, type, (
% 0.11/0.37 order: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_8_type, type, (
% 0.11/0.37 tptp_fun_X_8: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((M2!16 = M1!17) <=> (M1!17 = M2!16)),
% 0.11/0.37 inference(commutativity,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : refl((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[7, 5])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) <=> ((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))) <=> (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))), ((max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))), rewrite((max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))), ((max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))) <=> (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))), ((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> (((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))) & (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))))), rewrite((((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))) & (max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))), ((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))) <=> (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))) <=> ![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) <=> ![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[R: $i, E: $i, M: $i] : rewrite((max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X)))) <=> (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X)))) <=> ![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,axiom,(![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((member(X, E) & apply(R, M, X)) => (M = X))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','max')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (max(M, R, E) <=> (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.37 tff(19,plain,(
% 0.11/0.37 ![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | ((~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R)))))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![R: $i, E: $i, M: $i] : (((~max(M, R, E)) | (member(M, E) & ![X: $i] : ((~(member(X, E) & apply(R, M, X))) | (M = X)))) & (max(M, R, E) | (~member(M, E)) | (~((~(member(tptp_fun_X_10(M, E, R), E) & apply(R, M, tptp_fun_X_10(M, E, R)))) | (M = tptp_fun_X_10(M, E, R))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X)))))))) | (~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 8])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 3])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 ((~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((M1!17 = X) | (~member(X, E!14)) | (~apply(R!15, M1!17, X)))))))))) <=> (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((M1!17 = X) | (~member(X, E!14)) | (~apply(R!15, M1!17, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((M1!17 = X) | (~member(X, E!14)) | (~apply(R!15, M1!17, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((M1!17 = X) | (~member(X, E!14)) | (~apply(R!15, M1!17, X))))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (~((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (((~(max(M1!17, R!15, E!14) | (~member(M1!17, E!14)) | (~((~apply(R!15, M1!17, tptp_fun_X_10(M1!17, E!14, R!15))) | (~member(tptp_fun_X_10(M1!17, E!14, R!15), E!14)) | (M1!17 = tptp_fun_X_10(M1!17, E!14, R!15)))))) | (~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))))) | ((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 ((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 ((order(R!15, E!14) & (greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16)))) <=> (order(R!15, E!14) & greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 ((greatest(M!18, R!15, E!14) & (max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16)))) <=> (greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 ((order(R!15, E!14) & (greatest(M!18, R!15, E!14) & (max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16))))) <=> (order(R!15, E!14) & (greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 ((order(R!15, E!14) & (greatest(M!18, R!15, E!14) & (max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16))))) <=> (order(R!15, E!14) & greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 ((~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2))))))) <=> (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2)))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 ((~![R: $i, E: $i] : (order(R, E) => ![M1: $i, M2: $i] : (((max(M1, R, E) & max(M2, R, E)) & (~(M1 = M2))) => (~?[M: $i] : greatest(M, R, E))))) <=> (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2)))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(39,axiom,(~![R: $i, E: $i] : (order(R, E) => ![M1: $i, M2: $i] : (((max(M1, R, E) & max(M2, R, E)) & (~(M1 = M2))) => (~?[M: $i] : greatest(M, R, E))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIV15')).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (~![R: $i, E: $i] : ((~order(R, E)) | ![M1: $i, M2: $i] : ((~?[M: $i] : greatest(M, R, E)) | (~(max(M1, R, E) & max(M2, R, E) & (~(M1 = M2))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (order(R!15, E!14) & greatest(M!18, R!15, E!14) & max(M1!17, R!15, E!14) & max(M2!16, R!15, E!14) & (~(M1!17 = M2!16))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (max(M1!17, R!15, E!14)),
% 0.11/0.39 inference(and_elim,[status(thm)],[44])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 ((~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))) | (~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 ((~((~max(M1!17, R!15, E!14)) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))))) | (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (~((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[47, 32])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))) | member(M1!17, E!14)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (member(M1!17, E!14)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : refl((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))), rewrite((greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))) <=> (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))), rewrite((((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : rewrite((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (^[R: $i, E: $i, M: $i] : rewrite((greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.39 tff(65,axiom,(![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax','greatest')).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.11/0.39 tff(68,plain,(
% 0.11/0.39 ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[67])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[71, 52])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 ((~![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))) | (~((~(greatest(M!18, R!15, E!14) | (~member(M!18, E!14)) | (~((~member(tptp_fun_X_8(M!18, E!14, R!15), E!14)) | apply(R!15, tptp_fun_X_8(M!18, E!14, R!15), M!18))))) | (~((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (~((~(greatest(M!18, R!15, E!14) | (~member(M!18, E!14)) | (~((~member(tptp_fun_X_8(M!18, E!14, R!15), E!14)) | apply(R!15, tptp_fun_X_8(M!18, E!14, R!15), M!18))))) | (~((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.11/0.40 tff(75,plain,
% 0.11/0.40 (((~(greatest(M!18, R!15, E!14) | (~member(M!18, E!14)) | (~((~member(tptp_fun_X_8(M!18, E!14, R!15), E!14)) | apply(R!15, tptp_fun_X_8(M!18, E!14, R!15), M!18))))) | (~((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))))))) | ((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(76,plain,
% 0.11/0.40 ((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 (greatest(M!18, R!15, E!14)),
% 0.11/0.40 inference(and_elim,[status(thm)],[44])).
% 0.11/0.40 tff(78,plain,
% 0.11/0.40 ((~((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))))))) | (~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(79,plain,
% 0.11/0.40 ((~((~greatest(M!18, R!15, E!14)) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))))))) | (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (~((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.11/0.40 tff(81,plain,
% 0.11/0.40 (((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))) | ![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(82,plain,
% 0.11/0.40 (![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.11/0.40 tff(83,plain,
% 0.11/0.40 (((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | ((~member(M1!17, E!14)) | apply(R!15, M1!17, M!18))) <=> ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | (~member(M1!17, E!14)) | apply(R!15, M1!17, M!18))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(84,plain,
% 0.11/0.40 ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | ((~member(M1!17, E!14)) | apply(R!15, M1!17, M!18))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | (~member(M1!17, E!14)) | apply(R!15, M1!17, M!18)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (apply(R!15, M1!17, M!18)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[85, 82, 50])).
% 0.11/0.40 tff(87,plain,
% 0.11/0.40 (((~member(M1!17, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X))))) | ![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 (![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (((~member(M!18, E!14)) | (~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18)))) | member(M!18, E!14)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 (member(M!18, E!14)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[89, 80])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 (((~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))) | ((~member(M!18, E!14)) | (M1!17 = M!18) | (~apply(R!15, M1!17, M!18)))) <=> ((~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))) | (~member(M!18, E!14)) | (M1!17 = M!18) | (~apply(R!15, M1!17, M!18)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 ((~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))) | ((~member(M!18, E!14)) | (M1!17 = M!18) | (~apply(R!15, M1!17, M!18)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, E!14)) | (M1!17 = X) | (~apply(R!15, M1!17, X)))) | (~member(M!18, E!14)) | (M1!17 = M!18) | (~apply(R!15, M1!17, M!18))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 ((M1!17 = M!18) | (~apply(R!15, M1!17, M!18))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[93, 90, 88])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (M1!17 = M!18),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[94, 86])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (M!18 = M1!17),
% 0.18/0.40 inference(symmetry,[status(thm)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 ((M2!16 = M!18) <=> (M2!16 = M1!17)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 ((M2!16 = M!18) <=> (M1!17 = M2!16)),
% 0.18/0.40 inference(transitivity,[status(thm)],[97, 1])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((M1!17 = M2!16) <=> (M2!16 = M!18)),
% 0.18/0.40 inference(symmetry,[status(thm)],[98])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 ((~(M1!17 = M2!16)) <=> (~(M2!16 = M!18))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[99])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (~(M1!17 = M2!16)),
% 0.18/0.40 inference(and_elim,[status(thm)],[44])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (~(M2!16 = M!18)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 ((~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((M2!16 = X) | (~member(X, E!14)) | (~apply(R!15, M2!16, X)))))))))) <=> (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((M2!16 = X) | (~member(X, E!14)) | (~apply(R!15, M2!16, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[104])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((M2!16 = X) | (~member(X, E!14)) | (~apply(R!15, M2!16, X))))))))))) <=> ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[105, 103])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((M2!16 = X) | (~member(X, E!14)) | (~apply(R!15, M2!16, X))))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 ((~![R: $i, E: $i, M: $i] : (~((~(max(M, R, E) | (~member(M, E)) | (~((M = tptp_fun_X_10(M, E, R)) | (~member(tptp_fun_X_10(M, E, R), E)) | (~apply(R, M, tptp_fun_X_10(M, E, R))))))) | (~((~max(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((M = X) | (~member(X, E)) | (~apply(R, M, X))))))))))) | (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (~((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[108, 23])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (((~(max(M2!16, R!15, E!14) | (~member(M2!16, E!14)) | (~((~apply(R!15, M2!16, tptp_fun_X_10(M2!16, E!14, R!15))) | (~member(tptp_fun_X_10(M2!16, E!14, R!15), E!14)) | (M2!16 = tptp_fun_X_10(M2!16, E!14, R!15)))))) | (~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))))) | ((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 ((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (max(M2!16, R!15, E!14)),
% 0.18/0.41 inference(and_elim,[status(thm)],[44])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 ((~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))) | (~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 ((~((~max(M2!16, R!15, E!14)) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))))) | (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (~((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))) | member(M2!16, E!14)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (member(M2!16, E!14)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | ((~member(M2!16, E!14)) | apply(R!15, M2!16, M!18))) <=> ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | (~member(M2!16, E!14)) | apply(R!15, M2!16, M!18))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | ((~member(M2!16, E!14)) | apply(R!15, M2!16, M!18))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, E!14)) | apply(R!15, X, M!18))) | (~member(M2!16, E!14)) | apply(R!15, M2!16, M!18)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (apply(R!15, M2!16, M!18)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[120, 82, 117])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (((~member(M2!16, E!14)) | (~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X))))) | ![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (((~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))) | ((~member(M!18, E!14)) | (M2!16 = M!18) | (~apply(R!15, M2!16, M!18)))) <=> ((~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))) | (~member(M!18, E!14)) | (M2!16 = M!18) | (~apply(R!15, M2!16, M!18)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))) | ((~member(M!18, E!14)) | (M2!16 = M!18) | (~apply(R!15, M2!16, M!18)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, E!14)) | (M2!16 = X) | (~apply(R!15, M2!16, X)))) | (~member(M!18, E!14)) | (M2!16 = M!18) | (~apply(R!15, M2!16, M!18))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 ((M2!16 = M!18) | (~apply(R!15, M2!16, M!18))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[126, 90, 123])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (M2!16 = M!18),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[127, 121])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[128, 102])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------