%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET805+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:23 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET805+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 05:42:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_E_17_type, type, (
% 0.19/0.38 tptp_fun_E_17: $i)).
% 0.19/0.38 tff(tptp_fun_Z_6_type, type, (
% 0.19/0.38 tptp_fun_Z_6: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_R_18_type, type, (
% 0.19/0.38 tptp_fun_R_18: $i)).
% 0.19/0.38 tff(tptp_fun_X_19_type, type, (
% 0.19/0.38 tptp_fun_X_19: $i)).
% 0.19/0.38 tff(apply_type, type, (
% 0.19/0.38 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_8_type, type, (
% 0.19/0.38 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y_7_type, type, (
% 0.19/0.38 tptp_fun_Y_7: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y_4_type, type, (
% 0.19/0.38 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_5_type, type, (
% 0.19/0.38 tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(order_type, type, (
% 0.19/0.38 order: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_3_type, type, (
% 0.19/0.38 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,assumption,(~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))) | member(tptp_fun_X_5(X!19, R!18), X!19)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (member(tptp_fun_X_5(X!19, R!18), X!19)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[7, 5])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.38 tff(17,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))) | (~(subset(X!19, E!17) | (~((~member(tptp_fun_X_0(E!17, X!19), X!19)) | member(tptp_fun_X_0(E!17, X!19), E!17)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (~((~((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))) | (~(subset(X!19, E!17) | (~((~member(tptp_fun_X_0(E!17, X!19), X!19)) | member(tptp_fun_X_0(E!17, X!19), E!17))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (((~((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))) | (~(subset(X!19, E!17) | (~((~member(tptp_fun_X_0(E!17, X!19), X!19)) | member(tptp_fun_X_0(E!17, X!19), E!17)))))) | ((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X)))) <=> (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((~![R: $i, E: $i] : (order(R, E) => ![X: $i] : (subset(X, E) => order(R, X)))) <=> (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,axiom,(~![R: $i, E: $i] : (order(R, E) => ![X: $i] : (subset(X, E) => order(R, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIV17')).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (~![R: $i, E: $i] : ((~order(R, E)) | ![X: $i] : ((~subset(X, E)) | order(R, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (~((~subset(X!19, E!17)) | order(R!18, X!19))),
% 0.19/0.38 inference(and_elim,[status(thm)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (subset(X!19, E!17)),
% 0.19/0.38 inference(or_elim,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))) | (~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~((~subset(X!19, E!17)) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17)))) | ![X: $i] : ((~member(X, X!19)) | member(X, E!17))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![X: $i] : ((~member(X, X!19)) | member(X, E!17))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 23])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_5(X!19, R!18), X!19)) | member(tptp_fun_X_5(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | member(tptp_fun_X_5(X!19, R!18), E!17))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_5(X!19, R!18), X!19)) | member(tptp_fun_X_5(X!19, R!18), E!17))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | member(tptp_fun_X_5(X!19, R!18), E!17)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (member(tptp_fun_X_5(X!19, R!18), E!17)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[38, 35, 3])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))) | member(tptp_fun_Y_4(X!19, R!18), X!19)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (member(tptp_fun_Y_4(X!19, R!18), X!19)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | member(tptp_fun_Y_4(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)) | member(tptp_fun_Y_4(X!19, R!18), E!17))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | member(tptp_fun_Y_4(X!19, R!18), E!17))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)) | member(tptp_fun_Y_4(X!19, R!18), E!17)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (member(tptp_fun_Y_4(X!19, R!18), E!17)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 35, 41])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))) | (~(tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (~(tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 1])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))) | apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[48, 1])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))) | apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 1])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E)))))))) <=> (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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)))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (^[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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (^[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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (^[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_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) <=> (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E))))), rewrite((~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E))))) <=> (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))), ((order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))), rewrite((order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))) <=> (order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E)))))), ((order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,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')).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.40 tff(69,plain,(
% 0.19/0.40 ![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E))))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R)) & apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R)))) | (~(member(tptp_fun_X_8(E, R), E) & member(tptp_fun_Y_7(E, R), E) & member(tptp_fun_Z_6(E, R), E)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![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_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(E, R), E))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 58])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 53])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 ((~((~(order(R!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~member(tptp_fun_Y_4(E!17, R!18), E!17)))) | (~(apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_Z_6(E!17, R!18), E!17)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!17)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, E!17)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))))) <=> (~((~(order(R!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~member(tptp_fun_Y_4(E!17, R!18), E!17)))) | (~(apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_Z_6(E!17, R!18), E!17)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!17)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, E!17)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~member(tptp_fun_Y_4(E!17, R!18), E!17)))) | (~(apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_Z_6(E!17, R!18), E!17)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!17)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, E!17)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~member(tptp_fun_Y_4(E!17, R!18), E!17)))) | (~(apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_Z_6(E!17, R!18), E!17)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!17)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, E!17)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (~((~(order(R!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~(order(R!18, E!17) | (~((~member(tptp_fun_X_3(E!17, R!18), E!17)) | apply(R!18, tptp_fun_X_3(E!17, R!18), tptp_fun_X_3(E!17, R!18)))) | (~((~member(tptp_fun_Y_4(E!17, R!18), E!17)) | (~member(tptp_fun_X_5(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(E!17, R!18), tptp_fun_X_5(E!17, R!18))) | (~apply(R!18, tptp_fun_X_5(E!17, R!18), tptp_fun_Y_4(E!17, R!18))) | (tptp_fun_X_5(E!17, R!18) = tptp_fun_Y_4(E!17, R!18)))) | (~((~member(tptp_fun_Z_6(E!17, R!18), E!17)) | (~member(tptp_fun_Y_7(E!17, R!18), E!17)) | (~member(tptp_fun_X_8(E!17, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_7(E!17, R!18), tptp_fun_Z_6(E!17, R!18))) | (~apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Y_7(E!17, R!18))) | apply(R!18, tptp_fun_X_8(E!17, R!18), tptp_fun_Z_6(E!17, R!18)))))) | (~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))))) | ((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (order(R!18, E!17)),
% 0.19/0.42 inference(and_elim,[status(thm)],[30])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))) | (~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~((~order(R!18, E!17)) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))))) | (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (~((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))) | ![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | ((~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), E!17)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18)))) <=> ((~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | ((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), E!17)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | ((~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | ((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), E!17)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | ((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), E!17)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((~member(tptp_fun_Y_4(X!19, R!18), E!17)) | (~member(tptp_fun_X_5(X!19, R!18), E!17))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[94, 88, 51, 49, 47])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 45, 39])).
% 0.19/0.43 tff(97,plain,((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(98,assumption,(~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))), introduced(assumption)).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18))) | (~apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (~apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))) | ![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 86])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | ((~member(tptp_fun_X_3(X!19, R!18), E!17)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) <=> ((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~member(tptp_fun_X_3(X!19, R!18), E!17)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | ((~member(tptp_fun_X_3(X!19, R!18), E!17)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~member(tptp_fun_X_3(X!19, R!18), E!17)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (~member(tptp_fun_X_3(X!19, R!18), E!17)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 102, 100])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18))) | member(tptp_fun_X_3(X!19, R!18), X!19)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (member(tptp_fun_X_3(X!19, R!18), X!19)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 98])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_3(X!19, R!18), X!19)) | member(tptp_fun_X_3(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_3(X!19, R!18), X!19)) | member(tptp_fun_X_3(X!19, R!18), E!17))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_3(X!19, R!18), X!19)) | member(tptp_fun_X_3(X!19, R!18), E!17))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_3(X!19, R!18), X!19)) | member(tptp_fun_X_3(X!19, R!18), E!17)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[111, 35, 108, 106])).
% 0.19/0.43 tff(113,plain,((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 ((~((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)))) | (~(apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)) | (~member(Z, X!19)))))))))) <=> (~((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)))) | (~(apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)) | (~member(Z, X!19))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)))) | (~(apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)) | (~member(Z, X!19))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~member(tptp_fun_Y_4(X!19, R!18), X!19)))) | (~(apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)) | (~member(Z, X!19))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_3(E, R), E)) | apply(R, tptp_fun_X_3(E, R), tptp_fun_X_3(E, R)))) | (~((tptp_fun_X_5(E, R) = tptp_fun_Y_4(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_X_5(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)))) | (~(apply(R, tptp_fun_X_8(E, R), tptp_fun_Z_6(E, R)) | (~apply(R, tptp_fun_X_8(E, R), tptp_fun_Y_7(E, R))) | (~apply(R, tptp_fun_Y_7(E, R), tptp_fun_Z_6(E, R))) | (~member(tptp_fun_X_8(E, R), E)) | (~member(tptp_fun_Y_7(E, R), E)) | (~member(tptp_fun_Z_6(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!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (~((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19)))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[119, 73])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~order(R!18, X!19)) | (~((~![X: $i] : ((~member(X, X!19)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, X!19)) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, X)) | (~member(X, X!19)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!19)) | apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, X!19)) | (~member(Y, X!19))))))))) | (order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (~order(R!18, X!19)),
% 0.19/0.45 inference(or_elim,[status(thm)],[31])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 ((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 ((~(order(R!18, X!19) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))))) | (~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ((~((~member(tptp_fun_X_3(X!19, R!18), X!19)) | apply(R!18, tptp_fun_X_3(X!19, R!18), tptp_fun_X_3(X!19, R!18)))) | (~((~member(tptp_fun_Y_4(X!19, R!18), X!19)) | (~member(tptp_fun_X_5(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_4(X!19, R!18), tptp_fun_X_5(X!19, R!18))) | (~apply(R!18, tptp_fun_X_5(X!19, R!18), tptp_fun_Y_4(X!19, R!18))) | (tptp_fun_X_5(X!19, R!18) = tptp_fun_Y_4(X!19, R!18)))) | (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (~((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 113, 97])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | member(tptp_fun_Z_6(X!19, R!18), X!19)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (member(tptp_fun_Z_6(X!19, R!18), X!19)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | member(tptp_fun_Z_6(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)) | member(tptp_fun_Z_6(X!19, R!18), E!17))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | member(tptp_fun_Z_6(X!19, R!18), E!17))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Z_6(X!19, R!18), X!19)) | member(tptp_fun_Z_6(X!19, R!18), E!17)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (member(tptp_fun_Z_6(X!19, R!18), E!17)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[132, 35, 129])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | member(tptp_fun_X_8(X!19, R!18), X!19)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (member(tptp_fun_X_8(X!19, R!18), X!19)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 127])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_8(X!19, R!18), X!19)) | member(tptp_fun_X_8(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | member(tptp_fun_X_8(X!19, R!18), E!17))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_X_8(X!19, R!18), X!19)) | member(tptp_fun_X_8(X!19, R!18), E!17))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | member(tptp_fun_X_8(X!19, R!18), E!17)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (member(tptp_fun_X_8(X!19, R!18), E!17)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 35, 135])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | member(tptp_fun_Y_7(X!19, R!18), X!19)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (member(tptp_fun_Y_7(X!19, R!18), X!19)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 127])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Y_7(X!19, R!18), X!19)) | member(tptp_fun_Y_7(X!19, R!18), E!17))) <=> ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | member(tptp_fun_Y_7(X!19, R!18), E!17))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | ((~member(tptp_fun_Y_7(X!19, R!18), X!19)) | member(tptp_fun_Y_7(X!19, R!18), E!17))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, X!19)) | member(X, E!17))) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | member(tptp_fun_Y_7(X!19, R!18), E!17)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (member(tptp_fun_Y_7(X!19, R!18), E!17)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[144, 35, 141])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[146, 127])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[148, 127])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (((~member(tptp_fun_Z_6(X!19, R!18), X!19)) | (~member(tptp_fun_Y_7(X!19, R!18), X!19)) | (~member(tptp_fun_X_8(X!19, R!18), X!19)) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 (apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[150, 127])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, E!17)) | apply(R!18, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~apply(R!18, X, Y)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~apply(R!18, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17))))) | ![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[152, 86])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | ((~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 ((apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17))) <=> ((~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | ((~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (apply(R!18, X, Z) | (~apply(R!18, X, Y)) | (~apply(R!18, Y, Z)) | (~member(X, E!17)) | (~member(Y, E!17)) | (~member(Z, E!17)))) | (~apply(R!18, tptp_fun_Y_7(X!19, R!18), tptp_fun_Z_6(X!19, R!18))) | (~apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Y_7(X!19, R!18))) | apply(R!18, tptp_fun_X_8(X!19, R!18), tptp_fun_Z_6(X!19, R!18)) | (~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 ((~member(tptp_fun_X_8(X!19, R!18), E!17)) | (~member(tptp_fun_Y_7(X!19, R!18), E!17)) | (~member(tptp_fun_Z_6(X!19, R!18), E!17))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[159, 153, 151, 149, 147])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[160, 145, 139, 133])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------