%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET807+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET807+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:44:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_X_16_type, type, (
% 0.20/0.39 tptp_fun_X_16: ( $i * $i ) > $i)).
% 0.20/0.39 tff(subset_predicate_type, type, (
% 0.20/0.39 subset_predicate: $i)).
% 0.20/0.39 tff(power_set_type, type, (
% 0.20/0.39 power_set: $i > $i)).
% 0.20/0.39 tff(tptp_fun_E_20_type, type, (
% 0.20/0.39 tptp_fun_E_20: $i)).
% 0.20/0.39 tff(apply_type, type, (
% 0.20/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Z_17_type, type, (
% 0.20/0.39 tptp_fun_Z_17: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_19_type, type, (
% 0.20/0.39 tptp_fun_X_19: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_Y_18_type, type, (
% 0.20/0.39 tptp_fun_Y_18: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(pre_order_type, type, (
% 0.20/0.39 pre_order: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl((apply(subset_predicate, X, Y) <=> subset(X, Y)) <=> (apply(subset_predicate, X, Y) <=> subset(X, Y)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y)) <=> ![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y)) <=> ![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,axiom,(![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rel_subset')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))) | (apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[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)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,(
% 0.20/0.40 ![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)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![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(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~((~((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (((~((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))))) | ((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))) | (apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[30, 7])).
% 0.20/0.40 tff(32,assumption,(~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))), introduced(assumption)).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~(apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~(apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 31])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~((~subset(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | ![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[39, 29])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~![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(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (~((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 25])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))))) | (subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))) | (apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 7])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 32])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | (~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 46])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (~((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 44])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | ((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | ((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Z_17(power_set(E!20), subset_predicate)))) | (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 56, 40])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ((~![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(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (~((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 25])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))))))) | ((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (apply(subset_predicate, X, Y) <=> subset(X, Y))) | (apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 7])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 32])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 66])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))) | (~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~((~subset(tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate))))) | ![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 64])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 54])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | ((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | ((~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![X: $i] : ((~member(X, tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(X, tptp_fun_Y_18(power_set(E!20), subset_predicate)))) | (~member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_X_19(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_Z_17(power_set(E!20), subset_predicate), tptp_fun_X_19(power_set(E!20), subset_predicate)), tptp_fun_Y_18(power_set(E!20), subset_predicate))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 76, 74, 60])).
% 0.20/0.42 tff(81,plain,((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (^[R: $i, E: $i] : refl((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) <=> ((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))) <=> (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), rewrite((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))), rewrite((((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (^[R: $i, E: $i] : rewrite((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (^[R: $i, E: $i] : rewrite((pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![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))))) <=> (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![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] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.43 tff(96,axiom,(![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![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/sandbox2/benchmark/Axioms/SET006+2.ax','pre_order')).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.43 tff(99,plain,(
% 0.20/0.43 ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![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)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 88])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 83])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z)))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z)))))))))) <=> (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z)))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z)))))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[106, 104])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~(apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (~((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z)))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[109, 103])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~pre_order(subset_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(subset_predicate, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(subset_predicate, X, Z) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))) | (~member(X, power_set(E!20))) | (~apply(subset_predicate, X, Y)) | (~apply(subset_predicate, Y, Z))))))))) | (pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~![E: $i] : pre_order(subset_predicate, power_set(E))) <=> (~![E: $i] : pre_order(subset_predicate, power_set(E)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(114,axiom,(~![E: $i] : pre_order(subset_predicate, power_set(E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIV18a')).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~![E: $i] : pre_order(subset_predicate, power_set(E))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (~![E: $i] : pre_order(subset_predicate, power_set(E))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 113])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (~![E: $i] : pre_order(subset_predicate, power_set(E))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (~![E: $i] : pre_order(subset_predicate, power_set(E))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.44 tff(119,plain,(
% 0.20/0.44 ~pre_order(subset_predicate, power_set(E!20))),
% 0.20/0.44 inference(skolemize,[status(sab)],[118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~(pre_order(subset_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate)))))) | (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~((~member(tptp_fun_Z_17(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_Y_18(power_set(E!20), subset_predicate), power_set(E!20))) | (~member(tptp_fun_X_19(power_set(E!20), subset_predicate), power_set(E!20))) | (~apply(subset_predicate, tptp_fun_Y_18(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Y_18(power_set(E!20), subset_predicate))) | apply(subset_predicate, tptp_fun_X_19(power_set(E!20), subset_predicate), tptp_fun_Z_17(power_set(E!20), subset_predicate))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 112])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (~((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 81])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (((~member(tptp_fun_X_16(power_set(E!20), subset_predicate), power_set(E!20))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | (~apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (~apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~(apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~(apply(subset_predicate, tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) | (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[127, 9])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 ((~(~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (($false | (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))) <=> (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate)))))) <=> (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~$true) <=> $false),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | $true) <=> $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (![X: $i] : $true <=> $true),
% 0.20/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![X: $i] : $true <=> ![X: $i] : $true),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![X: $i] : $true <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[136, 135])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (^[X: $i] : rewrite(((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) <=> $true)),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) <=> ![X: $i] : $true),
% 0.20/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[139, 137])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate)))) <=> ((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | $true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate)))) <=> $true),
% 0.20/0.45 inference(transitivity,[status(thm)],[141, 134])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) <=> (~$true)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) <=> $false),
% 0.20/0.45 inference(transitivity,[status(thm)],[143, 133])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))))))) <=> ($false | (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[144, 132])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))))))) <=> (~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[145, 131])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ((~((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate)))))))) <=> (~(~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 ((~((~((~subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate)))))))) <=> subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.45 inference(transitivity,[status(thm)],[147, 130])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))))))))) <=> ((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))))))))) <=> ((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[149, 129])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ((~![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(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))) | ![X: $i] : ((~member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(X, tptp_fun_X_16(power_set(E!20), subset_predicate))))) | (~(subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)) | (~((~member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))) | member(tptp_fun_X_0(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate)), tptp_fun_X_16(power_set(E!20), subset_predicate))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_16(power_set(E!20), subset_predicate), tptp_fun_X_16(power_set(E!20), subset_predicate))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[152, 25, 128])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------