%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET347+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:25:38 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET347+4 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:54:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(empty_set_type, type, (
% 0.12/0.37 empty_set: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(sum_type, type, (
% 0.12/0.37 sum: $i > $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.37 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.12/0.37 tff(equal_set_type, type, (
% 0.12/0.37 equal_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (^[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)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.37 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.37 tff(14,plain,(
% 0.12/0.37 ![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)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![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(empty_set, sum(empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, sum(empty_set))))) | (~(subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~((~((~subset(empty_set, sum(empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, sum(empty_set))))) | (~(subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set)))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~((~subset(empty_set, sum(empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, sum(empty_set))))) | (~(subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))))))) | (subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set)))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,assumption,((~((~subset(sum(empty_set), empty_set)) | ![X: $i] : ((~member(X, sum(empty_set))) | member(X, empty_set)))) | (~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)))))), introduced(assumption)).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(sum(empty_set), empty_set)) | ![X: $i] : ((~member(X, sum(empty_set))) | member(X, empty_set)))) | (~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.12/0.38 tff(24,plain,(~((~((~subset(sum(empty_set), empty_set)) | ![X: $i] : ((~member(X, sum(empty_set))) | member(X, empty_set)))) | (~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (((~((~subset(sum(empty_set), empty_set)) | ![X: $i] : ((~member(X, sum(empty_set))) | member(X, empty_set)))) | (~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)))))) | (subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,assumption,((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))))), introduced(assumption)).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[31, 29])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(36,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','sum')).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,(
% 0.12/0.38 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))))))) | (~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))))) <=> (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))))))) | (~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))))))) | (~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[43, 41])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))))))) | (~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[46, 40, 27])).
% 0.12/0.38 tff(48,plain,(~((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (((~(member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), Y))))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))))) | ((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,assumption,(member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)), introduced(assumption)).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(55,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![X: $i] : (~member(X, empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.39 tff(57,plain,(
% 0.12/0.39 ![X: $i] : (~member(X, empty_set))),
% 0.12/0.39 inference(skolemize,[status(sab)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X: $i] : (~member(X, empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[59, 58, 51])).
% 0.12/0.39 tff(61,plain,(~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))) | member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))))) | (~member(tptp_fun_Y_1(empty_set, tptp_fun_X_0(empty_set, sum(empty_set))), empty_set)))))) | (~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 50])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)) | member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set))))) | subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~(subset(sum(empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, sum(empty_set)), sum(empty_set))) | member(tptp_fun_X_0(empty_set, sum(empty_set)), empty_set))))) | subset(sum(empty_set), empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (subset(sum(empty_set), empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 26])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(77,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.39 tff(79,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[78])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))) <=> equal_set(sum(empty_set), empty_set)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (~(((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))) <=> equal_set(sum(empty_set), empty_set))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 ((~equal_set(sum(empty_set), empty_set)) <=> (~equal_set(sum(empty_set), empty_set))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(85,axiom,(~equal_set(sum(empty_set), empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI38')).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (~equal_set(sum(empty_set), empty_set)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))) <=> equal_set(sum(empty_set), empty_set)) | ((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))) | equal_set(sum(empty_set), empty_set)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))) <=> equal_set(sum(empty_set), empty_set)) | ((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[88, 83])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 ((~((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set))))) | (~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 ((~subset(sum(empty_set), empty_set)) | (~subset(empty_set, sum(empty_set)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (~subset(empty_set, sum(empty_set))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[91, 71])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 ((~(subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set)))))) | subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ((~(subset(empty_set, sum(empty_set)) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set)))))) | (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (~((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[94, 20])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(sum(empty_set), empty_set), sum(empty_set))) | member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(sum(empty_set), empty_set), empty_set))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[98, 58, 97])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------