%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET812+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:24 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET812+4 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 05:43:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(intersection_type, type, (
% 0.19/0.38 intersection: ( $i * $i ) > $i)).
% 0.19/0.38 tff(power_set_type, type, (
% 0.19/0.38 power_set: $i > $i)).
% 0.19/0.38 tff(tptp_fun_A_13_type, type, (
% 0.19/0.38 tptp_fun_A_13: $i)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(strict_well_order_type, type, (
% 0.19/0.38 strict_well_order: ( $i * $i ) > $o)).
% 0.19/0.38 tff(member_predicate_type, type, (
% 0.19/0.38 member_predicate: $i)).
% 0.19/0.38 tff(set_type, type, (
% 0.19/0.38 set: $i > $o)).
% 0.19/0.38 tff(on_type, type, (
% 0.19/0.38 on: $i)).
% 0.19/0.38 tff(tptp_fun_X_3_type, type, (
% 0.19/0.38 tptp_fun_X_3: $i > $i)).
% 0.19/0.38 tff(equal_set_type, type, (
% 0.19/0.38 equal_set: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.38 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')).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.38 tff(14,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))))) | (subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,assumption,((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))), introduced(assumption)).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![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)))))))) | (~((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.19/0.39 tff(24,plain,(~((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))) | (subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,(
% 0.19/0.39 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))) <=> member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~(((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))) <=> member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,assumption,(~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))), introduced(assumption)).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))) <=> member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))) <=> member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.19/0.39 tff(45,assumption,(~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))), introduced(assumption)).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,(
% 0.19/0.39 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.39 inference(skolemize,[status(sab)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.19/0.39 tff(55,plain,(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 39])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (^[A: $i] : refl((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(rewrite(((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))), rewrite((member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))) <=> (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))), rewrite((((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (^[A: $i] : rewrite((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (^[A: $i] : rewrite((member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.40 tff(72,axiom,(![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax','ordinal_number')).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.40 tff(75,plain,(
% 0.19/0.40 ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 64])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 59])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))) <=> (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[85, 79])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))) | ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![A: $i] : (member(A, on) => equal_set(A, intersection(A, power_set(A))))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(91,axiom,(~![A: $i] : (member(A, on) => equal_set(A, intersection(A, power_set(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thV10')).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 89])).
% 0.19/0.40 tff(96,plain,(
% 0.19/0.40 ~((~member(A!13, on)) | equal_set(A!13, intersection(A!13, power_set(A!13))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[95])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (member(A!13, on)),
% 0.19/0.40 inference(or_elim,[status(thm)],[96])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 88])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))) | ![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))) <=> ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 102, 57])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) | (~subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 106, 55])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 57])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 108, 44])).
% 0.19/0.41 tff(112,plain,((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))) | subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 ((~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))) | subset(A!13, intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (subset(A!13, intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[114, 26])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(121,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')).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.41 tff(123,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[122])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))) <=> equal_set(A!13, intersection(A!13, power_set(A!13)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (~(((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))) <=> equal_set(A!13, intersection(A!13, power_set(A!13))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (~equal_set(A!13, intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[96])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))) <=> equal_set(A!13, intersection(A!13, power_set(A!13)))) | ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))) | equal_set(A!13, intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ((((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))) <=> equal_set(A!13, intersection(A!13, power_set(A!13)))) | ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))) | (~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (~subset(intersection(A!13, power_set(A!13)), A!13)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[133, 115])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 ((~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))) | subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[136, 20])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 137])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 ((((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))) <=> member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13))))) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))) <=> member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[144, 143, 141])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))) <=> member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[146, 36, 145])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------