%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET372+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:25:40 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET372+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 05:03:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_3: $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(power_set_type, type, (
% 0.12/0.38 power_set: $i > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equal_set_type, type, (
% 0.12/0.38 equal_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,assumption,((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,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))))))) <=> ![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,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))))))) <=> ![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,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))))))) <=> ![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)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(8,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))))) <=> ![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.38 tff(15,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)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[14])).
% 0.12/0.38 tff(16,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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.12/0.38 tff(17,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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.12/0.38 tff(18,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(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.12/0.38 tff(20,plain,(~((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))) | (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.39 tff(29,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)],[28, 27])).
% 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)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[29])).
% 0.19/0.39 tff(31,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)],[30, 26])).
% 0.19/0.39 tff(32,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)],[31, 24])).
% 0.19/0.39 tff(33,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!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,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(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 17])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))))) | (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,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(40,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)],[39])).
% 0.19/0.39 tff(41,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(42,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.19/0.39 tff(43,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)],[42, 41])).
% 0.19/0.39 tff(44,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)],[43])).
% 0.19/0.39 tff(45,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)],[44, 40])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.39 tff(48,assumption,(~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))), introduced(assumption)).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 38])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 34])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 17])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))) | ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 45])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (~(((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[68, 32])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 48])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 69])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 67])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 65])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 56])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 84, 82])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 17])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)))))) | ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 45])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 74])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 94])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[101, 92])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 84, 102])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 106, 88, 61])).
% 0.19/0.42 tff(109,plain,((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))) | subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))) | subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 22])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(118,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,(
% 0.19/0.42 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[119])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) <=> equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (~(((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) <=> equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))) <=> (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,axiom,(~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI21')).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.42 tff(131,plain,(
% 0.19/0.42 ~equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) <=> equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) <=> equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 124])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))) | (~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 112])).
% 0.19/0.42 tff(138,assumption,((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))), introduced(assumption)).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~![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(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 17, 138])).
% 0.19/0.42 tff(141,plain,(~((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))) | (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 ((~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))) | subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[145, 137])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.43 tff(149,assumption,(~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))), introduced(assumption)).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[150, 45, 149])).
% 0.19/0.43 tff(152,plain,(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 148])).
% 0.19/0.43 tff(156,assumption,((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))))), introduced(assumption)).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 17, 156])).
% 0.19/0.43 tff(159,plain,(~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))))) | ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 ((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 (![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[163, 155])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 17])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))))) | (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[169, 45])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (~(((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[171, 32])).
% 0.19/0.44 tff(173,assumption,(~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))), introduced(assumption)).
% 0.19/0.44 tff(174,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 ((((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 ((((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))) <=> member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[177, 172])).
% 0.19/0.44 tff(179,assumption,(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))), introduced(assumption)).
% 0.19/0.44 tff(180,plain,
% 0.19/0.44 ((~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(181,plain,
% 0.19/0.44 ((~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[184, 170])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[187, 168])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(190,plain,
% 0.19/0.44 (member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[157, 17])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[160, 191])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[150, 45])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[147, 173])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 194])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[195, 193])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 ((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[162, 196])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 (![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[197, 192])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[199, 188])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.19/0.45 tff(203,assumption,(((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))), introduced(assumption)).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[204, 32, 203])).
% 0.19/0.45 tff(206,plain,(~(((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(207,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(208,plain,
% 0.19/0.45 ((~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.19/0.45 tff(209,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[208, 202])).
% 0.19/0.45 tff(210,plain,
% 0.19/0.45 (((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(211,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(212,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.45 tff(213,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[212, 209, 198, 190])).
% 0.19/0.45 tff(214,plain,(((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(215,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[214, 146])).
% 0.19/0.45 tff(216,assumption,(~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))), introduced(assumption)).
% 0.19/0.45 tff(217,plain,
% 0.19/0.45 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(218,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[217, 45, 216])).
% 0.19/0.45 tff(219,plain,(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(220,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[221, 215])).
% 0.19/0.46 tff(223,assumption,((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))), introduced(assumption)).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(225,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[224, 17, 223])).
% 0.19/0.46 tff(226,plain,(~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))) | (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.19/0.46 tff(229,plain,
% 0.19/0.46 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(230,plain,
% 0.19/0.46 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[230, 222])).
% 0.19/0.46 tff(232,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 (member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.19/0.46 tff(234,assumption,(member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))), introduced(assumption)).
% 0.19/0.46 tff(235,assumption,(![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))), introduced(assumption)).
% 0.19/0.46 tff(236,assumption,(~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))), introduced(assumption)).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[239, 236, 235, 234])).
% 0.19/0.46 tff(241,plain,((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) | (~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 (member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[241, 233, 164])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[243, 231])).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(246,plain,
% 0.19/0.47 ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.19/0.47 tff(247,assumption,(((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))), introduced(assumption)).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(249,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[248, 32, 247])).
% 0.19/0.47 tff(250,plain,(~(((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(251,plain,
% 0.19/0.47 ((((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) <=> member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(252,plain,
% 0.19/0.47 ((~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.19/0.47 tff(253,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[252, 246, 242])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------