%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET694+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 05:26:10 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET694+4 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:42:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(member_type, type, (
% 0.20/0.37 member: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_A_4_type, type, (
% 0.20/0.37 tptp_fun_A_4: $i)).
% 0.20/0.37 tff(tptp_fun_X_0_type, type, (
% 0.20/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.37 tff(union_type, type, (
% 0.20/0.37 union: ( $i * $i ) > $i)).
% 0.20/0.37 tff(power_set_type, type, (
% 0.20/0.37 power_set: $i > $i)).
% 0.20/0.37 tff(tptp_fun_B_3_type, type, (
% 0.20/0.37 tptp_fun_B_3: $i)).
% 0.20/0.37 tff(subset_type, type, (
% 0.20/0.37 subset: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.37 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.37 tff(14,plain,(
% 0.20/0.37 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[13])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (~((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))))))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))))) | ((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,(
% 0.20/0.38 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.20/0.38 inference(skolemize,[status(sab)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,assumption,(~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3))), introduced(assumption)).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 27, 30])).
% 0.20/0.38 tff(33,plain,(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(34,assumption,((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3)))))), introduced(assumption)).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~![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(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[35, 16, 34])).
% 0.20/0.38 tff(37,plain,(~((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3)))))) | ((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.38 tff(40,assumption,(![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))), introduced(assumption)).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.38 tff(46,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.38 tff(49,plain,(
% 0.20/0.38 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((~![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(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, union(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (~((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, union(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[53, 16])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, union(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))))))) | (subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 27])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(power_set(A!4), power_set(B!3)))) | member(X, power_set(union(A!4, B!3)))))) | (~(subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (~((~((~subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(power_set(A!4), power_set(B!3)))) | member(X, power_set(union(A!4, B!3)))))) | (~(subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 16])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~((~subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(power_set(A!4), power_set(B!3)))) | member(X, power_set(union(A!4, B!3)))))) | (~(subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))))))) | (subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))) <=> (~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(64,axiom,(~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI22')).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(union(power_set(A), power_set(B)), power_set(union(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.39 tff(69,plain,(
% 0.20/0.39 ~subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~(subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))))) | subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~(subset(union(power_set(A!4), power_set(B!3)), power_set(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (~((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 62])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))) | (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))) | (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)))) | (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[76, 58])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))))) | subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 ((~(subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (~((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[79, 56])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))) | (~(member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~(member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 52])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), union(A!4, B!3))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[88, 80])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 89, 87, 40])).
% 0.20/0.40 tff(94,plain,(~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[96, 39])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3))) | (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3))) | subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), B!3))) | (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 33])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3))) <=> (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3))) <=> (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 50])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(union(A!4, B!3)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[103, 72])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3))) <=> (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))))) | (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3)))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), union(power_set(A!4), power_set(B!3))) <=> (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))))) | (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)))) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(B!3)) | member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[109, 100])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4))) | (~member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4))) | subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4))) | subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 29])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~((~subset(tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[115, 20])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ((member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[117, 85])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(union(A!4, B!3), tptp_fun_X_0(power_set(union(A!4, B!3)), union(power_set(A!4), power_set(B!3)))), A!4)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[121, 89, 118, 116])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------