%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET690+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:09 AM UTC 2025
% Result : Theorem 0.86s 1.05s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET690+4 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 05:38:24 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.86/1.05 % SZS status Theorem
% 0.86/1.05 % SZS output start Proof
% 0.86/1.05 tff(member_type, type, (
% 0.86/1.05 member: ( $i * $i ) > $o)).
% 0.86/1.05 tff(intersection_type, type, (
% 0.86/1.05 intersection: ( $i * $i ) > $i)).
% 0.86/1.05 tff(union_type, type, (
% 0.86/1.05 union: ( $i * $i ) > $i)).
% 0.86/1.05 tff(tptp_fun_C_3_type, type, (
% 0.86/1.05 tptp_fun_C_3: $i)).
% 0.86/1.05 tff(tptp_fun_B_4_type, type, (
% 0.86/1.05 tptp_fun_B_4: $i)).
% 0.86/1.05 tff(tptp_fun_A_5_type, type, (
% 0.86/1.05 tptp_fun_A_5: $i)).
% 0.86/1.05 tff(difference_type, type, (
% 0.86/1.05 difference: ( $i * $i ) > $i)).
% 0.86/1.05 tff(subset_type, type, (
% 0.86/1.05 subset: ( $i * $i ) > $o)).
% 0.86/1.05 tff(tptp_fun_X_0_type, type, (
% 0.86/1.05 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.86/1.05 tff(equal_set_type, type, (
% 0.86/1.05 equal_set: ( $i * $i ) > $o)).
% 0.86/1.05 tff(1,assumption,((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))), introduced(assumption)).
% 0.86/1.05 tff(2,plain,
% 0.86/1.05 (^[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))))))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(3,plain,
% 0.86/1.05 (![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)))))))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[2])).
% 0.86/1.05 tff(4,plain,
% 0.86/1.05 (^[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))))))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(5,plain,
% 0.86/1.05 (![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)))))))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[4])).
% 0.86/1.05 tff(6,plain,
% 0.86/1.05 (![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)))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[5, 3])).
% 0.86/1.05 tff(7,plain,
% 0.86/1.05 (^[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)))))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(8,plain,
% 0.86/1.06 (![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)))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[7])).
% 0.86/1.06 tff(9,plain,
% 0.86/1.06 (![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)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(10,plain,
% 0.86/1.06 (^[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))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(11,plain,
% 0.86/1.06 (![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)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[10])).
% 0.86/1.06 tff(12,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.86/1.06 tff(13,plain,
% 0.86/1.06 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.86/1.06 tff(14,plain,
% 0.86/1.06 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.86/1.06 tff(15,plain,(
% 0.86/1.06 ![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)))))),
% 0.86/1.06 inference(skolemize,[status(sab)],[14])).
% 0.86/1.06 tff(16,plain,
% 0.86/1.06 (![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)))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.86/1.06 tff(17,plain,
% 0.86/1.06 (![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)))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.86/1.06 tff(18,plain,
% 0.86/1.06 (((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))))) <=> ((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(19,plain,
% 0.86/1.06 ((~((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))))))) <=> (~((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(20,plain,
% 0.86/1.06 (((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))))))))) <=> ((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[19])).
% 0.86/1.06 tff(21,plain,
% 0.86/1.06 (((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))))))))) <=> ((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[20, 18])).
% 0.86/1.06 tff(22,plain,
% 0.86/1.06 ((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(23,plain,
% 0.86/1.06 ((~![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(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.86/1.06 tff(24,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[23, 17, 1])).
% 0.86/1.06 tff(25,plain,(~((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(26,plain,
% 0.86/1.06 (((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))) | ((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(27,plain,
% 0.86/1.06 ((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.86/1.06 tff(28,plain,
% 0.86/1.06 (((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))))) | ((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(29,plain,
% 0.86/1.06 ((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.86/1.06 tff(30,plain,
% 0.86/1.06 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(31,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[30])).
% 0.86/1.06 tff(32,plain,
% 0.86/1.06 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(33,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[32])).
% 0.86/1.06 tff(34,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(35,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.86/1.06 tff(36,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.86/1.06 tff(37,plain,(
% 0.86/1.06 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.86/1.06 inference(skolemize,[status(sab)],[36])).
% 0.86/1.06 tff(38,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.86/1.06 tff(39,plain,
% 0.86/1.06 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.86/1.06 tff(40,plain,
% 0.86/1.06 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(41,plain,
% 0.86/1.06 (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.86/1.06 tff(42,assumption,(~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))), introduced(assumption)).
% 0.86/1.06 tff(43,plain,
% 0.86/1.06 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(44,plain,
% 0.86/1.06 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.86/1.06 tff(45,plain,
% 0.86/1.06 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(46,plain,
% 0.86/1.06 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.86/1.06 tff(47,plain,
% 0.86/1.06 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[46, 41])).
% 0.86/1.06 tff(48,plain,
% 0.86/1.06 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(49,plain,
% 0.86/1.06 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[48, 42])).
% 0.86/1.06 tff(50,plain,
% 0.86/1.06 (^[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)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(51,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[50])).
% 0.86/1.06 tff(52,plain,
% 0.86/1.06 (^[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))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(53,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[52])).
% 0.86/1.06 tff(54,plain,
% 0.86/1.06 (![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)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(55,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.86/1.06 tff(56,plain,
% 0.86/1.06 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.86/1.06 tff(57,plain,(
% 0.86/1.06 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.86/1.06 inference(skolemize,[status(sab)],[56])).
% 0.86/1.06 tff(58,plain,
% 0.86/1.06 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.86/1.06 tff(59,plain,
% 0.86/1.06 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.86/1.06 tff(60,plain,
% 0.86/1.06 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(61,plain,
% 0.86/1.06 (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.86/1.06 tff(62,assumption,(~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))), introduced(assumption)).
% 0.86/1.06 tff(63,plain,
% 0.86/1.06 ((~![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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(64,plain,
% 0.86/1.06 (~((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[63, 17])).
% 0.86/1.06 tff(65,plain,
% 0.86/1.06 (((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))) | (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(66,plain,
% 0.86/1.06 (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.86/1.06 tff(67,plain,
% 0.86/1.06 ((~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))) | subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(68,plain,
% 0.86/1.07 (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.86/1.07 tff(69,plain,
% 0.86/1.07 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[68, 62])).
% 0.86/1.07 tff(70,plain,
% 0.86/1.07 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(71,plain,
% 0.86/1.07 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.86/1.07 tff(72,plain,
% 0.86/1.07 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(73,plain,
% 0.86/1.07 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.86/1.07 tff(74,plain,
% 0.86/1.07 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[73, 61])).
% 0.86/1.07 tff(75,assumption,(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))), introduced(assumption)).
% 0.86/1.07 tff(76,plain,
% 0.86/1.07 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(77,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[76, 59, 75])).
% 0.86/1.07 tff(78,plain,(~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(79,plain,
% 0.86/1.07 (^[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))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(80,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[79])).
% 0.86/1.07 tff(81,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(82,plain,
% 0.86/1.07 (^[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))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(83,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[82])).
% 0.86/1.07 tff(84,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.86/1.07 tff(85,plain,
% 0.86/1.07 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.86/1.07 tff(86,plain,
% 0.86/1.07 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.86/1.07 tff(87,plain,(
% 0.86/1.07 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[86])).
% 0.86/1.07 tff(88,plain,
% 0.86/1.07 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.86/1.07 tff(89,plain,
% 0.86/1.07 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(90,plain,
% 0.86/1.07 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.86/1.07 tff(91,plain,
% 0.86/1.07 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(92,plain,
% 0.86/1.07 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[91, 69])).
% 0.86/1.07 tff(93,plain,
% 0.86/1.07 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(94,plain,
% 0.86/1.07 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.86/1.07 tff(95,plain,
% 0.86/1.07 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.86/1.07 tff(96,plain,
% 0.86/1.07 (((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) | subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(97,plain,
% 0.86/1.07 ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[96, 62])).
% 0.86/1.07 tff(98,plain,
% 0.86/1.07 (^[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))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(99,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[98])).
% 0.86/1.07 tff(100,plain,
% 0.86/1.07 (^[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)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(101,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[100])).
% 0.86/1.07 tff(102,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(103,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.86/1.07 tff(104,plain,
% 0.86/1.07 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.86/1.07 tff(105,plain,(
% 0.86/1.07 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[104])).
% 0.86/1.07 tff(106,plain,
% 0.86/1.07 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.86/1.07 tff(107,plain,
% 0.86/1.07 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.86/1.07 tff(108,plain,
% 0.86/1.07 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) <=> equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(109,plain,
% 0.86/1.07 (~(((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) <=> equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.86/1.07 tff(110,plain,
% 0.86/1.07 ((((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) <=> equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))) | (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(111,plain,
% 0.86/1.07 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))) | (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.86/1.07 tff(112,plain,
% 0.86/1.07 (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.86/1.07 tff(113,plain,
% 0.86/1.07 ((~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5))) <=> (~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(114,plain,
% 0.86/1.07 ((~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))) <=> (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(115,axiom,(~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI12')).
% 0.86/1.07 tff(116,plain,
% 0.86/1.07 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.86/1.07 tff(117,plain,
% 0.86/1.07 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.86/1.07 tff(118,plain,
% 0.86/1.07 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.86/1.07 tff(119,plain,
% 0.86/1.07 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.86/1.07 tff(120,plain,(
% 0.86/1.07 ~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5))),
% 0.86/1.07 inference(skolemize,[status(sab)],[119])).
% 0.86/1.07 tff(121,plain,
% 0.86/1.07 (~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.86/1.07 tff(122,plain,
% 0.86/1.07 ((equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5)) | equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | subset(C!3, A!5)),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(123,plain,
% 0.86/1.07 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | subset(C!3, A!5)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.86/1.07 tff(124,plain,
% 0.86/1.07 (subset(C!3, A!5)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[123, 112])).
% 0.86/1.07 tff(125,plain,
% 0.86/1.07 ((~![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(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(126,plain,
% 0.86/1.07 (~((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[125, 17])).
% 0.86/1.07 tff(127,plain,
% 0.86/1.07 (((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))) | ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(128,plain,
% 0.86/1.07 ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.86/1.07 tff(129,plain,
% 0.86/1.07 ((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(130,plain,
% 0.86/1.07 ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.86/1.07 tff(131,plain,
% 0.86/1.07 (![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.86/1.07 tff(132,assumption,((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))), introduced(assumption)).
% 0.86/1.07 tff(133,assumption,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)), introduced(assumption)).
% 0.86/1.07 tff(134,plain,
% 0.86/1.07 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(135,plain,
% 0.86/1.07 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.86/1.07 tff(136,assumption,(~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))), introduced(assumption)).
% 0.86/1.07 tff(137,plain,
% 0.86/1.07 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(138,plain,
% 0.86/1.07 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(139,plain,
% 0.86/1.07 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[138])).
% 0.86/1.07 tff(140,plain,
% 0.86/1.07 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[139, 137])).
% 0.86/1.07 tff(141,plain,
% 0.86/1.07 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(142,plain,
% 0.86/1.07 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.86/1.08 tff(143,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[142, 88, 136])).
% 0.86/1.08 tff(144,plain,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(145,plain,
% 0.86/1.08 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(146,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.86/1.08 tff(147,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[146, 135])).
% 0.86/1.08 tff(148,plain,
% 0.86/1.08 ((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(149,plain,
% 0.86/1.08 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[148, 147, 132])).
% 0.86/1.08 tff(150,assumption,(![X: $i] : ((~member(X, C!3)) | member(X, A!5))), introduced(assumption)).
% 0.86/1.08 tff(151,plain,
% 0.86/1.08 (((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))) <=> ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(152,plain,
% 0.86/1.08 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(153,plain,
% 0.86/1.08 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.86/1.08 tff(154,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[153, 150, 133, 149])).
% 0.86/1.08 tff(155,plain,((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | (~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(156,plain,
% 0.86/1.08 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[155, 131, 74])).
% 0.86/1.08 tff(157,plain,
% 0.86/1.08 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(158,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[157, 156, 95])).
% 0.86/1.08 tff(159,plain,
% 0.86/1.08 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(160,plain,
% 0.86/1.08 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[159, 158, 78])).
% 0.86/1.08 tff(161,plain,
% 0.86/1.08 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(162,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.86/1.08 tff(163,plain,
% 0.86/1.08 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[148, 162, 74])).
% 0.86/1.08 tff(164,plain,
% 0.86/1.08 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(165,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.86/1.08 tff(166,plain,
% 0.86/1.08 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(167,plain,
% 0.86/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.86/1.08 tff(168,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[146, 167, 163])).
% 0.86/1.08 tff(169,plain,(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(170,plain,
% 0.86/1.08 (((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))) | ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(171,plain,
% 0.86/1.08 ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[170, 64])).
% 0.86/1.08 tff(172,plain,
% 0.86/1.08 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(tautology,[status(thm)],[])).
% 0.86/1.08 tff(173,plain,
% 0.86/1.08 ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.86/1.08 tff(174,plain,
% 0.86/1.08 (![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[173, 169])).
% 0.86/1.08 tff(175,plain,
% 0.86/1.08 (((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) <=> ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(176,plain,
% 0.86/1.08 ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(177,plain,
% 0.86/1.08 ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.92/1.08 tff(178,plain,
% 0.92/1.08 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[177, 174, 49])).
% 0.92/1.08 tff(179,assumption,(~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))), introduced(assumption)).
% 0.92/1.08 tff(180,plain,
% 0.92/1.08 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(181,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[180, 88, 179])).
% 0.92/1.08 tff(182,plain,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(183,plain,
% 0.92/1.08 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(184,plain,
% 0.92/1.08 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.92/1.08 tff(185,plain,
% 0.92/1.08 (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[184, 178])).
% 0.92/1.08 tff(186,plain,
% 0.92/1.08 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3))),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(187,plain,
% 0.92/1.08 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.92/1.08 tff(188,plain,
% 0.92/1.08 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), C!3)),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(189,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[188, 187, 47])).
% 0.92/1.08 tff(190,plain,((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(191,plain,
% 0.92/1.08 ((~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(192,plain,
% 0.92/1.08 ((~((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), difference(C!3, intersection(A!5, B!4))), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3))))) | subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.92/1.08 tff(193,plain,
% 0.92/1.08 (subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[192, 29])).
% 0.92/1.08 tff(194,plain,
% 0.92/1.08 ((~((~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~subset(difference(C!3, intersection(A!5, B!4)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(195,plain,
% 0.92/1.08 (![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[194, 193, 27])).
% 0.92/1.08 tff(196,assumption,(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))), introduced(assumption)).
% 0.92/1.08 tff(197,plain,
% 0.92/1.08 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(198,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[197, 59, 196])).
% 0.92/1.08 tff(199,plain,(~(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(200,assumption,((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))))), introduced(assumption)).
% 0.92/1.08 tff(201,plain,
% 0.92/1.08 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(202,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[201, 17, 200])).
% 0.92/1.08 tff(203,plain,(~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(204,plain,
% 0.92/1.08 (((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))))) | (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(205,plain,
% 0.92/1.08 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.92/1.08 tff(206,plain,
% 0.92/1.08 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(207,plain,
% 0.92/1.08 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[206, 88])).
% 0.92/1.09 tff(208,plain,
% 0.92/1.09 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(209,plain,
% 0.92/1.09 (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[208, 59])).
% 0.92/1.09 tff(210,assumption,(~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))), introduced(assumption)).
% 0.92/1.09 tff(211,plain,
% 0.92/1.09 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(212,plain,
% 0.92/1.09 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.92/1.09 tff(213,plain,
% 0.92/1.09 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(214,plain,
% 0.92/1.09 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.92/1.09 tff(215,plain,
% 0.92/1.09 (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[214, 209])).
% 0.92/1.09 tff(216,plain,
% 0.92/1.09 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(217,plain,
% 0.92/1.09 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.92/1.09 tff(218,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(219,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.92/1.09 tff(220,plain,
% 0.92/1.09 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[219, 207])).
% 0.92/1.09 tff(221,plain,
% 0.92/1.09 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(222,plain,
% 0.92/1.09 (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[221, 59])).
% 0.92/1.09 tff(223,plain,
% 0.92/1.09 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(224,plain,
% 0.92/1.09 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[223, 88])).
% 0.92/1.09 tff(225,plain,
% 0.92/1.09 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(226,plain,
% 0.92/1.09 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[225, 210])).
% 0.92/1.09 tff(227,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(228,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))) | (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.92/1.09 tff(229,plain,
% 0.92/1.09 (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[228, 224])).
% 0.92/1.09 tff(230,plain,
% 0.92/1.09 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(231,plain,
% 0.92/1.09 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.92/1.09 tff(232,plain,
% 0.92/1.09 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(233,plain,
% 0.92/1.09 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.92/1.09 tff(234,plain,
% 0.92/1.09 ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[233, 222])).
% 0.92/1.09 tff(235,plain,
% 0.92/1.09 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(236,plain,
% 0.92/1.09 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[235, 215])).
% 0.92/1.09 tff(237,plain,
% 0.92/1.09 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(238,plain,
% 0.92/1.09 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.92/1.09 tff(239,plain,
% 0.92/1.09 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[238, 234])).
% 0.92/1.09 tff(240,plain,
% 0.92/1.09 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(241,plain,
% 0.92/1.09 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[240, 229])).
% 0.92/1.09 tff(242,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(243,plain,
% 0.92/1.09 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.92/1.09 tff(244,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[243, 239, 220])).
% 0.92/1.09 tff(245,plain,((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(246,plain,
% 0.92/1.09 ((~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))) | subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(247,plain,
% 0.92/1.09 ((~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))) | subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.92/1.09 tff(248,plain,
% 0.92/1.09 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[247, 205])).
% 0.92/1.09 tff(249,plain,
% 0.92/1.09 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(250,plain,
% 0.92/1.09 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.92/1.09 tff(251,plain,
% 0.92/1.09 (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[250, 169])).
% 0.92/1.09 tff(252,plain,
% 0.92/1.09 ((((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) <=> equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) | equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(253,plain,
% 0.92/1.09 (((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))) | equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[252, 109])).
% 0.92/1.09 tff(254,plain,
% 0.92/1.09 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[253, 251])).
% 0.92/1.09 tff(255,plain,
% 0.92/1.09 ((equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5)) | (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(C!3, A!5))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(256,plain,
% 0.92/1.09 ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(C!3, A!5))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[255, 121])).
% 0.92/1.09 tff(257,plain,
% 0.92/1.09 (~subset(C!3, A!5)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[256, 254])).
% 0.92/1.09 tff(258,plain,
% 0.92/1.09 (((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))) | (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(259,plain,
% 0.92/1.09 (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[258, 126])).
% 0.92/1.09 tff(260,plain,
% 0.92/1.09 ((~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))) | subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(261,plain,
% 0.92/1.10 (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.92/1.10 tff(262,plain,
% 0.92/1.10 (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[261, 257])).
% 0.92/1.10 tff(263,plain,
% 0.92/1.10 (((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), A!5))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(264,plain,
% 0.92/1.10 (~member(tptp_fun_X_0(A!5, C!3), A!5)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.92/1.10 tff(265,plain,
% 0.92/1.10 (((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) | member(tptp_fun_X_0(A!5, C!3), A!5)),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(266,plain,
% 0.92/1.10 ((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.92/1.10 tff(267,plain,
% 0.92/1.10 ((((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3))))) | (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(268,plain,
% 0.92/1.10 ((((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.92/1.10 tff(269,plain,
% 0.92/1.10 (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[268, 199])).
% 0.92/1.10 tff(270,plain,
% 0.92/1.10 (((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)) | member(tptp_fun_X_0(A!5, C!3), C!3)),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(271,plain,
% 0.92/1.10 (member(tptp_fun_X_0(A!5, C!3), C!3)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[270, 262])).
% 0.92/1.10 tff(272,plain,
% 0.92/1.10 (((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))) | member(tptp_fun_X_0(A!5, C!3), A!5)),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(273,plain,
% 0.92/1.10 ((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[272, 264])).
% 0.92/1.10 tff(274,assumption,(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))), introduced(assumption)).
% 0.92/1.10 tff(275,plain,
% 0.92/1.10 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(276,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[275, 59, 274])).
% 0.92/1.10 tff(277,plain,(~(((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(278,plain,
% 0.92/1.10 ((((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4))) <=> member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4)))) | (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(279,plain,
% 0.92/1.10 ((~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), B!4)))) | (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.92/1.10 tff(280,plain,
% 0.92/1.10 (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[279, 273])).
% 0.92/1.10 tff(281,plain,
% 0.92/1.10 ((~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))) | (~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(282,plain,
% 0.92/1.10 (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[281, 280, 271])).
% 0.92/1.10 tff(283,plain,
% 0.92/1.10 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(284,plain,
% 0.92/1.10 (~(((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4))))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[283, 39])).
% 0.92/1.10 tff(285,plain,
% 0.92/1.10 ((((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) <=> member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))) | ((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) | member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(286,plain,
% 0.92/1.10 (((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) | member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.92/1.10 tff(287,plain,
% 0.92/1.10 (member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[286, 282])).
% 0.92/1.10 tff(288,plain,
% 0.92/1.10 (((~![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))) <=> ((~![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(289,plain,
% 0.92/1.10 ((~![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(290,plain,
% 0.92/1.10 ((~![X: $i] : ((~member(X, difference(C!3, intersection(A!5, B!4)))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(A!5, C!3), difference(C!3, intersection(A!5, B!4)))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.92/1.10 tff(291,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[290, 287, 269, 195])).
% 0.92/1.10 % SZS output end Proof
% 0.92/1.10 % E exiting
%------------------------------------------------------------------------------