%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET169+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:23 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET169+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:28:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_C_3_type, type, (
% 0.12/0.38 tptp_fun_C_3: $i)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equal_set_type, type, (
% 0.12/0.38 equal_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,assumption,(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))), introduced(assumption)).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 10, 13])).
% 0.12/0.38 tff(16,plain,(~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(17,assumption,(~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4)))), introduced(assumption)).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (~(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 10])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.39 tff(32,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.39 tff(35,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (~((~((~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (((~((~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))))) | (subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,assumption,((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))))))), introduced(assumption)).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[43, 37, 42])).
% 0.12/0.39 tff(45,plain,(~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), intersection(A!5, C!3)))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))))))) | (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.40 tff(53,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.40 tff(56,plain,(
% 0.12/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[55])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((~![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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(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(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (((~![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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(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(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (((~![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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(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(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[60, 58])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 ((~![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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 ((~![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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[63, 57])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~![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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 10])).
% 0.21/0.41 tff(67,assumption,(~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))), introduced(assumption)).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[71, 66])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 64])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ((~![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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[78, 10])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~![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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[80, 57])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[82, 67])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 81])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[90, 79])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[92, 72])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~![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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~(((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 10])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 86])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3))) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), intersection(A!5, C!3))) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 93])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[105, 103])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[107, 106, 96, 77])).
% 0.21/0.43 tff(109,plain,((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))))) | subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ((~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))))))) | subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[111, 47])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(118,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.43 tff(120,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[119])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))) <=> equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (~(((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))) <=> equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))) <=> (~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(126,axiom,(~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI10')).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : equal_set(intersection(A, union(B, C)), union(intersection(A, B), intersection(A, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.21/0.43 tff(131,plain,(
% 0.21/0.43 ~equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[130])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ((((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))) <=> equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))) | equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))) <=> equal_set(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[133, 124])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 ((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (~subset(union(intersection(A!5, B!4), intersection(A!5, C!3)), intersection(A!5, union(B!4, C!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[136, 112])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~(subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))))) | subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 ((~(subset(union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[139, 41])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[144, 21])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 ((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[147, 19])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[149, 17])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.21/0.44 tff(153,assumption,(~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))), introduced(assumption)).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (((~![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), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (((~![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), intersection(A!5, 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), intersection(A!5, C!3))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (((~![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), intersection(A!5, 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), intersection(A!5, C!3))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[156, 154])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 ((~![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), intersection(A!5, 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), intersection(A!5, C!3))), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[159, 57, 153])).
% 0.21/0.44 tff(161,plain,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[163, 152, 148])).
% 0.21/0.45 tff(165,plain,((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, B!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[167, 16])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 ((~![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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[169, 57])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[171, 140])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(intersection(A!5, B!4), intersection(A!5, C!3))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[174, 170])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, 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), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, B!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.21/0.45 tff(178,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[177, 168])).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 ((((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), intersection(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[180, 12])).
% 0.21/0.45 tff(182,plain,
% 0.21/0.45 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(183,plain,
% 0.21/0.45 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.21/0.45 tff(184,plain,
% 0.21/0.45 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), union(B!4, C!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[147, 183])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[185, 181])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), intersection(A!5, C!3))), C!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[163, 188, 184])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------