%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET143+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:20 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET143+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:24:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(intersection_type, type, (
% 0.12/0.37 intersection: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_4_type, type, (
% 0.12/0.37 tptp_fun_B_4: $i)).
% 0.12/0.37 tff(tptp_fun_A_5_type, type, (
% 0.12/0.37 tptp_fun_A_5: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C_3_type, type, (
% 0.12/0.37 tptp_fun_C_3: $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(equal_set_type, type, (
% 0.12/0.37 equal_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[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))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 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')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![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(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, 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(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,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(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~(((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[18, 16])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, intersection(B!4, C!3)))) | member(X, intersection(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~((~((~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, intersection(B!4, C!3)))) | member(X, intersection(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (((~((~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, intersection(B!4, C!3)))) | member(X, intersection(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))))) | (subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.38 tff(35,assumption,((~((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))))), introduced(assumption)).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[36, 30, 35])).
% 0.21/0.38 tff(38,plain,(~((~((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (((~((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))))) | (subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[41, 10])).
% 0.21/0.39 tff(43,assumption,(~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))), introduced(assumption)).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))) | ((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))) | ((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 ((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[47, 42])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 10])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 10])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[53, 43])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[56, 52])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[61, 50])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[65, 64, 48])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[67, 57])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[69, 62])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 ((~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[71, 70, 68])).
% 0.21/0.40 tff(73,assumption,(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))), introduced(assumption)).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 10, 73])).
% 0.21/0.40 tff(76,plain,(~(((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) <=> member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))) | ((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(B!4, C!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[78, 72, 66])).
% 0.21/0.40 tff(80,plain,((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 ((~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))))) | subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((~(subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)), intersection(A!5, intersection(B!4, C!3))))))) | subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[82, 40])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(89,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')).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.41 tff(91,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[90])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))) <=> equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (~(((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))) <=> equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))) <=> (~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(97,axiom,(~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI08')).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[98, 96])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : equal_set(intersection(intersection(A, B), C), intersection(A, intersection(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.41 tff(102,plain,(
% 0.21/0.41 ~equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[101])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 ((((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))) <=> equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))) | equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 ((((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))) <=> equal_set(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | ((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 ((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[104, 95])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ((~((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))))) | (~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 ((~subset(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3)))) | (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (~subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[107, 83])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 ((~(subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))))) | subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~(subset(intersection(A!5, intersection(B!4, C!3)), intersection(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))))) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[110, 34])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 14])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 12])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[124, 116])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[126, 125, 123])).
% 0.21/0.42 tff(128,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(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (~(((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[128, 10])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 111])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))) | ((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(intersection(A!5, B!4), C!3))) | ((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[133, 129])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 121])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ((~((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), C!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[137, 136, 134])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 ((((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))) | ((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4))) | member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[139, 138, 127])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), B!4))) <=> member(tptp_fun_X_0(intersection(intersection(A!5, B!4), C!3), intersection(A!5, intersection(B!4, C!3))), intersection(A!5, B!4))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[141, 10, 140])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------