%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET586+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:25:55 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET586+3 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:29:18 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(tptp_fun_B_4_type, type, (
% 0.12/0.37 tptp_fun_B_4: $i)).
% 0.12/0.37 tff(tptp_fun_D_0_type, type, (
% 0.12/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(intersection_type, type, (
% 0.12/0.37 intersection: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_D_2_type, type, (
% 0.12/0.37 tptp_fun_D_2: $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(1,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.38 tff(26,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(B!4, D!2), intersection(C!3, D!2))) | ![D: $i] : ((~member(D, intersection(B!4, D!2))) | member(D, intersection(C!3, D!2))))) | (~(subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (~((~((~subset(intersection(B!4, D!2), intersection(C!3, D!2))) | ![D: $i] : ((~member(D, intersection(B!4, D!2))) | member(D, intersection(C!3, D!2))))) | (~(subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((~((~subset(intersection(B!4, D!2), intersection(C!3, D!2))) | ![D: $i] : ((~member(D, intersection(B!4, D!2))) | member(D, intersection(C!3, D!2))))) | (~(subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))))) | (subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(intersection(B, D), intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,axiom,(~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(intersection(B, D), intersection(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_of_subset')).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.12/0.38 tff(40,plain,(
% 0.12/0.38 ~((~subset(B!4, C!3)) | subset(intersection(B!4, D!2), intersection(C!3, D!2)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (~subset(intersection(B!4, D!2), intersection(C!3, D!2))),
% 0.12/0.38 inference(or_elim,[status(thm)],[40])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~(subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))))) | subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~(subset(intersection(B!4, D!2), intersection(C!3, D!2)) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 12])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[52, 10])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(B!4, D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[54, 44])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), intersection(C!3, D!2))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[57, 53])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[59, 49])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2)))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), D!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 60, 58])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 28])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3)))))) | ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (subset(B!4, C!3)),
% 0.12/0.39 inference(or_elim,[status(thm)],[40])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), B!4)) | member(tptp_fun_D_0(intersection(C!3, D!2), intersection(B!4, D!2)), C!3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[73, 70, 62, 51])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------