%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET594+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:25:56 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET594+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 05:31:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(intersection_type, type, (
% 0.19/0.38 intersection: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_4_type, type, (
% 0.19/0.38 tptp_fun_B_4: $i)).
% 0.19/0.38 tff(tptp_fun_D_2_type, type, (
% 0.19/0.38 tptp_fun_D_2: $i)).
% 0.19/0.38 tff(tptp_fun_D_0_type, type, (
% 0.19/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(union_type, type, (
% 0.19/0.38 union: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_C_3_type, type, (
% 0.19/0.38 tptp_fun_C_3: $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![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))))))) <=> ![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![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))))))) <=> ![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![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))))))) <=> ![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)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (^[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)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![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))))) <=> ![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.38 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.38 tff(26,plain,(
% 0.19/0.38 ![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)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[25])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 ((~![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(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (~((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~![B: $i, C: $i, D: $i] : ((union(intersection(B, C), intersection(B, D)) = B) => subset(B, union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(35,axiom,(~![B: $i, C: $i, D: $i] : ((union(intersection(B, C), intersection(B, D)) = B) => subset(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th53')).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (~![B: $i, C: $i, D: $i] : ((~(union(intersection(B, C), intersection(B, D)) = B)) | subset(B, union(C, D)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.19/0.38 tff(40,plain,(
% 0.19/0.38 ~((~(union(intersection(B!4, C!3), intersection(B!4, D!2)) = B!4)) | subset(B!4, union(C!3, D!2)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[39])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (~subset(B!4, union(C!3, D!2))),
% 0.19/0.38 inference(or_elim,[status(thm)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))) | subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) | (~(member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) | (~(member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (~(member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[48, 12])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.38 tff(54,assumption,(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))), introduced(assumption)).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,(
% 0.19/0.39 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))) <=> (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[70, 65])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 64, 54])).
% 0.19/0.39 tff(75,plain,(~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[76, 49])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[83, 10])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (union(intersection(B!4, C!3), intersection(B!4, D!2)) = B!4),
% 0.19/0.39 inference(or_elim,[status(thm)],[40])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(89,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.39 tff(91,plain,(
% 0.19/0.39 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[90])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!4, C!3), intersection(B!4, D!2)) = union(intersection(B!4, D!2), intersection(B!4, C!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (union(intersection(B!4, C!3), intersection(B!4, D!2)) = union(intersection(B!4, D!2), intersection(B!4, C!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (union(intersection(B!4, D!2), intersection(B!4, C!3)) = union(intersection(B!4, C!3), intersection(B!4, D!2))),
% 0.19/0.39 inference(symmetry,[status(thm)],[94])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(99,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.39 tff(101,plain,(
% 0.19/0.39 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[100])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 0.19/0.39 inference(symmetry,[status(thm)],[104])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, D!2) = intersection(D!2, B!4))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (intersection(B!4, D!2) = intersection(D!2, B!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (intersection(D!2, B!4) = intersection(B!4, D!2)),
% 0.19/0.40 inference(symmetry,[status(thm)],[107])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (union(intersection(D!2, B!4), intersection(C!3, B!4)) = union(intersection(B!4, D!2), intersection(B!4, C!3))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[108, 105])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (union(intersection(D!2, B!4), intersection(C!3, B!4)) = B!4),
% 0.19/0.40 inference(transitivity,[status(thm)],[109, 95, 85])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[113, 44])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[114, 112])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(intersection(D!2, B!4), intersection(C!3, B!4)))) | (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[116, 115, 84])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 82])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ((((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[121, 120, 53])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 ((((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))) <=> (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))) <=> (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[128, 123])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(union(C!3, D!2), B!4), intersection(D!2, B!4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 64, 122])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------