%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET612+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:00 AM UTC 2025
% Result : Theorem 29.36s 29.55s
% Output : Proof 29.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET612+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 05:31:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 29.36/29.55 % SZS status Theorem
% 29.36/29.55 % SZS output start Proof
% 29.36/29.55 tff(member_type, type, (
% 29.36/29.55 member: ( $i * $i ) > $o)).
% 29.36/29.55 tff(intersection_type, type, (
% 29.36/29.55 intersection: ( $i * $i ) > $i)).
% 29.36/29.55 tff(difference_type, type, (
% 29.36/29.55 difference: ( $i * $i ) > $i)).
% 29.36/29.55 tff(tptp_fun_C_3_type, type, (
% 29.36/29.55 tptp_fun_C_3: $i)).
% 29.36/29.55 tff(tptp_fun_B_4_type, type, (
% 29.36/29.55 tptp_fun_B_4: $i)).
% 29.36/29.55 tff(tptp_fun_D_2_type, type, (
% 29.36/29.55 tptp_fun_D_2: $i)).
% 29.36/29.55 tff(tptp_fun_D_1_type, type, (
% 29.36/29.55 tptp_fun_D_1: ( $i * $i ) > $i)).
% 29.36/29.55 tff(union_type, type, (
% 29.36/29.55 union: ( $i * $i ) > $i)).
% 29.36/29.55 tff(subset_type, type, (
% 29.36/29.55 subset: ( $i * $i ) > $o)).
% 29.36/29.55 tff(tptp_fun_D_0_type, type, (
% 29.36/29.55 tptp_fun_D_0: ( $i * $i ) > $i)).
% 29.36/29.55 tff(1,plain,
% 29.36/29.55 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 29.36/29.55 inference(bind,[status(th)],[])).
% 29.36/29.55 tff(2,plain,
% 29.36/29.55 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 29.36/29.55 inference(quant_intro,[status(thm)],[1])).
% 29.36/29.55 tff(3,plain,
% 29.36/29.55 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 29.36/29.55 inference(rewrite,[status(thm)],[])).
% 29.36/29.55 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 29.36/29.55 tff(5,plain,
% 29.36/29.55 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 29.36/29.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 29.36/29.55 tff(6,plain,(
% 29.36/29.55 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 29.36/29.55 inference(skolemize,[status(sab)],[5])).
% 29.36/29.55 tff(7,plain,
% 29.36/29.55 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 29.36/29.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 29.36/29.55 tff(8,plain,
% 29.36/29.55 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(difference(B!4, C!3), difference(B!4, D!2)) = intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.36/29.55 inference(quant_inst,[status(thm)],[])).
% 29.36/29.55 tff(9,plain,
% 29.36/29.55 (intersection(difference(B!4, C!3), difference(B!4, D!2)) = intersection(difference(B!4, D!2), difference(B!4, C!3))),
% 29.36/29.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 29.36/29.55 tff(10,assumption,((~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))))))), introduced(assumption)).
% 29.36/29.55 tff(11,plain,
% 29.36/29.55 (^[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))))))))),
% 29.36/29.55 inference(bind,[status(th)],[])).
% 29.36/29.55 tff(12,plain,
% 29.36/29.55 (![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)))))))),
% 29.36/29.55 inference(quant_intro,[status(thm)],[11])).
% 29.36/29.55 tff(13,plain,
% 29.36/29.55 (^[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))))))))),
% 29.36/29.55 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(14,plain,
% 29.36/29.56 (![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)))))))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[13])).
% 29.36/29.56 tff(15,plain,
% 29.36/29.56 (![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)))))))),
% 29.36/29.56 inference(transitivity,[status(thm)],[14, 12])).
% 29.36/29.56 tff(16,plain,
% 29.36/29.56 (^[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)))))))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(17,plain,
% 29.36/29.56 (![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)))))))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[16])).
% 29.36/29.56 tff(18,plain,
% 29.36/29.56 (![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)))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(19,plain,
% 29.36/29.56 (^[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))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(20,plain,
% 29.36/29.56 (![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)))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[19])).
% 29.36/29.56 tff(21,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')).
% 29.36/29.56 tff(22,plain,
% 29.36/29.56 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[21, 20])).
% 29.36/29.56 tff(23,plain,
% 29.36/29.56 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[22, 18])).
% 29.36/29.56 tff(24,plain,(
% 29.36/29.56 ![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)))))),
% 29.36/29.56 inference(skolemize,[status(sab)],[23])).
% 29.36/29.56 tff(25,plain,
% 29.36/29.56 (![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)))))))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[24, 17])).
% 29.36/29.56 tff(26,plain,
% 29.36/29.56 (![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)))))))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[25, 15])).
% 29.36/29.56 tff(27,plain,
% 29.36/29.56 ((~![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(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))))))))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(28,plain,
% 29.36/29.56 ($false),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[27, 26, 10])).
% 29.36/29.56 tff(29,plain,(~((~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))))))), inference(lemma,lemma(discharge,[]))).
% 29.36/29.56 tff(30,plain,
% 29.36/29.56 (((~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))))))) | (subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(31,plain,
% 29.36/29.56 (subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[30, 29])).
% 29.36/29.56 tff(32,assumption,(~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))), introduced(assumption)).
% 29.36/29.56 tff(33,plain,
% 29.36/29.56 (((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(34,plain,
% 29.36/29.56 (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[33, 32])).
% 29.36/29.56 tff(35,assumption,(~(member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))))), introduced(assumption)).
% 29.36/29.56 tff(36,plain,
% 29.36/29.56 (^[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))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(37,plain,
% 29.36/29.56 (![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)))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[36])).
% 29.36/29.56 tff(38,plain,
% 29.36/29.56 (![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)))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(39,plain,
% 29.36/29.56 (^[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))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(40,plain,
% 29.36/29.56 (![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)))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[39])).
% 29.36/29.56 tff(41,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')).
% 29.36/29.56 tff(42,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[41, 40])).
% 29.36/29.56 tff(43,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[42, 38])).
% 29.36/29.56 tff(44,plain,(
% 29.36/29.56 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 29.36/29.56 inference(skolemize,[status(sab)],[43])).
% 29.36/29.56 tff(45,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[44, 37])).
% 29.36/29.56 tff(46,plain,
% 29.36/29.56 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(47,plain,
% 29.36/29.56 ($false),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[46, 45, 35])).
% 29.36/29.56 tff(48,plain,(member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2))))), inference(lemma,lemma(discharge,[]))).
% 29.36/29.56 tff(49,plain,
% 29.36/29.56 ((~(member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))))) | (~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(50,plain,
% 29.36/29.56 ((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[49, 48])).
% 29.36/29.56 tff(51,plain,
% 29.36/29.56 (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[50, 34])).
% 29.36/29.56 tff(52,plain,
% 29.36/29.56 (((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))) | (~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(53,plain,
% 29.36/29.56 (~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[52, 32])).
% 29.36/29.56 tff(54,plain,
% 29.36/29.56 ((~(member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2))))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(55,plain,
% 29.36/29.56 (member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[54, 53, 51])).
% 29.36/29.56 tff(56,plain,
% 29.36/29.56 ((~![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(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, D!2))))))))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(57,plain,
% 29.36/29.56 (~((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, D!2)))))))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[56, 26])).
% 29.36/29.56 tff(58,plain,
% 29.36/29.56 (((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), difference(B!4, union(C!3, D!2))), difference(B!4, D!2))))))) | ((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(59,plain,
% 29.36/29.56 ((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[58, 57])).
% 29.36/29.56 tff(60,plain,
% 29.36/29.56 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(61,plain,
% 29.36/29.56 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[60])).
% 29.36/29.56 tff(62,plain,
% 29.36/29.56 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(63,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 29.36/29.56 tff(64,plain,
% 29.36/29.56 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[63, 62])).
% 29.36/29.56 tff(65,plain,(
% 29.36/29.56 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 29.36/29.56 inference(skolemize,[status(sab)],[64])).
% 29.36/29.56 tff(66,plain,
% 29.36/29.56 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[65, 61])).
% 29.36/29.56 tff(67,plain,
% 29.36/29.56 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(68,plain,
% 29.36/29.56 (union(D!2, C!3) = union(C!3, D!2)),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[67, 66])).
% 29.36/29.56 tff(69,plain,
% 29.36/29.56 (subset(D!2, union(D!2, C!3)) <=> subset(D!2, union(C!3, D!2))),
% 29.36/29.56 inference(monotonicity,[status(thm)],[68])).
% 29.36/29.56 tff(70,plain,
% 29.36/29.56 (^[B: $i, C: $i] : refl(subset(B, union(B, C)) <=> subset(B, union(B, C)))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(71,plain,
% 29.36/29.56 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[70])).
% 29.36/29.56 tff(72,plain,
% 29.36/29.56 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(73,axiom,(![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_of_union')).
% 29.36/29.56 tff(74,plain,
% 29.36/29.56 (![B: $i, C: $i] : subset(B, union(B, C))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[73, 72])).
% 29.36/29.56 tff(75,plain,(
% 29.36/29.56 ![B: $i, C: $i] : subset(B, union(B, C))),
% 29.36/29.56 inference(skolemize,[status(sab)],[74])).
% 29.36/29.56 tff(76,plain,
% 29.36/29.56 (![B: $i, C: $i] : subset(B, union(B, C))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[75, 71])).
% 29.36/29.56 tff(77,plain,
% 29.36/29.56 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(D!2, union(D!2, C!3))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(78,plain,
% 29.36/29.56 (subset(D!2, union(D!2, C!3))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[77, 76])).
% 29.36/29.56 tff(79,plain,
% 29.36/29.56 (subset(D!2, union(C!3, D!2))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[78, 69])).
% 29.36/29.56 tff(80,plain,
% 29.36/29.56 (^[B: $i, C: $i, D: $i] : refl(((~subset(B, C)) | subset(difference(D, C), difference(D, B))) <=> ((~subset(B, C)) | subset(difference(D, C), difference(D, B))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(81,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[80])).
% 29.36/29.56 tff(82,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(83,plain,
% 29.36/29.56 (^[B: $i, C: $i, D: $i] : rewrite((subset(B, C) => subset(difference(D, C), difference(D, B))) <=> ((~subset(B, C)) | subset(difference(D, C), difference(D, B))))),
% 29.36/29.56 inference(bind,[status(th)],[])).
% 29.36/29.56 tff(84,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : (subset(B, C) => subset(difference(D, C), difference(D, B))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(quant_intro,[status(thm)],[83])).
% 29.36/29.56 tff(85,axiom,(![B: $i, C: $i, D: $i] : (subset(B, C) => subset(difference(D, C), difference(D, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_difference')).
% 29.36/29.56 tff(86,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[85, 84])).
% 29.36/29.56 tff(87,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[86, 82])).
% 29.36/29.56 tff(88,plain,(
% 29.36/29.56 ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(skolemize,[status(sab)],[87])).
% 29.36/29.56 tff(89,plain,
% 29.36/29.56 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[88, 81])).
% 29.36/29.56 tff(90,plain,
% 29.36/29.56 (((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | ((~subset(D!2, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | (~subset(D!2, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(91,plain,
% 29.36/29.56 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | ((~subset(D!2, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(92,plain,
% 29.36/29.56 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | (~subset(D!2, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[91, 90])).
% 29.36/29.56 tff(93,plain,
% 29.36/29.56 ((~subset(D!2, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[92, 89])).
% 29.36/29.56 tff(94,plain,
% 29.36/29.56 (subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[93, 79])).
% 29.36/29.56 tff(95,plain,
% 29.36/29.56 ((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))) | (~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(96,plain,
% 29.36/29.56 ((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2))))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[95, 94])).
% 29.36/29.56 tff(97,plain,
% 29.36/29.56 (![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[96, 59])).
% 29.36/29.56 tff(98,plain,
% 29.36/29.56 (((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | ((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))) <=> ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | (~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))),
% 29.36/29.56 inference(rewrite,[status(thm)],[])).
% 29.36/29.56 tff(99,plain,
% 29.36/29.56 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | ((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))),
% 29.36/29.56 inference(quant_inst,[status(thm)],[])).
% 29.36/29.56 tff(100,plain,
% 29.36/29.56 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | (~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))),
% 29.36/29.56 inference(modus_ponens,[status(thm)],[99, 98])).
% 29.36/29.56 tff(101,plain,
% 29.36/29.56 ($false),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[100, 97, 53, 55])).
% 29.36/29.56 tff(102,plain,((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))), inference(lemma,lemma(discharge,[]))).
% 29.36/29.56 tff(103,plain,
% 29.36/29.56 ((~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))))) | subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2))))),
% 29.36/29.56 inference(tautology,[status(thm)],[])).
% 29.36/29.56 tff(104,plain,
% 29.36/29.56 ((~(subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)) | (~((~member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | member(tptp_fun_D_0(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))), difference(B!4, D!2)))))) | subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))),
% 29.36/29.56 inference(unit_resolution,[status(thm)],[103, 102])).
% 29.36/29.56 tff(105,plain,
% 29.36/29.57 (subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[104, 31])).
% 29.36/29.57 tff(106,plain,
% 29.36/29.57 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(B!4, D!2), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.57 inference(quant_inst,[status(thm)],[])).
% 29.36/29.57 tff(107,plain,
% 29.36/29.57 (union(difference(B!4, D!2), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[106, 66])).
% 29.36/29.57 tff(108,plain,
% 29.36/29.57 (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = union(difference(B!4, D!2), difference(B!4, union(C!3, D!2)))),
% 29.36/29.57 inference(symmetry,[status(thm)],[107])).
% 29.36/29.57 tff(109,plain,
% 29.36/29.57 (subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> subset(difference(B!4, D!2), union(difference(B!4, D!2), difference(B!4, union(C!3, D!2))))),
% 29.36/29.57 inference(monotonicity,[status(thm)],[108])).
% 29.36/29.57 tff(110,plain,
% 29.36/29.57 (subset(difference(B!4, D!2), union(difference(B!4, D!2), difference(B!4, union(C!3, D!2)))) <=> subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.57 inference(symmetry,[status(thm)],[109])).
% 29.36/29.57 tff(111,plain,
% 29.36/29.57 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(difference(B!4, D!2), union(difference(B!4, D!2), difference(B!4, union(C!3, D!2))))),
% 29.36/29.57 inference(quant_inst,[status(thm)],[])).
% 29.36/29.57 tff(112,plain,
% 29.36/29.57 (subset(difference(B!4, D!2), union(difference(B!4, D!2), difference(B!4, union(C!3, D!2))))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[111, 76])).
% 29.36/29.57 tff(113,plain,
% 29.36/29.57 (subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[112, 110])).
% 29.36/29.57 tff(114,plain,
% 29.36/29.57 ((~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))) | (~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.36/29.57 inference(tautology,[status(thm)],[])).
% 29.36/29.57 tff(115,plain,
% 29.36/29.57 ((~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))) | (~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2)))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[114, 113])).
% 29.36/29.57 tff(116,plain,
% 29.36/29.57 (~((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[115, 105])).
% 29.36/29.57 tff(117,plain,
% 29.36/29.57 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(118,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[117])).
% 29.36/29.57 tff(119,plain,
% 29.36/29.57 (^[B: $i, C: $i] : trans(trans(monotonicity(rewrite((subset(B, C) & subset(C, B)) <=> (~((~subset(B, C)) | (~subset(C, B))))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))), rewrite(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))), rewrite((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(120,plain,
% 29.36/29.57 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[119])).
% 29.36/29.57 tff(121,plain,
% 29.36/29.57 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 29.36/29.57 inference(rewrite,[status(thm)],[])).
% 29.36/29.57 tff(122,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 29.36/29.57 tff(123,plain,
% 29.36/29.57 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[122, 121])).
% 29.36/29.57 tff(124,plain,(
% 29.36/29.57 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 29.36/29.57 inference(skolemize,[status(sab)],[123])).
% 29.36/29.57 tff(125,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[124, 120])).
% 29.36/29.57 tff(126,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[125, 118])).
% 29.36/29.57 tff(127,plain,
% 29.36/29.57 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) <=> (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2))))),
% 29.36/29.57 inference(quant_inst,[status(thm)],[])).
% 29.36/29.57 tff(128,plain,
% 29.36/29.57 (~(((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) <=> (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2)))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[127, 126])).
% 29.36/29.57 tff(129,plain,
% 29.36/29.57 ((((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) <=> (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2))) | ((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) | (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2))),
% 29.36/29.57 inference(tautology,[status(thm)],[])).
% 29.36/29.57 tff(130,plain,
% 29.36/29.57 (((~subset(union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)), difference(B!4, D!2))) | (~subset(difference(B!4, D!2), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) | (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[129, 128])).
% 29.36/29.57 tff(131,plain,
% 29.36/29.57 (union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)) = difference(B!4, D!2)),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[130, 116])).
% 29.36/29.57 tff(132,plain,
% 29.36/29.57 (intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) = intersection(difference(B!4, C!3), difference(B!4, D!2))),
% 29.36/29.57 inference(monotonicity,[status(thm)],[131])).
% 29.36/29.57 tff(133,plain,
% 29.36/29.57 (intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) = intersection(difference(B!4, D!2), difference(B!4, C!3))),
% 29.36/29.57 inference(transitivity,[status(thm)],[132, 9])).
% 29.36/29.57 tff(134,plain,
% 29.36/29.57 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.36/29.57 inference(monotonicity,[status(thm)],[133])).
% 29.36/29.57 tff(135,plain,
% 29.36/29.57 ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) <=> (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))))),
% 29.36/29.57 inference(monotonicity,[status(thm)],[134])).
% 29.36/29.57 tff(136,assumption,(~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)) <=> (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)))), introduced(assumption)).
% 29.36/29.57 tff(137,plain,
% 29.36/29.57 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)) <=> (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)))),
% 29.36/29.57 inference(quant_inst,[status(thm)],[])).
% 29.36/29.57 tff(138,plain,
% 29.36/29.57 ($false),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[137, 45, 136])).
% 29.36/29.57 tff(139,plain,(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)) <=> (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))), inference(lemma,lemma(discharge,[]))).
% 29.36/29.57 tff(140,assumption,(~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))), introduced(assumption)).
% 29.36/29.57 tff(141,plain,
% 29.36/29.57 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(142,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[141])).
% 29.36/29.57 tff(143,plain,
% 29.36/29.57 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(144,plain,
% 29.36/29.57 (![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, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[143])).
% 29.36/29.57 tff(145,plain,
% 29.36/29.57 (![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)))),
% 29.36/29.57 inference(rewrite,[status(thm)],[])).
% 29.36/29.57 tff(146,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')).
% 29.36/29.57 tff(147,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[146, 145])).
% 29.36/29.57 tff(148,plain,(
% 29.36/29.57 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 29.36/29.57 inference(skolemize,[status(sab)],[147])).
% 29.36/29.57 tff(149,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[148, 144])).
% 29.36/29.57 tff(150,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[149, 142])).
% 29.36/29.57 tff(151,plain,
% 29.36/29.57 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))))),
% 29.36/29.57 inference(quant_inst,[status(thm)],[])).
% 29.36/29.57 tff(152,plain,
% 29.36/29.57 (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[151, 150])).
% 29.36/29.57 tff(153,plain,
% 29.36/29.57 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.36/29.57 inference(tautology,[status(thm)],[])).
% 29.36/29.57 tff(154,plain,
% 29.36/29.57 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[153, 152])).
% 29.36/29.57 tff(155,plain,
% 29.36/29.57 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.36/29.57 inference(unit_resolution,[status(thm)],[154, 140])).
% 29.36/29.57 tff(156,plain,
% 29.36/29.57 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[155, 134])).
% 29.36/29.57 tff(157,plain,
% 29.36/29.57 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(158,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[157])).
% 29.36/29.57 tff(159,plain,
% 29.36/29.57 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(pull_quant,[status(thm)],[])).
% 29.36/29.57 tff(160,plain,
% 29.36/29.57 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(161,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[160])).
% 29.36/29.57 tff(162,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(transitivity,[status(thm)],[161, 159])).
% 29.36/29.57 tff(163,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(transitivity,[status(thm)],[162, 158])).
% 29.36/29.57 tff(164,plain,
% 29.36/29.57 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(165,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[164])).
% 29.36/29.57 tff(166,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(transitivity,[status(thm)],[165, 163])).
% 29.36/29.57 tff(167,plain,
% 29.36/29.57 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))) <=> (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 29.36/29.57 inference(bind,[status(th)],[])).
% 29.36/29.57 tff(168,plain,
% 29.36/29.57 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(quant_intro,[status(thm)],[167])).
% 29.36/29.57 tff(169,plain,
% 29.36/29.57 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 29.36/29.57 inference(rewrite,[status(thm)],[])).
% 29.36/29.57 tff(170,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 29.36/29.57 tff(171,plain,
% 29.36/29.57 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[170, 169])).
% 29.36/29.57 tff(172,plain,(
% 29.36/29.57 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 29.36/29.57 inference(skolemize,[status(sab)],[171])).
% 29.36/29.57 tff(173,plain,
% 29.36/29.57 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[172, 168])).
% 29.36/29.57 tff(174,plain,
% 29.36/29.57 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 29.36/29.57 inference(modus_ponens,[status(thm)],[173, 166])).
% 29.36/29.57 tff(175,plain,
% 29.36/29.57 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))))))),
% 29.36/29.58 inference(rewrite,[status(thm)],[])).
% 29.36/29.58 tff(176,plain,
% 29.36/29.58 ((~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) | (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))))))) <=> (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))))))),
% 29.36/29.58 inference(rewrite,[status(thm)],[])).
% 29.36/29.58 tff(177,plain,
% 29.36/29.58 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) | (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))))))),
% 29.36/29.58 inference(monotonicity,[status(thm)],[176])).
% 29.36/29.58 tff(178,plain,
% 29.36/29.58 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) | (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))))))),
% 29.36/29.58 inference(transitivity,[status(thm)],[177, 175])).
% 29.36/29.58 tff(179,plain,
% 29.36/29.58 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) | (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))))))))),
% 29.36/29.58 inference(quant_inst,[status(thm)],[])).
% 29.36/29.58 tff(180,plain,
% 29.36/29.58 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))))))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[179, 178])).
% 29.36/29.58 tff(181,plain,
% 29.36/29.58 (~((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[180, 174])).
% 29.36/29.58 tff(182,plain,
% 29.36/29.58 (((~((~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))) | (member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, D!2), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, union(C!3, D!2)))))) | (~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))))) | ((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(tautology,[status(thm)],[])).
% 29.36/29.58 tff(183,plain,
% 29.36/29.58 ((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[182, 181])).
% 29.36/29.58 tff(184,plain,
% 29.36/29.58 ((intersection(difference(B!4, C!3), difference(B!4, D!2)) = difference(B!4, union(C!3, D!2))) <=> (difference(B!4, union(C!3, D!2)) = intersection(difference(B!4, C!3), difference(B!4, D!2)))),
% 29.36/29.58 inference(commutativity,[status(thm)],[])).
% 29.36/29.58 tff(185,plain,
% 29.36/29.58 (intersection(difference(B!4, D!2), difference(B!4, C!3)) = intersection(difference(B!4, C!3), difference(B!4, D!2))),
% 29.36/29.58 inference(symmetry,[status(thm)],[9])).
% 29.36/29.58 tff(186,plain,
% 29.36/29.58 ((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) <=> (intersection(difference(B!4, C!3), difference(B!4, D!2)) = difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(monotonicity,[status(thm)],[185])).
% 29.36/29.58 tff(187,plain,
% 29.36/29.58 ((intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))) <=> (difference(B!4, union(C!3, D!2)) = intersection(difference(B!4, C!3), difference(B!4, D!2)))),
% 29.36/29.58 inference(transitivity,[status(thm)],[186, 184])).
% 29.36/29.58 tff(188,plain,
% 29.36/29.58 ((difference(B!4, union(C!3, D!2)) = intersection(difference(B!4, C!3), difference(B!4, D!2))) <=> (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(symmetry,[status(thm)],[187])).
% 29.36/29.58 tff(189,plain,
% 29.36/29.58 ((~(difference(B!4, union(C!3, D!2)) = intersection(difference(B!4, C!3), difference(B!4, D!2)))) <=> (~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(monotonicity,[status(thm)],[188])).
% 29.36/29.58 tff(190,plain,
% 29.36/29.58 ((~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))) <=> (~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D))))),
% 29.36/29.58 inference(rewrite,[status(thm)],[])).
% 29.36/29.58 tff(191,axiom,(~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th85')).
% 29.36/29.58 tff(192,plain,
% 29.36/29.58 (~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[191, 190])).
% 29.36/29.58 tff(193,plain,
% 29.36/29.58 (~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[192, 190])).
% 29.36/29.58 tff(194,plain,
% 29.36/29.58 (~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[193, 190])).
% 29.36/29.58 tff(195,plain,
% 29.36/29.58 (~![B: $i, C: $i, D: $i] : (difference(B, union(C, D)) = intersection(difference(B, C), difference(B, D)))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[194, 190])).
% 29.36/29.58 tff(196,plain,(
% 29.36/29.58 ~(difference(B!4, union(C!3, D!2)) = intersection(difference(B!4, C!3), difference(B!4, D!2)))),
% 29.36/29.58 inference(skolemize,[status(sab)],[195])).
% 29.36/29.58 tff(197,plain,
% 29.36/29.58 (~(intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[196, 189])).
% 29.36/29.58 tff(198,plain,
% 29.36/29.58 ((~((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2))))) | (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))) | (intersection(difference(B!4, D!2), difference(B!4, C!3)) = difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(tautology,[status(thm)],[])).
% 29.36/29.58 tff(199,plain,
% 29.36/29.58 (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[198, 197, 183])).
% 29.36/29.58 tff(200,plain,
% 29.36/29.58 ((member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(tautology,[status(thm)],[])).
% 29.36/29.58 tff(201,plain,
% 29.36/29.58 ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[200, 199])).
% 29.36/29.58 tff(202,plain,
% 29.36/29.58 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[201, 156])).
% 29.36/29.58 tff(203,plain,
% 29.36/29.58 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 29.36/29.58 inference(bind,[status(th)],[])).
% 29.36/29.58 tff(204,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 29.36/29.58 inference(quant_intro,[status(thm)],[203])).
% 29.36/29.58 tff(205,plain,
% 29.36/29.58 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 29.36/29.58 inference(bind,[status(th)],[])).
% 29.36/29.58 tff(206,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 29.36/29.58 inference(quant_intro,[status(thm)],[205])).
% 29.36/29.58 tff(207,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 29.36/29.58 inference(rewrite,[status(thm)],[])).
% 29.36/29.58 tff(208,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 29.36/29.58 tff(209,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[208, 207])).
% 29.36/29.58 tff(210,plain,(
% 29.36/29.58 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 29.36/29.58 inference(skolemize,[status(sab)],[209])).
% 29.36/29.58 tff(211,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[210, 206])).
% 29.36/29.58 tff(212,plain,
% 29.36/29.58 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 29.36/29.58 inference(modus_ponens,[status(thm)],[211, 204])).
% 29.36/29.58 tff(213,plain,
% 29.36/29.58 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))))),
% 29.36/29.58 inference(quant_inst,[status(thm)],[])).
% 29.36/29.58 tff(214,plain,
% 29.36/29.58 (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2))))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[213, 212])).
% 29.36/29.58 tff(215,plain,
% 29.36/29.58 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(tautology,[status(thm)],[])).
% 29.36/29.58 tff(216,plain,
% 29.36/29.58 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[215, 214])).
% 29.36/29.58 tff(217,plain,
% 29.36/29.58 ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[216, 202])).
% 29.36/29.58 tff(218,plain,
% 29.36/29.58 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))))),
% 29.36/29.58 inference(quant_inst,[status(thm)],[])).
% 29.36/29.58 tff(219,plain,
% 29.36/29.58 (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)))),
% 29.36/29.58 inference(unit_resolution,[status(thm)],[218, 212])).
% 29.36/29.58 tff(220,plain,
% 29.36/29.58 (difference(B!4, D!2) = union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))),
% 29.36/29.58 inference(symmetry,[status(thm)],[131])).
% 29.36/29.58 tff(221,plain,
% 29.36/29.58 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.36/29.58 inference(monotonicity,[status(thm)],[220])).
% 29.36/29.58 tff(222,plain,
% 29.36/29.58 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))),
% 29.36/29.58 inference(symmetry,[status(thm)],[221])).
% 29.36/29.58 tff(223,plain,
% 29.36/29.58 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.44/29.59 inference(symmetry,[status(thm)],[134])).
% 29.44/29.59 tff(224,assumption,(~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))), introduced(assumption)).
% 29.44/29.59 tff(225,plain,
% 29.44/29.59 (((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)))) <=> ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)))),
% 29.44/29.59 inference(rewrite,[status(thm)],[])).
% 29.44/29.59 tff(226,plain,
% 29.44/29.59 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)))),
% 29.44/29.59 inference(quant_inst,[status(thm)],[])).
% 29.44/29.59 tff(227,plain,
% 29.44/29.59 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))),
% 29.44/29.59 inference(modus_ponens,[status(thm)],[226, 225])).
% 29.44/29.59 tff(228,plain,
% 29.44/29.59 ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[227, 97])).
% 29.44/29.59 tff(229,plain,
% 29.44/29.59 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[228, 224])).
% 29.44/29.59 tff(230,plain,
% 29.44/29.59 ((member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(231,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[230, 199])).
% 29.44/29.59 tff(232,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[231, 229])).
% 29.44/29.59 tff(233,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.44/29.59 inference(modus_ponens,[status(thm)],[232, 223])).
% 29.44/29.59 tff(234,plain,
% 29.44/29.59 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))) | (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(235,plain,
% 29.44/29.59 ((~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[234, 152])).
% 29.44/29.59 tff(236,plain,
% 29.44/29.59 (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[235, 233])).
% 29.44/29.59 tff(237,plain,
% 29.44/29.59 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(238,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[237, 236])).
% 29.44/29.59 tff(239,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))),
% 29.44/29.59 inference(modus_ponens,[status(thm)],[238, 222])).
% 29.44/29.59 tff(240,plain,
% 29.44/29.59 ($false),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[224, 239])).
% 29.44/29.59 tff(241,plain,(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))), inference(lemma,lemma(discharge,[]))).
% 29.44/29.59 tff(242,plain,
% 29.44/29.59 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))) | (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2)))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(243,plain,
% 29.44/29.59 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, D!2))) | (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[242, 241])).
% 29.44/29.59 tff(244,plain,
% 29.44/29.59 (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[243, 219])).
% 29.44/29.59 tff(245,plain,
% 29.44/29.59 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(246,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[245, 244])).
% 29.44/29.59 tff(247,plain,
% 29.44/29.59 ((~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(248,plain,
% 29.44/29.59 ((~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[247, 246])).
% 29.44/29.59 tff(249,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[248, 217])).
% 29.44/29.59 tff(250,plain,
% 29.44/29.59 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))),
% 29.44/29.59 inference(quant_inst,[status(thm)],[])).
% 29.44/29.59 tff(251,plain,
% 29.44/29.59 (~(((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[250, 212])).
% 29.44/29.59 tff(252,plain,
% 29.44/29.59 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(253,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[252, 140])).
% 29.44/29.59 tff(254,plain,
% 29.44/29.59 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))) | (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(255,plain,
% 29.44/29.59 ((((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)) <=> member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))) | (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[254, 253])).
% 29.44/29.59 tff(256,plain,
% 29.44/29.59 (~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[255, 251])).
% 29.44/29.59 tff(257,plain,
% 29.44/29.59 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(258,plain,
% 29.44/29.59 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[257, 256])).
% 29.44/29.59 tff(259,plain,
% 29.44/29.59 (((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), B!4)) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(260,plain,
% 29.44/29.59 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2)),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[259, 244])).
% 29.44/29.59 tff(261,plain,
% 29.44/29.59 ((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(262,plain,
% 29.44/29.59 ((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[261, 260])).
% 29.44/29.59 tff(263,plain,
% 29.44/29.59 (~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[262, 258])).
% 29.44/29.59 tff(264,plain,
% 29.44/29.59 ((~(member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2)) <=> (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(C!3, D!2))) | (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), D!2) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), C!3))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.59 tff(265,plain,
% 29.44/29.59 ($false),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[264, 263, 249, 139])).
% 29.44/29.59 tff(266,plain,((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 29.44/29.59 tff(267,plain,
% 29.44/29.59 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, C!3), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2))))),
% 29.44/29.59 inference(unit_resolution,[status(thm)],[235, 266])).
% 29.44/29.59 tff(268,plain,
% 29.44/29.59 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.44/29.59 inference(modus_ponens,[status(thm)],[267, 135])).
% 29.44/29.59 tff(269,plain,
% 29.44/29.59 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))),
% 29.44/29.59 inference(modus_ponens,[status(thm)],[241, 221])).
% 29.44/29.59 tff(270,plain,
% 29.44/29.59 ((~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.59 inference(tautology,[status(thm)],[])).
% 29.44/29.60 tff(271,plain,
% 29.44/29.60 ((~((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), union(difference(B!4, union(C!3, D!2)), difference(B!4, D!2)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.60 inference(unit_resolution,[status(thm)],[270, 269])).
% 29.44/29.60 tff(272,plain,
% 29.44/29.60 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))),
% 29.44/29.60 inference(unit_resolution,[status(thm)],[271, 266])).
% 29.44/29.60 tff(273,plain,
% 29.44/29.60 ((~![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(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)) | (~((~member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, C!3))))))))),
% 29.44/29.60 inference(quant_inst,[status(thm)],[])).
% 29.44/29.60 tff(274,plain,
% 29.44/29.60 (~((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)) | (~((~member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, C!3)))))))),
% 29.44/29.60 inference(unit_resolution,[status(thm)],[273, 26])).
% 29.44/29.60 tff(275,plain,
% 29.44/29.60 (((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))) | (~(subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)) | (~((~member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_0(difference(B!4, C!3), difference(B!4, union(C!3, D!2))), difference(B!4, C!3))))))) | ((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))),
% 29.44/29.60 inference(tautology,[status(thm)],[])).
% 29.44/29.60 tff(276,plain,
% 29.44/29.60 ((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))),
% 29.44/29.60 inference(unit_resolution,[status(thm)],[275, 274])).
% 29.44/29.60 tff(277,plain,
% 29.44/29.60 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(C!3, union(C!3, D!2))),
% 29.44/29.60 inference(quant_inst,[status(thm)],[])).
% 29.44/29.60 tff(278,plain,
% 29.44/29.60 (subset(C!3, union(C!3, D!2))),
% 29.44/29.60 inference(unit_resolution,[status(thm)],[277, 76])).
% 29.44/29.60 tff(279,plain,
% 29.44/29.60 (((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | ((~subset(C!3, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | (~subset(C!3, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)))),
% 29.44/29.60 inference(rewrite,[status(thm)],[])).
% 29.44/29.60 tff(280,plain,
% 29.44/29.60 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | ((~subset(C!3, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3)))),
% 29.44/29.60 inference(quant_inst,[status(thm)],[])).
% 29.44/29.60 tff(281,plain,
% 29.44/29.60 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(D, C), difference(D, B)))) | (~subset(C!3, union(C!3, D!2))) | subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))),
% 29.44/29.61 inference(modus_ponens,[status(thm)],[280, 279])).
% 29.44/29.61 tff(282,plain,
% 29.44/29.61 (subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[281, 89, 278])).
% 29.44/29.61 tff(283,plain,
% 29.44/29.61 ((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))) | (~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))),
% 29.44/29.61 inference(tautology,[status(thm)],[])).
% 29.44/29.61 tff(284,plain,
% 29.44/29.61 ((~((~subset(difference(B!4, union(C!3, D!2)), difference(B!4, C!3))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3))))) | ![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[283, 282])).
% 29.44/29.61 tff(285,plain,
% 29.44/29.61 (![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[284, 276])).
% 29.44/29.61 tff(286,plain,
% 29.44/29.61 (((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))) <=> ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.61 inference(rewrite,[status(thm)],[])).
% 29.44/29.61 tff(287,plain,
% 29.44/29.61 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))) | ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3)))),
% 29.44/29.61 inference(quant_inst,[status(thm)],[])).
% 29.44/29.61 tff(288,plain,
% 29.44/29.61 ((~![D: $i] : ((~member(D, difference(B!4, union(C!3, D!2)))) | member(D, difference(B!4, C!3)))) | (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))),
% 29.44/29.61 inference(modus_ponens,[status(thm)],[287, 286])).
% 29.44/29.61 tff(289,plain,
% 29.44/29.61 ((~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))) | member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, C!3))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[288, 285])).
% 29.44/29.61 tff(290,plain,
% 29.44/29.61 (~member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[289, 272])).
% 29.44/29.61 tff(291,plain,
% 29.44/29.61 (member(tptp_fun_D_1(difference(B!4, union(C!3, D!2)), intersection(difference(B!4, D!2), difference(B!4, C!3))), intersection(difference(B!4, D!2), difference(B!4, C!3)))),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[231, 290])).
% 29.44/29.61 tff(292,plain,
% 29.44/29.61 ($false),
% 29.44/29.61 inference(unit_resolution,[status(thm)],[291, 268])).
% 29.44/29.61 % SZS output end Proof
% 29.44/29.62 % E exiting
%------------------------------------------------------------------------------