%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET607+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:59 AM UTC 2025
% Result : Theorem 0.48s 0.64s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET607+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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
% 0.18/0.33 % DateTime : Fri Jun 20 05:30:35 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.48/0.64 % SZS status Theorem
% 0.48/0.64 % SZS output start Proof
% 0.48/0.64 tff(member_type, type, (
% 0.48/0.64 member: ( $i * $i ) > $o)).
% 0.48/0.64 tff(tptp_fun_C_2_type, type, (
% 0.48/0.64 tptp_fun_C_2: $i)).
% 0.48/0.64 tff(tptp_fun_D_1_type, type, (
% 0.48/0.64 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.48/0.64 tff(union_type, type, (
% 0.48/0.64 union: ( $i * $i ) > $i)).
% 0.48/0.64 tff(tptp_fun_B_3_type, type, (
% 0.48/0.64 tptp_fun_B_3: $i)).
% 0.48/0.64 tff(difference_type, type, (
% 0.48/0.64 difference: ( $i * $i ) > $i)).
% 0.48/0.64 tff(subset_type, type, (
% 0.48/0.64 subset: ( $i * $i ) > $o)).
% 0.48/0.64 tff(tptp_fun_D_0_type, type, (
% 0.48/0.64 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.48/0.64 tff(1,plain,
% 0.48/0.64 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(2,plain,
% 0.48/0.64 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.64 tff(3,plain,
% 0.48/0.64 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(4,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.48/0.64 tff(5,plain,
% 0.48/0.64 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.48/0.64 tff(6,plain,(
% 0.48/0.64 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.48/0.64 inference(skolemize,[status(sab)],[5])).
% 0.48/0.64 tff(7,plain,
% 0.48/0.64 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.48/0.64 tff(8,plain,
% 0.48/0.64 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(C!2, B!3), C!2) = union(C!2, difference(C!2, B!3)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(9,plain,
% 0.48/0.64 (union(difference(C!2, B!3), C!2) = union(C!2, difference(C!2, B!3))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.48/0.64 tff(10,assumption,(~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))), introduced(assumption)).
% 0.48/0.64 tff(11,assumption,(~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)), introduced(assumption)).
% 0.48/0.64 tff(12,assumption,((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))))), introduced(assumption)).
% 0.48/0.64 tff(13,plain,
% 0.48/0.64 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(14,plain,
% 0.48/0.64 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[13])).
% 0.48/0.64 tff(15,plain,
% 0.48/0.64 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(16,plain,
% 0.48/0.64 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[15])).
% 0.48/0.64 tff(17,plain,
% 0.48/0.64 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[16, 14])).
% 0.48/0.64 tff(18,plain,
% 0.48/0.64 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(19,plain,
% 0.48/0.64 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[18])).
% 0.48/0.64 tff(20,plain,
% 0.48/0.64 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(21,plain,
% 0.48/0.64 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(22,plain,
% 0.48/0.64 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[21])).
% 0.48/0.64 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.48/0.64 tff(24,plain,
% 0.48/0.64 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.48/0.64 tff(25,plain,
% 0.48/0.64 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.48/0.64 tff(26,plain,(
% 0.48/0.64 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.48/0.64 inference(skolemize,[status(sab)],[25])).
% 0.48/0.64 tff(27,plain,
% 0.48/0.64 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.48/0.64 tff(28,plain,
% 0.48/0.64 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.48/0.64 tff(29,plain,
% 0.48/0.64 ((~![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(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(30,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[29, 28, 12])).
% 0.48/0.64 tff(31,plain,(~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(32,plain,
% 0.48/0.64 (((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))))) | ((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(33,plain,
% 0.48/0.64 ((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.48/0.64 tff(34,plain,
% 0.48/0.64 (((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))))) | (subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(35,plain,
% 0.48/0.64 (subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.48/0.64 tff(36,assumption,(~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))), introduced(assumption)).
% 0.48/0.64 tff(37,plain,
% 0.48/0.64 (((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(38,plain,
% 0.48/0.64 (~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.48/0.64 tff(39,assumption,(((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))), introduced(assumption)).
% 0.48/0.64 tff(40,plain,
% 0.48/0.64 (^[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)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(41,plain,
% 0.48/0.64 (![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))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[40])).
% 0.48/0.64 tff(42,plain,
% 0.48/0.64 (^[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))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(43,plain,
% 0.48/0.64 (![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))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[42])).
% 0.48/0.64 tff(44,plain,
% 0.48/0.64 (![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))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(45,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')).
% 0.48/0.64 tff(46,plain,
% 0.48/0.64 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.48/0.64 tff(47,plain,(
% 0.48/0.64 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.48/0.64 inference(skolemize,[status(sab)],[46])).
% 0.48/0.64 tff(48,plain,
% 0.48/0.64 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.48/0.64 tff(49,plain,
% 0.48/0.64 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.48/0.64 tff(50,plain,
% 0.48/0.64 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(51,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[50, 49, 39])).
% 0.48/0.64 tff(52,plain,(~(((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(53,plain,
% 0.48/0.64 (((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(54,plain,
% 0.48/0.64 (member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[53, 36])).
% 0.48/0.64 tff(55,plain,
% 0.48/0.64 ((((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3))) | (~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(56,plain,
% 0.48/0.64 (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[55, 54, 52])).
% 0.48/0.64 tff(57,plain,
% 0.48/0.64 (((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), B!3)) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(58,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[57, 56, 38])).
% 0.48/0.64 tff(59,plain,((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(60,plain,
% 0.48/0.64 ((~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))))) | subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(61,plain,
% 0.48/0.64 ((~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_0(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, difference(C!2, B!3)), C!2))))) | subset(difference(C!2, B!3), C!2)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.48/0.64 tff(62,plain,
% 0.48/0.64 (subset(difference(C!2, B!3), C!2)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[61, 35])).
% 0.48/0.64 tff(63,plain,
% 0.48/0.64 ((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(64,plain,
% 0.48/0.64 (![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[63, 62, 33])).
% 0.48/0.64 tff(65,plain,
% 0.48/0.64 (((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))) <=> ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(66,plain,
% 0.48/0.64 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(67,plain,
% 0.48/0.64 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.48/0.64 tff(68,plain,
% 0.48/0.64 ((~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.48/0.64 tff(69,plain,
% 0.48/0.64 (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[68, 11])).
% 0.48/0.64 tff(70,plain,
% 0.48/0.64 ((member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(71,plain,
% 0.48/0.64 (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[70, 11, 10])).
% 0.48/0.64 tff(72,assumption,(~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))), introduced(assumption)).
% 0.48/0.64 tff(73,plain,
% 0.48/0.64 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(74,plain,
% 0.48/0.64 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[73])).
% 0.48/0.65 tff(75,plain,
% 0.48/0.65 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(76,plain,
% 0.48/0.65 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(77,plain,
% 0.48/0.65 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[76])).
% 0.48/0.65 tff(78,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.48/0.65 tff(79,plain,
% 0.48/0.65 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.48/0.65 tff(80,plain,
% 0.48/0.65 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.48/0.65 tff(81,plain,(
% 0.48/0.65 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[80])).
% 0.48/0.65 tff(82,plain,
% 0.48/0.65 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.48/0.65 tff(83,plain,
% 0.48/0.65 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(84,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[83, 82, 72])).
% 0.48/0.65 tff(85,plain,(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(86,plain,
% 0.48/0.65 ((~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2))) | (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(87,plain,
% 0.48/0.65 ((~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2))) | (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.48/0.65 tff(88,plain,
% 0.48/0.65 (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[87, 71])).
% 0.48/0.65 tff(89,plain,
% 0.48/0.65 ((~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3)))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(90,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[89, 88, 69, 11])).
% 0.48/0.65 tff(91,plain,(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(92,plain,
% 0.48/0.65 (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[91, 10])).
% 0.48/0.65 tff(93,plain,
% 0.48/0.65 ((member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2))) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(94,plain,
% 0.48/0.65 (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[93, 92, 10])).
% 0.48/0.65 tff(95,plain,
% 0.48/0.65 ((member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))) | (~member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(96,plain,
% 0.48/0.65 (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[95, 92])).
% 0.48/0.65 tff(97,plain,
% 0.48/0.65 ((~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(98,plain,
% 0.48/0.65 (member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2) | member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), difference(C!2, B!3))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[97, 85])).
% 0.48/0.65 tff(99,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[98, 96, 94])).
% 0.48/0.65 tff(100,plain,(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(101,plain,
% 0.48/0.65 (^[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))))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(102,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[101])).
% 0.48/0.65 tff(103,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(pull_quant,[status(thm)],[])).
% 0.48/0.65 tff(104,plain,
% 0.48/0.65 (^[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)))))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(105,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[104])).
% 0.48/0.65 tff(106,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(transitivity,[status(thm)],[105, 103])).
% 0.48/0.65 tff(107,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(transitivity,[status(thm)],[106, 102])).
% 0.48/0.65 tff(108,plain,
% 0.48/0.65 (^[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))))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(109,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[108])).
% 0.48/0.65 tff(110,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(transitivity,[status(thm)],[109, 107])).
% 0.48/0.65 tff(111,plain,
% 0.48/0.65 (^[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)))))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(112,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[111])).
% 0.48/0.65 tff(113,plain,
% 0.48/0.65 (![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)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(114,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')).
% 0.48/0.65 tff(115,plain,
% 0.48/0.65 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.48/0.65 tff(116,plain,(
% 0.48/0.65 ![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)))))),
% 0.48/0.65 inference(skolemize,[status(sab)],[115])).
% 0.48/0.65 tff(117,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.48/0.65 tff(118,plain,
% 0.48/0.65 (![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)))))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.48/0.65 tff(119,plain,
% 0.48/0.65 ((~![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)))))))) | (~((~((~(union(difference(C!2, B!3), C!2) = C!2)) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))) | (~((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)))))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(120,plain,
% 0.48/0.65 (~((~((~(union(difference(C!2, B!3), C!2) = C!2)) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))) | (~((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.48/0.65 tff(121,plain,
% 0.48/0.65 (((~((~(union(difference(C!2, B!3), C!2) = C!2)) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))) | (~((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)))))) | ((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(122,plain,
% 0.48/0.65 ((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.48/0.65 tff(123,plain,
% 0.48/0.65 ((~((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2))))) | (union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(124,plain,
% 0.48/0.65 ((union(difference(C!2, B!3), C!2) = C!2) | (~(member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), union(difference(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, union(difference(C!2, B!3), C!2)), C!2)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.48/0.65 tff(125,plain,
% 0.48/0.65 (union(difference(C!2, B!3), C!2) = C!2),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[124, 100])).
% 0.48/0.65 tff(126,plain,
% 0.48/0.65 (C!2 = union(difference(C!2, B!3), C!2)),
% 0.48/0.65 inference(symmetry,[status(thm)],[125])).
% 0.48/0.65 tff(127,plain,
% 0.48/0.65 (C!2 = union(C!2, difference(C!2, B!3))),
% 0.48/0.65 inference(transitivity,[status(thm)],[126, 9])).
% 0.48/0.65 tff(128,plain,
% 0.48/0.65 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[127])).
% 0.48/0.65 tff(129,plain,
% 0.48/0.65 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2)),
% 0.48/0.65 inference(symmetry,[status(thm)],[128])).
% 0.48/0.65 tff(130,plain,
% 0.48/0.65 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[129])).
% 0.48/0.65 tff(131,plain,
% 0.48/0.65 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, C!2) = union(C!2, B!3))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(132,plain,
% 0.48/0.65 (union(B!3, C!2) = union(C!2, B!3)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[131, 7])).
% 0.48/0.65 tff(133,plain,
% 0.48/0.65 (union(C!2, difference(C!2, B!3)) = union(difference(C!2, B!3), C!2)),
% 0.48/0.65 inference(symmetry,[status(thm)],[9])).
% 0.48/0.65 tff(134,plain,
% 0.48/0.65 (union(C!2, difference(C!2, B!3)) = C!2),
% 0.48/0.65 inference(transitivity,[status(thm)],[133, 125])).
% 0.48/0.65 tff(135,assumption,(~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))), introduced(assumption)).
% 0.48/0.65 tff(136,assumption,(((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))), introduced(assumption)).
% 0.48/0.65 tff(137,plain,
% 0.48/0.65 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(138,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[137, 49, 136])).
% 0.48/0.65 tff(139,plain,(~(((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(140,assumption,(~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))), introduced(assumption)).
% 0.48/0.65 tff(141,plain,
% 0.48/0.65 ((member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(142,plain,
% 0.48/0.65 (member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[141, 140, 135])).
% 0.48/0.65 tff(143,plain,
% 0.48/0.65 (((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(144,plain,
% 0.48/0.65 ((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.48/0.65 tff(145,plain,
% 0.48/0.65 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(146,plain,
% 0.48/0.65 (~(((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[145, 49])).
% 0.48/0.65 tff(147,plain,
% 0.48/0.65 ((((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))) | ((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(148,plain,
% 0.48/0.66 ((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[147, 140, 146])).
% 0.48/0.66 tff(149,plain,
% 0.48/0.66 ((~((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3)))) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(150,plain,
% 0.48/0.66 (member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[149, 142, 148])).
% 0.48/0.66 tff(151,plain,
% 0.48/0.66 ((((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) | (~((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), C!2)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3))) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3)))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(152,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[151, 150, 144, 139])).
% 0.48/0.66 tff(153,plain,(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))) | (member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(154,plain,
% 0.48/0.66 (member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[153, 135])).
% 0.48/0.66 tff(155,plain,
% 0.48/0.66 ((member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(156,plain,
% 0.48/0.66 (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[155, 154, 135])).
% 0.48/0.66 tff(157,plain,
% 0.48/0.66 ((((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))) | (~((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3)))) | (~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(158,plain,
% 0.48/0.66 (~((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[157, 154, 146])).
% 0.48/0.66 tff(159,plain,
% 0.48/0.66 (((~member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(C!2, B!3))) | member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3)),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(160,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[159, 158, 156])).
% 0.48/0.66 tff(161,plain,(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(162,plain,
% 0.48/0.66 ((~![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!3 = difference(B!3, difference(C!2, B!3)))) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))))) | (~((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(163,plain,
% 0.48/0.66 (~((~((~(B!3 = difference(B!3, difference(C!2, B!3)))) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))))) | (~((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[162, 118])).
% 0.48/0.66 tff(164,plain,
% 0.48/0.66 (((~((~(B!3 = difference(B!3, difference(C!2, B!3)))) | (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))))) | (~((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))))) | ((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(165,plain,
% 0.48/0.66 ((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.48/0.66 tff(166,plain,
% 0.48/0.66 ((~((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3))))))) | (B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(167,plain,
% 0.48/0.66 ((B!3 = difference(B!3, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_1(difference(B!3, difference(C!2, B!3)), B!3), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.48/0.66 tff(168,plain,
% 0.48/0.66 (B!3 = difference(B!3, difference(C!2, B!3))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.48/0.66 tff(169,plain,
% 0.48/0.66 (difference(B!3, difference(C!2, B!3)) = B!3),
% 0.48/0.66 inference(symmetry,[status(thm)],[168])).
% 0.48/0.66 tff(170,plain,
% 0.48/0.66 (union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))) = union(B!3, C!2)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[169, 134])).
% 0.48/0.66 tff(171,plain,
% 0.48/0.66 (union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))) = union(C!2, B!3)),
% 0.48/0.66 inference(transitivity,[status(thm)],[170, 132])).
% 0.48/0.66 tff(172,plain,
% 0.48/0.66 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[171])).
% 0.48/0.66 tff(173,plain,
% 0.48/0.66 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.66 inference(symmetry,[status(thm)],[172])).
% 0.48/0.66 tff(174,plain,
% 0.48/0.66 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[173])).
% 0.48/0.66 tff(175,plain,
% 0.48/0.66 (union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))) = union(difference(C!2, B!3), B!3)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[169])).
% 0.48/0.66 tff(176,plain,
% 0.48/0.66 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[175])).
% 0.48/0.66 tff(177,plain,
% 0.48/0.66 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(178,plain,
% 0.48/0.66 (~(((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[177, 49])).
% 0.48/0.66 tff(179,plain,
% 0.48/0.66 (difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))) = difference(C!2, B!3)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[134, 169])).
% 0.48/0.66 tff(180,plain,
% 0.48/0.66 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[179])).
% 0.48/0.66 tff(181,plain,
% 0.48/0.66 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.66 inference(symmetry,[status(thm)],[180])).
% 0.48/0.66 tff(182,plain,
% 0.48/0.66 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[181])).
% 0.48/0.66 tff(183,assumption,(~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))))), introduced(assumption)).
% 0.48/0.66 tff(184,plain,
% 0.48/0.66 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(185,plain,
% 0.48/0.66 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(186,plain,
% 0.48/0.66 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[185])).
% 0.48/0.66 tff(187,plain,
% 0.48/0.66 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[186, 184])).
% 0.48/0.66 tff(188,plain,
% 0.48/0.66 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(189,plain,
% 0.48/0.66 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.48/0.67 tff(190,plain,
% 0.48/0.67 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[189, 82])).
% 0.48/0.67 tff(191,plain,
% 0.48/0.67 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(192,plain,
% 0.48/0.67 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.48/0.67 tff(193,plain,
% 0.48/0.67 (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[192, 183])).
% 0.48/0.67 tff(194,plain,
% 0.48/0.67 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(195,plain,
% 0.48/0.67 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.48/0.67 tff(196,plain,
% 0.48/0.67 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[195, 182])).
% 0.48/0.67 tff(197,plain,
% 0.48/0.67 ((((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))))) | ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(union(C!2, difference(C!2, B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(198,plain,
% 0.48/0.67 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[197, 196, 178])).
% 0.48/0.67 tff(199,plain,
% 0.48/0.67 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(200,plain,
% 0.48/0.67 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[199, 193])).
% 0.48/0.67 tff(201,plain,
% 0.48/0.67 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[176])).
% 0.48/0.67 tff(202,plain,
% 0.48/0.67 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[183, 201])).
% 0.48/0.67 tff(203,plain,
% 0.48/0.67 ((~![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)))))))) | (~((~((~(union(difference(C!2, B!3), B!3) = union(C!2, B!3))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))))) | (~((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))))))))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(204,plain,
% 0.48/0.67 (~((~((~(union(difference(C!2, B!3), B!3) = union(C!2, B!3))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))))) | (~((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[203, 118])).
% 0.48/0.67 tff(205,plain,
% 0.48/0.67 (((~((~(union(difference(C!2, B!3), B!3) = union(C!2, B!3))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))))) | (~((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))))))) | ((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(206,plain,
% 0.48/0.67 ((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.48/0.67 tff(207,plain,
% 0.48/0.67 (union(C!2, B!3) = union(B!3, C!2)),
% 0.48/0.67 inference(symmetry,[status(thm)],[132])).
% 0.48/0.67 tff(208,plain,
% 0.48/0.67 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(209,plain,
% 0.48/0.67 (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[208, 7])).
% 0.48/0.67 tff(210,plain,
% 0.48/0.67 (union(difference(C!2, B!3), B!3) = union(B!3, difference(C!2, B!3))),
% 0.48/0.67 inference(symmetry,[status(thm)],[209])).
% 0.48/0.67 tff(211,plain,
% 0.48/0.67 ((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) <=> (union(B!3, difference(C!2, B!3)) = union(B!3, C!2))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[210, 207])).
% 0.48/0.67 tff(212,plain,
% 0.48/0.67 ((union(B!3, difference(C!2, B!3)) = union(B!3, C!2)) <=> (union(difference(C!2, B!3), B!3) = union(C!2, B!3))),
% 0.48/0.67 inference(symmetry,[status(thm)],[211])).
% 0.48/0.67 tff(213,plain,
% 0.48/0.67 ((~(union(B!3, difference(C!2, B!3)) = union(B!3, C!2))) <=> (~(union(difference(C!2, B!3), B!3) = union(C!2, B!3)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[212])).
% 0.48/0.67 tff(214,plain,
% 0.48/0.67 ((~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))) <=> (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(215,axiom,(~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th79')).
% 0.48/0.67 tff(216,plain,
% 0.48/0.67 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.48/0.67 tff(217,plain,
% 0.48/0.67 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[216, 214])).
% 0.48/0.67 tff(218,plain,
% 0.48/0.67 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.48/0.67 tff(219,plain,
% 0.48/0.67 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.48/0.67 tff(220,plain,(
% 0.48/0.67 ~(union(B!3, difference(C!2, B!3)) = union(B!3, C!2))),
% 0.48/0.67 inference(skolemize,[status(sab)],[219])).
% 0.48/0.67 tff(221,plain,
% 0.48/0.67 (~(union(difference(C!2, B!3), B!3) = union(C!2, B!3))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.48/0.67 tff(222,plain,
% 0.48/0.67 ((~((union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))))) | (union(difference(C!2, B!3), B!3) = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(223,plain,
% 0.48/0.67 (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[222, 221, 206])).
% 0.48/0.67 tff(224,plain,
% 0.48/0.67 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(225,plain,
% 0.48/0.67 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.48/0.67 tff(226,plain,
% 0.48/0.67 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[225, 202])).
% 0.48/0.67 tff(227,plain,
% 0.48/0.67 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[226, 173])).
% 0.48/0.67 tff(228,plain,
% 0.48/0.67 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(229,plain,
% 0.48/0.67 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(230,plain,
% 0.48/0.67 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[229])).
% 0.48/0.67 tff(231,plain,
% 0.48/0.67 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))))),
% 0.48/0.67 inference(transitivity,[status(thm)],[230, 228])).
% 0.48/0.67 tff(232,plain,
% 0.48/0.67 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(233,plain,
% 0.48/0.68 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.48/0.68 tff(234,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[233, 82])).
% 0.48/0.68 tff(235,plain,
% 0.48/0.68 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(236,plain,
% 0.48/0.68 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.48/0.68 tff(237,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[236, 227])).
% 0.48/0.68 tff(238,plain,
% 0.48/0.68 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(239,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[238, 237, 200])).
% 0.48/0.68 tff(240,plain,
% 0.48/0.68 ((~((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(241,plain,
% 0.48/0.68 ((~((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[240, 200])).
% 0.48/0.68 tff(242,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[241, 239, 198])).
% 0.48/0.68 tff(243,plain,(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(244,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[243, 176])).
% 0.48/0.68 tff(245,plain,
% 0.48/0.68 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(246,plain,
% 0.48/0.68 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[245, 223])).
% 0.48/0.68 tff(247,plain,
% 0.48/0.68 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, B!3))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[246, 244])).
% 0.48/0.68 tff(248,plain,
% 0.48/0.68 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[247, 174])).
% 0.48/0.68 tff(249,plain,
% 0.48/0.68 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(250,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(B!3, difference(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[249, 234])).
% 0.48/0.68 tff(251,plain,
% 0.48/0.68 (~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[250, 248])).
% 0.48/0.68 tff(252,plain,
% 0.48/0.68 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(253,plain,
% 0.48/0.68 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.48/0.68 tff(254,plain,
% 0.48/0.68 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[253, 130])).
% 0.48/0.68 tff(255,plain,
% 0.48/0.68 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3)))) <=> (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(256,plain,
% 0.48/0.68 ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), difference(B!3, difference(C!2, B!3))))) | (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[255, 190])).
% 0.48/0.68 tff(257,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[256, 243])).
% 0.48/0.68 tff(258,plain,
% 0.48/0.68 ((member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), union(C!2, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(259,plain,
% 0.48/0.68 (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[258, 251])).
% 0.48/0.68 tff(260,plain,
% 0.48/0.68 ((~(member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3))))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(B!3, difference(C!2, B!3)))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(261,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[260, 259, 257])).
% 0.48/0.68 tff(262,plain,
% 0.48/0.68 (((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2))) <=> ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(263,plain,
% 0.48/0.68 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(264,plain,
% 0.48/0.68 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.48/0.68 tff(265,plain,
% 0.48/0.68 (member(tptp_fun_D_1(union(C!2, B!3), union(difference(C!2, B!3), B!3)), C!2)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[264, 64, 261])).
% 0.48/0.68 tff(266,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[265, 254])).
% 0.48/0.68 % SZS output end Proof
% 0.48/0.68 % E exiting
%------------------------------------------------------------------------------