%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET173+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:24 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET173+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:31:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun_B_3_type, type, (
% 0.19/0.39 tptp_fun_B_3: $i)).
% 0.19/0.39 tff(intersection_type, type, (
% 0.19/0.39 intersection: ( $i * $i ) > $i)).
% 0.19/0.39 tff(union_type, type, (
% 0.19/0.39 union: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_2_type, type, (
% 0.19/0.39 tptp_fun_C_2: $i)).
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_D_1_type, type, (
% 0.19/0.39 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,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')).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![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 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (~((~((~(B!3 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (((~((~(B!3 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))))) | ((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(26,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.40 tff(28,plain,(
% 0.19/0.40 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, C!2) = union(C!2, B!3))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (union(B!3, C!2) = union(C!2, B!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (union(C!2, B!3) = union(B!3, C!2)),
% 0.19/0.40 inference(symmetry,[status(thm)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (intersection(union(C!2, B!3), B!3) = intersection(union(B!3, C!2), B!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))),
% 0.19/0.40 inference(symmetry,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))) <=> (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.40 tff(37,assumption,(~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))), introduced(assumption)).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(44,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.41 tff(46,plain,(
% 0.19/0.41 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))) <=> (((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[54, 49])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 48])).
% 0.19/0.41 tff(59,assumption,(~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) <=> (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)))), introduced(assumption)).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.41 tff(68,plain,(
% 0.19/0.41 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) <=> (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 69, 59])).
% 0.19/0.41 tff(72,plain,(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) <=> (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,(
% 0.19/0.41 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[77])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, union(B!3, C!2)) = intersection(union(B!3, C!2), B!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (intersection(B!3, union(B!3, C!2)) = intersection(union(B!3, C!2), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (intersection(B!3, union(C!2, B!3)) = intersection(B!3, union(B!3, C!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (intersection(B!3, union(C!2, B!3)) = intersection(union(B!3, C!2), B!3)),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 81])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~![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 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (~((~((~(B!3 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 18])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~((~(B!3 = intersection(union(B!3, C!2), B!3))) | (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), C!2), intersection(union(B!3, C!2), B!3))))) | (~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))))) | ((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((B!3 = intersection(B!3, union(B!3, C!2))) <=> (intersection(B!3, union(B!3, C!2)) = B!3)),
% 0.19/0.42 inference(commutativity,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (intersection(union(B!3, C!2), B!3) = intersection(B!3, union(B!3, C!2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[81])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((B!3 = intersection(union(B!3, C!2), B!3)) <=> (B!3 = intersection(B!3, union(B!3, C!2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((B!3 = intersection(union(B!3, C!2), B!3)) <=> (intersection(B!3, union(B!3, C!2)) = B!3)),
% 0.19/0.42 inference(transitivity,[status(thm)],[92, 90])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((intersection(B!3, union(B!3, C!2)) = B!3) <=> (B!3 = intersection(union(B!3, C!2), B!3))),
% 0.19/0.42 inference(symmetry,[status(thm)],[93])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~(intersection(B!3, union(B!3, C!2)) = B!3)) <=> (~(B!3 = intersection(union(B!3, C!2), B!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)) <=> (~![B: $i, C: $i] : (intersection(B, union(B, C)) = B))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(97,axiom,(~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_absorbtion_for_intersection')).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 96])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (~![B: $i, C: $i] : (intersection(B, union(B, C)) = B)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.42 tff(102,plain,(
% 0.19/0.42 ~(intersection(B!3, union(B!3, C!2)) = B!3)),
% 0.19/0.42 inference(skolemize,[status(sab)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (~(B!3 = intersection(union(B!3, C!2), B!3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))) | (B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 103, 89])).
% 0.19/0.42 tff(106,assumption,(~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)), introduced(assumption)).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 106, 105])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 85])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (~(((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 48])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[112, 106])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3)))) | (~((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(B!3, union(C!2, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[114, 113, 111])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[115, 109])).
% 0.19/0.42 tff(117,plain,(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) <=> (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)) <=> (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), C!2)))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 72])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ((~((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (~((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[123, 117, 122])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))) | ((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((((~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), union(C!2, B!3)))) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))) | member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(C!2, B!3), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[126, 58])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[127, 38])).
% 0.19/0.42 tff(129,plain,(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[130, 117, 129])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 ((~((B!3 = intersection(union(B!3, C!2), B!3)) | (~(member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(union(B!3, C!2), B!3), B!3), intersection(union(B!3, C!2), B!3)))))) | (B!3 = intersection(union(B!3, C!2), B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 131])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (B!3 = intersection(union(B!3, C!2), B!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[132, 22])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (intersection(union(B!3, C!2), B!3) = B!3),
% 0.19/0.43 inference(symmetry,[status(thm)],[133])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 (intersection(B!3, union(B!3, C!2)) = B!3),
% 0.19/0.43 inference(transitivity,[status(thm)],[81, 134])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 135])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------