%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET577+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:53 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET577+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:28:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_C_3_type, type, (
% 0.19/0.40 tptp_fun_C_3: $i)).
% 0.19/0.40 tff(tptp_fun_D_1_type, type, (
% 0.19/0.40 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.19/0.40 tff(union_type, type, (
% 0.19/0.40 union: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_D_2_type, type, (
% 0.19/0.40 tptp_fun_D_2: $i)).
% 0.19/0.40 tff(tptp_fun_B_4_type, type, (
% 0.19/0.40 tptp_fun_B_4: $i)).
% 0.19/0.40 tff(tptp_fun_D_0_type, type, (
% 0.19/0.40 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.40 tff(1,assumption,(~member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,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: $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)],[2])).
% 0.19/0.40 tff(4,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: $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(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 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(quant_intro,[status(thm)],[5])).
% 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, 4])).
% 0.19/0.40 tff(8,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)],[7, 3])).
% 0.19/0.40 tff(9,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(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] : (~((~((~(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)],[9])).
% 0.19/0.40 tff(11,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)],[10, 8])).
% 0.19/0.40 tff(12,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(13,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)],[12])).
% 0.19/0.40 tff(14,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(15,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(16,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)],[15, 14])).
% 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(skolemize,[status(sab)],[16])).
% 0.19/0.40 tff(18,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)],[17, 13])).
% 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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.40 tff(20,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)))))))) | (~((~((~(union(D!2, C!3) = B!4)) | (member(tptp_fun_D_0(C!3, D!2), union(D!2, C!3)) <=> member(tptp_fun_D_0(C!3, D!2), B!4)))) | (~((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~((~((~(union(D!2, C!3) = B!4)) | (member(tptp_fun_D_0(C!3, D!2), union(D!2, C!3)) <=> member(tptp_fun_D_0(C!3, D!2), B!4)))) | (~((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (((~((~(union(D!2, C!3) = B!4)) | (member(tptp_fun_D_0(C!3, D!2), union(D!2, C!3)) <=> member(tptp_fun_D_0(C!3, D!2), B!4)))) | (~((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)))))) | ((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 ((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((union(C!3, D!2) = B!4) <=> (B!4 = union(C!3, D!2))),
% 0.19/0.40 inference(commutativity,[status(thm)],[])).
% 0.19/0.40 tff(25,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(26,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)],[25])).
% 0.19/0.40 tff(27,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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,(
% 0.19/0.41 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, D!2) = union(D!2, C!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (union(C!3, D!2) = union(D!2, C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (union(D!2, C!3) = union(C!3, D!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((union(D!2, C!3) = B!4) <=> (union(C!3, D!2) = B!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((union(D!2, C!3) = B!4) <=> (B!4 = union(C!3, D!2))),
% 0.19/0.41 inference(transitivity,[status(thm)],[35, 24])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((B!4 = union(C!3, D!2)) <=> (union(D!2, C!3) = B!4)),
% 0.19/0.41 inference(symmetry,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~(B!4 = union(C!3, D!2))) <=> (~(union(D!2, C!3) = B!4))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2)))) <=> (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) | member(E, D))) => (B = union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,axiom,(~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) | member(E, D))) => (B = union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th18')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~(B!4 = union(C!3, D!2))),
% 0.19/0.41 inference(and_elim,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (~(union(D!2, C!3) = B!4)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~((union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))))) | (union(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 49, 23])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 1])).
% 0.19/0.41 tff(55,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(56,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)],[55])).
% 0.19/0.41 tff(57,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(58,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(59,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)],[58])).
% 0.19/0.41 tff(60,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(61,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)],[60, 59])).
% 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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.41 tff(63,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)],[62])).
% 0.19/0.41 tff(64,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)],[63, 56])).
% 0.19/0.41 tff(65,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(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)))) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))) | (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))) | (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 54])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[E: $i] : refl((member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) <=> (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) <=> ![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[47])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)))) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 1])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 82, 80, 69])).
% 0.19/0.41 tff(85,plain,(member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)))) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)) | (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)) | (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4)) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[89, 51])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[90, 85])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) <=> (member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)))) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (member(tptp_fun_D_1(B!4, union(D!2, C!3)), union(D!2, C!3)) | (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 66])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 91])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)) | (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (~member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3))) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), D!2) | member(tptp_fun_D_1(B!4, union(D!2, C!3)), C!3)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 98, 96, 88])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------