%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET185+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:25:25 AM UTC 2025
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET185+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:32:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(member_type, type, (
% 0.13/0.41 member: ( $i * $i ) > $o)).
% 0.13/0.41 tff(union_type, type, (
% 0.13/0.41 union: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_B_3_type, type, (
% 0.13/0.41 tptp_fun_B_3: $i)).
% 0.13/0.41 tff(tptp_fun_C_2_type, type, (
% 0.13/0.41 tptp_fun_C_2: $i)).
% 0.13/0.41 tff(tptp_fun_D_1_type, type, (
% 0.13/0.41 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_D_0_type, type, (
% 0.13/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.41 tff(subset_type, type, (
% 0.13/0.41 subset: ( $i * $i ) > $o)).
% 0.13/0.41 tff(1,assumption,((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))))), introduced(assumption)).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(pull_quant,[status(thm)],[])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[6, 4])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[7, 3])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[10, 8])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(15,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.41 tff(17,plain,(
% 0.13/0.41 ![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)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[16])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 0.13/0.41 tff(22,plain,(~((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((B!3 = union(B!3, B!3)) <=> (union(B!3, B!3) = B!3)),
% 0.13/0.41 inference(commutativity,[status(thm)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 ((union(B!3, B!3) = B!3) <=> (B!3 = union(B!3, B!3))),
% 0.13/0.41 inference(symmetry,[status(thm)],[23])).
% 0.13/0.41 tff(25,assumption,(~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))), introduced(assumption)).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(30,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.42 tff(31,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.13/0.42 tff(32,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.42 tff(34,plain,(
% 0.13/0.42 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[33])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 ((member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> (member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3) | member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))) <=> (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> (member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3) | member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> (member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3) | member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> (member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3) | member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(41,plain,
% 0.13/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.42 tff(42,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[41, 35, 25])).
% 0.22/0.42 tff(43,plain,(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 ((~![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)))))))) | (~((~((~(union(B!3, B!3) = B!3)) | (member(tptp_fun_D_0(B!3, C!2), union(B!3, B!3)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))) | (~((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (~((~((~(union(B!3, B!3) = B!3)) | (member(tptp_fun_D_0(B!3, C!2), union(B!3, B!3)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))) | (~((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[44, 19])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (((~((~(union(B!3, B!3) = B!3)) | (member(tptp_fun_D_0(B!3, C!2), union(B!3, B!3)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))) | (~((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))))) | ((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 ((~((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3))))) | (union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 ((union(B!3, B!3) = B!3) | (~(member(tptp_fun_D_1(B!3, union(B!3, B!3)), union(B!3, B!3)) <=> member(tptp_fun_D_1(B!3, union(B!3, B!3)), B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (union(B!3, B!3) = B!3),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (B!3 = union(B!3, B!3)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[50, 24])).
% 0.22/0.42 tff(52,assumption,(B!3 = union(B!3, B!3)), introduced(assumption)).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (union(B!3, B!3) = B!3),
% 0.22/0.42 inference(symmetry,[status(thm)],[52])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (union(C!2, union(B!3, B!3)) = union(C!2, B!3)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[53])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))),
% 0.22/0.42 inference(symmetry,[status(thm)],[55])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.22/0.42 tff(58,assumption,(~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))), introduced(assumption)).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, 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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 ((member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))) <=> ((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))) <=> ((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[62, 60])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 ((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 ((~![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), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[65, 35])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))) <=> (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.22/0.42 tff(68,assumption,(~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))), introduced(assumption)).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))) | (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[69, 68, 66])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (~((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))))) | ((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 ((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ((C!2 = union(B!3, C!2)) <=> (union(B!3, C!2) = C!2)),
% 0.22/0.43 inference(commutativity,[status(thm)],[])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(79,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.22/0.43 tff(81,plain,(
% 0.22/0.43 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.22/0.43 inference(skolemize,[status(sab)],[80])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, C!2) = union(C!2, B!3))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (union(B!3, C!2) = union(C!2, B!3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (union(C!2, B!3) = union(B!3, C!2)),
% 0.22/0.43 inference(symmetry,[status(thm)],[84])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 ((C!2 = union(C!2, B!3)) <=> (C!2 = union(B!3, C!2))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[85])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 ((C!2 = union(C!2, B!3)) <=> (union(B!3, C!2) = C!2)),
% 0.22/0.43 inference(transitivity,[status(thm)],[86, 75])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 ((union(B!3, C!2) = C!2) <=> (C!2 = union(C!2, B!3))),
% 0.22/0.43 inference(symmetry,[status(thm)],[87])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 ((~(union(B!3, C!2) = C!2)) <=> (~(C!2 = union(C!2, B!3)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 ((~![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(92,axiom,(~![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_subset_union')).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[95, 90])).
% 0.22/0.43 tff(97,plain,(
% 0.22/0.43 ~((~subset(B!3, C!2)) | (union(B!3, C!2) = C!2))),
% 0.22/0.43 inference(skolemize,[status(sab)],[96])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (~(union(B!3, C!2) = C!2)),
% 0.22/0.43 inference(or_elim,[status(thm)],[97])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (~(C!2 = union(C!2, B!3))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[98, 89])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 ((~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))) | (C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[100, 99, 74])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 ((member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[102, 68])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 ((member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[104, 103, 101])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[105, 71])).
% 0.22/0.43 tff(107,plain,((member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))) | (~(B!3 = union(B!3, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[107, 52])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3))) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, union(B!3, B!3)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[110, 66])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[111, 59])).
% 0.22/0.43 tff(113,plain,(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) | (~(B!3 = union(B!3, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[113, 51])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)),
% 0.22/0.43 inference(symmetry,[status(thm)],[115])).
% 0.22/0.43 tff(117,assumption,(~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)), introduced(assumption)).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(B!3, B!3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[118, 117, 108])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 (^[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))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (^[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))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[124, 122])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (^[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)))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.22/0.44 tff(128,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(129,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(130,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.22/0.44 tff(131,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.22/0.44 tff(132,plain,
% 0.22/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.22/0.44 tff(134,plain,(
% 0.22/0.44 ![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)))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[133])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 (![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)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 (![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)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(138,plain,
% 0.22/0.44 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))) | ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 (subset(B!3, C!2)),
% 0.22/0.44 inference(or_elim,[status(thm)],[97])).
% 0.22/0.44 tff(142,plain,
% 0.22/0.44 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.22/0.44 tff(145,plain,
% 0.22/0.44 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(146,plain,
% 0.22/0.44 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[148, 117])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[149, 120])).
% 0.22/0.44 tff(151,plain,(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | (~(B!3 = union(B!3, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[151, 51])).
% 0.22/0.44 tff(153,plain,
% 0.22/0.44 ((member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(154,plain,
% 0.22/0.44 (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[153, 152, 114])).
% 0.22/0.44 tff(155,assumption,(C!2 = union(C!2, B!3)), introduced(assumption)).
% 0.22/0.44 tff(156,plain,
% 0.22/0.44 (union(C!2, B!3) = C!2),
% 0.22/0.44 inference(symmetry,[status(thm)],[155])).
% 0.22/0.44 tff(157,plain,
% 0.22/0.44 (union(B!3, C!2) = C!2),
% 0.22/0.44 inference(transitivity,[status(thm)],[84, 156])).
% 0.22/0.44 tff(158,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[98, 157])).
% 0.22/0.44 tff(159,plain,(~(C!2 = union(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(160,plain,
% 0.22/0.44 (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[100, 159, 154])).
% 0.22/0.44 tff(161,plain,
% 0.22/0.44 ((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), tptp_fun_D_0(B!3, C!2)), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[73, 160])).
% 0.22/0.44 tff(162,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[161, 22])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------