%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET595+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:56 AM UTC 2025
% Result : Theorem 1.06s 1.25s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET595+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:30:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.06/1.25 % SZS status Theorem
% 1.06/1.25 % SZS output start Proof
% 1.06/1.25 tff(member_type, type, (
% 1.06/1.25 member: ( $i * $i ) > $o)).
% 1.06/1.25 tff(tptp_fun_C_2_type, type, (
% 1.06/1.25 tptp_fun_C_2: $i)).
% 1.06/1.25 tff(tptp_fun_D_0_type, type, (
% 1.06/1.25 tptp_fun_D_0: ( $i * $i ) > $i)).
% 1.06/1.25 tff(union_type, type, (
% 1.06/1.25 union: ( $i * $i ) > $i)).
% 1.06/1.25 tff(tptp_fun_B_3_type, type, (
% 1.06/1.25 tptp_fun_B_3: $i)).
% 1.06/1.25 tff(difference_type, type, (
% 1.06/1.25 difference: ( $i * $i ) > $i)).
% 1.06/1.25 tff(tptp_fun_D_1_type, type, (
% 1.06/1.25 tptp_fun_D_1: ( $i * $i ) > $i)).
% 1.06/1.25 tff(subset_type, type, (
% 1.06/1.25 subset: ( $i * $i ) > $o)).
% 1.06/1.25 tff(1,assumption,((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))))), introduced(assumption)).
% 1.06/1.25 tff(2,plain,
% 1.06/1.25 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(3,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[2])).
% 1.06/1.25 tff(4,plain,
% 1.06/1.25 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(pull_quant,[status(thm)],[])).
% 1.06/1.25 tff(5,plain,
% 1.06/1.25 (^[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_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(6,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[5])).
% 1.06/1.25 tff(7,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(transitivity,[status(thm)],[6, 4])).
% 1.06/1.25 tff(8,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(transitivity,[status(thm)],[7, 3])).
% 1.06/1.25 tff(9,plain,
% 1.06/1.25 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(10,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[9])).
% 1.06/1.25 tff(11,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(transitivity,[status(thm)],[10, 8])).
% 1.06/1.25 tff(12,plain,
% 1.06/1.25 (^[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_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) <=> (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(13,plain,
% 1.06/1.25 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[12])).
% 1.06/1.25 tff(14,plain,
% 1.06/1.25 (![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)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 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')).
% 1.06/1.25 tff(16,plain,
% 1.06/1.25 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.06/1.25 tff(17,plain,(
% 1.06/1.25 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 1.06/1.25 inference(skolemize,[status(sab)],[16])).
% 1.06/1.25 tff(18,plain,
% 1.06/1.25 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.06/1.25 tff(19,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.06/1.25 tff(20,plain,
% 1.06/1.25 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))))))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(21,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 1.06/1.25 tff(22,plain,(~((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))))))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(23,assumption,(~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))), introduced(assumption)).
% 1.06/1.25 tff(24,plain,
% 1.06/1.25 (^[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))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(25,plain,
% 1.06/1.25 (![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)))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[24])).
% 1.06/1.25 tff(26,plain,
% 1.06/1.25 (![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)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(27,plain,
% 1.06/1.25 (^[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))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(28,plain,
% 1.06/1.25 (![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)))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[27])).
% 1.06/1.25 tff(29,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')).
% 1.06/1.25 tff(30,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.06/1.25 tff(31,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.06/1.25 tff(32,plain,(
% 1.06/1.25 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.06/1.25 inference(skolemize,[status(sab)],[31])).
% 1.06/1.25 tff(33,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.06/1.25 tff(34,plain,
% 1.06/1.25 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(35,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[34, 33, 23])).
% 1.06/1.25 tff(36,plain,(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(37,assumption,(((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))), introduced(assumption)).
% 1.06/1.25 tff(38,plain,
% 1.06/1.25 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(39,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[38])).
% 1.06/1.25 tff(40,plain,
% 1.06/1.25 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(41,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[40])).
% 1.06/1.25 tff(42,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(43,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 1.06/1.25 tff(44,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.06/1.25 tff(45,plain,(
% 1.06/1.25 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 1.06/1.25 inference(skolemize,[status(sab)],[44])).
% 1.06/1.25 tff(46,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.06/1.25 tff(47,plain,
% 1.06/1.25 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.06/1.25 tff(48,plain,
% 1.06/1.25 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(49,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[48, 47, 37])).
% 1.06/1.25 tff(50,plain,(~(((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(51,assumption,(~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))), introduced(assumption)).
% 1.06/1.25 tff(52,plain,
% 1.06/1.25 ((member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(53,plain,
% 1.06/1.25 (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.06/1.25 tff(54,plain,
% 1.06/1.25 ((member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3))),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(55,plain,
% 1.06/1.25 (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[54, 51])).
% 1.06/1.25 tff(56,plain,
% 1.06/1.25 (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.06/1.25 tff(57,plain,
% 1.06/1.25 (~((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))))))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.06/1.25 tff(58,plain,
% 1.06/1.25 (((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))))) | ((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))))),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(59,plain,
% 1.06/1.25 ((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.06/1.25 tff(60,plain,
% 1.06/1.25 ((union(B!3, difference(C!2, B!3)) = C!2) <=> (C!2 = union(B!3, difference(C!2, B!3)))),
% 1.06/1.25 inference(commutativity,[status(thm)],[])).
% 1.06/1.25 tff(61,plain,
% 1.06/1.25 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(62,plain,
% 1.06/1.25 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[61])).
% 1.06/1.25 tff(63,plain,
% 1.06/1.25 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(64,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 1.06/1.25 tff(65,plain,
% 1.06/1.25 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.06/1.25 tff(66,plain,(
% 1.06/1.25 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.06/1.25 inference(skolemize,[status(sab)],[65])).
% 1.06/1.25 tff(67,plain,
% 1.06/1.25 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.06/1.25 tff(68,plain,
% 1.06/1.25 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(69,plain,
% 1.06/1.25 (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.06/1.25 tff(70,plain,
% 1.06/1.25 (union(difference(C!2, B!3), B!3) = union(B!3, difference(C!2, B!3))),
% 1.06/1.25 inference(symmetry,[status(thm)],[69])).
% 1.06/1.25 tff(71,plain,
% 1.06/1.25 ((union(difference(C!2, B!3), B!3) = C!2) <=> (union(B!3, difference(C!2, B!3)) = C!2)),
% 1.06/1.25 inference(monotonicity,[status(thm)],[70])).
% 1.06/1.25 tff(72,plain,
% 1.06/1.25 ((union(difference(C!2, B!3), B!3) = C!2) <=> (C!2 = union(B!3, difference(C!2, B!3)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[71, 60])).
% 1.06/1.25 tff(73,plain,
% 1.06/1.25 ((C!2 = union(B!3, difference(C!2, B!3))) <=> (union(difference(C!2, B!3), B!3) = C!2)),
% 1.06/1.25 inference(symmetry,[status(thm)],[72])).
% 1.06/1.25 tff(74,plain,
% 1.06/1.25 ((~(C!2 = union(B!3, difference(C!2, B!3)))) <=> (~(union(difference(C!2, B!3), B!3) = C!2))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[73])).
% 1.06/1.25 tff(75,plain,
% 1.06/1.25 ((~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B))))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B)))))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(76,plain,
% 1.06/1.25 ((~![B: $i, C: $i] : (subset(B, C) => (C = union(B, difference(C, B))))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B)))))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(77,axiom,(~![B: $i, C: $i] : (subset(B, C) => (C = union(B, difference(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th54')).
% 1.06/1.25 tff(78,plain,
% 1.06/1.25 (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.06/1.25 tff(79,plain,
% 1.06/1.25 (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[78, 75])).
% 1.06/1.25 tff(80,plain,
% 1.06/1.25 (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.06/1.25 tff(81,plain,
% 1.06/1.25 (~![B: $i, C: $i] : ((~subset(B, C)) | (C = union(B, difference(C, B))))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[80, 75])).
% 1.06/1.25 tff(82,plain,(
% 1.06/1.25 ~((~subset(B!3, C!2)) | (C!2 = union(B!3, difference(C!2, B!3))))),
% 1.06/1.25 inference(skolemize,[status(sab)],[81])).
% 1.06/1.25 tff(83,plain,
% 1.06/1.25 (~(C!2 = union(B!3, difference(C!2, B!3)))),
% 1.06/1.25 inference(or_elim,[status(thm)],[82])).
% 1.06/1.25 tff(84,plain,
% 1.06/1.25 (~(union(difference(C!2, B!3), B!3) = C!2)),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[83, 74])).
% 1.06/1.25 tff(85,plain,
% 1.06/1.25 ((~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))))) | (union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(86,plain,
% 1.06/1.25 (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[85, 84, 59])).
% 1.06/1.25 tff(87,assumption,(~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)), introduced(assumption)).
% 1.06/1.25 tff(88,plain,
% 1.06/1.25 ((member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(89,plain,
% 1.06/1.25 (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[88, 87, 86])).
% 1.06/1.25 tff(90,plain,
% 1.06/1.25 ((~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))),
% 1.06/1.25 inference(tautology,[status(thm)],[])).
% 1.06/1.25 tff(91,plain,
% 1.06/1.25 (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[90, 89, 56])).
% 1.06/1.25 tff(92,plain,
% 1.06/1.25 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(93,plain,
% 1.06/1.26 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[92])).
% 1.06/1.26 tff(94,plain,
% 1.06/1.26 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(95,plain,
% 1.06/1.26 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[94])).
% 1.06/1.26 tff(96,plain,
% 1.06/1.26 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(transitivity,[status(thm)],[95, 93])).
% 1.06/1.26 tff(97,plain,
% 1.06/1.26 (^[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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(98,plain,
% 1.06/1.26 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[97])).
% 1.06/1.26 tff(99,plain,
% 1.06/1.26 (![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)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(100,plain,
% 1.06/1.26 (^[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))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(101,plain,
% 1.06/1.26 (![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)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[100])).
% 1.06/1.26 tff(102,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 1.06/1.26 tff(103,plain,
% 1.06/1.26 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.06/1.26 tff(104,plain,
% 1.06/1.26 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.06/1.26 tff(105,plain,(
% 1.06/1.26 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))),
% 1.06/1.26 inference(skolemize,[status(sab)],[104])).
% 1.06/1.26 tff(106,plain,
% 1.06/1.26 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.06/1.26 tff(107,plain,
% 1.06/1.26 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[106, 96])).
% 1.06/1.26 tff(108,plain,
% 1.06/1.26 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))))))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(109,plain,
% 1.06/1.26 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2))))))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.06/1.26 tff(110,plain,
% 1.06/1.26 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))))) | ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(111,plain,
% 1.06/1.26 ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[110, 109])).
% 1.06/1.26 tff(112,plain,
% 1.06/1.26 (subset(B!3, C!2)),
% 1.06/1.26 inference(or_elim,[status(thm)],[82])).
% 1.06/1.26 tff(113,plain,
% 1.06/1.26 ((~((~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))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(114,plain,
% 1.06/1.26 ((~((~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))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[113, 112])).
% 1.06/1.26 tff(115,plain,
% 1.06/1.26 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[114, 111])).
% 1.06/1.26 tff(116,plain,
% 1.06/1.26 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(117,plain,
% 1.06/1.26 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(118,plain,
% 1.06/1.26 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.06/1.26 tff(119,plain,
% 1.06/1.26 ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[118, 115])).
% 1.06/1.26 tff(120,plain,
% 1.06/1.26 (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[119, 87])).
% 1.06/1.26 tff(121,assumption,(~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))), introduced(assumption)).
% 1.06/1.26 tff(122,plain,
% 1.06/1.26 (((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | (~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(123,plain,
% 1.06/1.26 (~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[122, 121])).
% 1.06/1.26 tff(124,plain,
% 1.06/1.26 (((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(125,plain,
% 1.06/1.26 (member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[124, 121])).
% 1.06/1.26 tff(126,assumption,(((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))), introduced(assumption)).
% 1.06/1.26 tff(127,plain,
% 1.06/1.26 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(128,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[127, 47, 126])).
% 1.06/1.26 tff(129,plain,(~(((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(130,plain,
% 1.06/1.26 ((((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3))) | (~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(131,plain,
% 1.06/1.26 ((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3))) | (~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.06/1.26 tff(132,plain,
% 1.06/1.26 (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[131, 125])).
% 1.06/1.26 tff(133,plain,
% 1.06/1.26 (((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), B!3)) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(134,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[133, 132, 123])).
% 1.06/1.26 tff(135,plain,((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(136,plain,
% 1.06/1.26 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))))))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(137,plain,
% 1.06/1.26 ((~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))))))) <=> (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)))))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(138,plain,
% 1.06/1.26 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[137])).
% 1.06/1.26 tff(139,plain,
% 1.06/1.26 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))))))),
% 1.06/1.26 inference(transitivity,[status(thm)],[138, 136])).
% 1.06/1.26 tff(140,plain,
% 1.06/1.26 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~(subset(difference(C!2, B!3), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2)))))))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(141,plain,
% 1.06/1.26 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)))))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.06/1.26 tff(142,plain,
% 1.06/1.26 (~((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[141, 107])).
% 1.06/1.26 tff(143,plain,
% 1.06/1.26 (((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)))) | ((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(144,plain,
% 1.06/1.26 ((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.06/1.26 tff(145,plain,
% 1.06/1.26 ((~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2))) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(146,plain,
% 1.06/1.26 ((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.06/1.26 tff(147,plain,
% 1.06/1.26 (subset(difference(C!2, B!3), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[146, 135])).
% 1.06/1.26 tff(148,plain,
% 1.06/1.26 (((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | member(tptp_fun_D_1(C!2, difference(C!2, B!3)), C!2))) | subset(difference(C!2, B!3), C!2)))) | ((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(149,plain,
% 1.06/1.26 ((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[148, 142])).
% 1.06/1.26 tff(150,plain,
% 1.06/1.26 ((~((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2)))) | (~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(151,plain,
% 1.06/1.26 ((~subset(difference(C!2, B!3), C!2)) | ![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.06/1.26 tff(152,plain,
% 1.06/1.26 (![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[151, 147])).
% 1.06/1.26 tff(153,plain,
% 1.06/1.26 (((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))) <=> ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(154,plain,
% 1.06/1.26 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(155,plain,
% 1.06/1.26 ((~![D: $i] : ((~member(D, difference(C!2, B!3))) | member(D, C!2))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.06/1.26 tff(156,plain,
% 1.06/1.26 ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[155, 152])).
% 1.06/1.26 tff(157,plain,
% 1.06/1.26 (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[156, 87])).
% 1.06/1.26 tff(158,plain,
% 1.06/1.26 ((~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3)))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(159,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[158, 157, 120, 91])).
% 1.06/1.26 tff(160,plain,(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(161,plain,
% 1.06/1.26 ((~((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(162,plain,
% 1.06/1.26 ((~((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[161, 160])).
% 1.06/1.26 tff(163,plain,
% 1.06/1.26 (~((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[162, 55])).
% 1.06/1.26 tff(164,plain,
% 1.06/1.26 ((((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))) | ((~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3)) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(165,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[164, 163, 53, 50])).
% 1.06/1.26 tff(166,plain,(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(167,plain,
% 1.06/1.26 ((~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))),
% 1.06/1.26 inference(tautology,[status(thm)],[])).
% 1.06/1.26 tff(168,plain,
% 1.06/1.26 ((~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), B!3) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), difference(C!2, B!3))))) | member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.06/1.27 tff(169,plain,
% 1.06/1.27 (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[168, 36])).
% 1.06/1.27 tff(170,plain,
% 1.06/1.27 ((member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))) | (~member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))),
% 1.06/1.27 inference(tautology,[status(thm)],[])).
% 1.06/1.27 tff(171,plain,
% 1.06/1.27 (member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[170, 160, 169])).
% 1.06/1.27 tff(172,assumption,(union(difference(C!2, B!3), B!3) = C!2), introduced(assumption)).
% 1.06/1.27 tff(173,plain,
% 1.06/1.27 (C!2 = union(difference(C!2, B!3), B!3)),
% 1.06/1.27 inference(symmetry,[status(thm)],[172])).
% 1.06/1.27 tff(174,plain,
% 1.06/1.27 (C!2 = union(B!3, difference(C!2, B!3))),
% 1.06/1.27 inference(transitivity,[status(thm)],[173, 70])).
% 1.06/1.27 tff(175,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[83, 174])).
% 1.06/1.27 tff(176,plain,(~(union(difference(C!2, B!3), B!3) = C!2)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(177,plain,
% 1.06/1.27 (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2))))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[85, 176, 171])).
% 1.06/1.27 tff(178,plain,
% 1.06/1.27 ((~((~(union(difference(C!2, B!3), B!3) = C!2)) | (member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(union(difference(C!2, B!3), B!3), union(union(C!2, tptp_fun_D_1(B!3, C!2)), difference(C!2, B!3))), C!2)))) | (~((union(difference(C!2, B!3), B!3) = C!2) | (~(member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3)) <=> member(tptp_fun_D_0(C!2, union(difference(C!2, B!3), B!3)), C!2)))))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[58, 177])).
% 1.06/1.27 tff(179,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[178, 22])).
% 1.06/1.27 % SZS output end Proof
% 1.06/1.27 % E exiting
%------------------------------------------------------------------------------