%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET175+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:24 AM UTC 2025
% Result : Theorem 5.40s 5.59s
% Output : Proof 5.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET175+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:31:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.40/5.59 % SZS status Theorem
% 5.40/5.59 % SZS output start Proof
% 5.40/5.59 tff(tptp_fun_B_3_type, type, (
% 5.40/5.59 tptp_fun_B_3: $i)).
% 5.40/5.59 tff(union_type, type, (
% 5.40/5.59 union: ( $i * $i ) > $i)).
% 5.40/5.59 tff(intersection_type, type, (
% 5.40/5.59 intersection: ( $i * $i ) > $i)).
% 5.40/5.59 tff(tptp_fun_C_2_type, type, (
% 5.40/5.59 tptp_fun_C_2: $i)).
% 5.40/5.59 tff(member_type, type, (
% 5.40/5.59 member: ( $i * $i ) > $o)).
% 5.40/5.59 tff(tptp_fun_D_1_type, type, (
% 5.40/5.59 tptp_fun_D_1: ( $i * $i ) > $i)).
% 5.40/5.59 tff(subset_type, type, (
% 5.40/5.59 subset: ( $i * $i ) > $o)).
% 5.40/5.59 tff(tptp_fun_D_0_type, type, (
% 5.40/5.59 tptp_fun_D_0: ( $i * $i ) > $i)).
% 5.40/5.59 tff(1,assumption,(~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))), introduced(assumption)).
% 5.40/5.59 tff(2,plain,
% 5.40/5.59 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(3,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[2])).
% 5.40/5.59 tff(4,plain,
% 5.40/5.59 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(5,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[4])).
% 5.40/5.59 tff(6,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(7,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 5.40/5.59 tff(8,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[7, 6])).
% 5.40/5.59 tff(9,plain,(
% 5.40/5.59 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 5.40/5.59 inference(skolemize,[status(sab)],[8])).
% 5.40/5.59 tff(10,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[9, 5])).
% 5.40/5.59 tff(11,plain,
% 5.40/5.59 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[10, 3])).
% 5.40/5.59 tff(12,plain,
% 5.40/5.59 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(13,plain,
% 5.40/5.59 ((~(~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(14,plain,
% 5.40/5.59 ((~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(15,plain,
% 5.40/5.59 (((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(16,plain,
% 5.40/5.59 (((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(17,plain,
% 5.40/5.59 ((((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> ((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 5.40/5.59 inference(monotonicity,[status(thm)],[16])).
% 5.40/5.59 tff(18,plain,
% 5.40/5.59 ((((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[17, 15])).
% 5.40/5.59 tff(19,plain,
% 5.40/5.59 ((((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[18, 14])).
% 5.40/5.59 tff(20,plain,
% 5.40/5.59 ((~(((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))),
% 5.40/5.59 inference(monotonicity,[status(thm)],[19])).
% 5.40/5.59 tff(21,plain,
% 5.40/5.59 ((~(((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 5.40/5.59 inference(transitivity,[status(thm)],[20, 13])).
% 5.40/5.59 tff(22,plain,
% 5.40/5.59 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(monotonicity,[status(thm)],[21])).
% 5.40/5.59 tff(23,plain,
% 5.40/5.59 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[22, 12])).
% 5.40/5.59 tff(24,plain,
% 5.40/5.59 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.40/5.59 inference(quant_inst,[status(thm)],[])).
% 5.40/5.59 tff(25,plain,
% 5.40/5.59 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[24, 23])).
% 5.40/5.59 tff(26,plain,
% 5.40/5.59 ($false),
% 5.40/5.59 inference(unit_resolution,[status(thm)],[25, 11, 1])).
% 5.40/5.59 tff(27,plain,(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))), inference(lemma,lemma(discharge,[]))).
% 5.40/5.59 tff(28,plain,
% 5.40/5.59 (^[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))))))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(29,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[28])).
% 5.40/5.59 tff(30,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(pull_quant,[status(thm)],[])).
% 5.40/5.59 tff(31,plain,
% 5.40/5.59 (^[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)))))))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(32,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[31])).
% 5.40/5.59 tff(33,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[32, 30])).
% 5.40/5.59 tff(34,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[33, 29])).
% 5.40/5.59 tff(35,plain,
% 5.40/5.59 (^[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))))))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(36,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[35])).
% 5.40/5.59 tff(37,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(transitivity,[status(thm)],[36, 34])).
% 5.40/5.59 tff(38,plain,
% 5.40/5.59 (^[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)))))))))),
% 5.40/5.59 inference(bind,[status(th)],[])).
% 5.40/5.59 tff(39,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(quant_intro,[status(thm)],[38])).
% 5.40/5.59 tff(40,plain,
% 5.40/5.59 (![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)))),
% 5.40/5.59 inference(rewrite,[status(thm)],[])).
% 5.40/5.59 tff(41,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')).
% 5.40/5.59 tff(42,plain,
% 5.40/5.59 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[41, 40])).
% 5.40/5.59 tff(43,plain,(
% 5.40/5.59 ![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)))))),
% 5.40/5.59 inference(skolemize,[status(sab)],[42])).
% 5.40/5.59 tff(44,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[43, 39])).
% 5.40/5.59 tff(45,plain,
% 5.40/5.59 (![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)))))))),
% 5.40/5.59 inference(modus_ponens,[status(thm)],[44, 37])).
% 5.40/5.59 tff(46,plain,
% 5.40/5.59 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_1(C!2, B!3), B!3) <=> member(tptp_fun_D_1(C!2, B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))))),
% 5.40/5.59 inference(quant_inst,[status(thm)],[])).
% 5.40/5.59 tff(47,plain,
% 5.40/5.59 (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_1(C!2, B!3), B!3) <=> member(tptp_fun_D_1(C!2, B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))))),
% 5.40/5.59 inference(unit_resolution,[status(thm)],[46, 45])).
% 5.40/5.59 tff(48,plain,
% 5.40/5.59 (((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_1(C!2, B!3), B!3) <=> member(tptp_fun_D_1(C!2, B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))) | ((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(49,plain,
% 5.45/5.60 ((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[48, 47])).
% 5.45/5.60 tff(50,plain,
% 5.45/5.60 ((~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))) | (B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(51,plain,
% 5.45/5.60 ((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[50, 49])).
% 5.45/5.60 tff(52,plain,
% 5.45/5.60 (B!3 = intersection(B!3, B!3)),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[51, 27])).
% 5.45/5.60 tff(53,plain,
% 5.45/5.60 (intersection(B!3, B!3) = B!3),
% 5.45/5.60 inference(symmetry,[status(thm)],[52])).
% 5.45/5.60 tff(54,plain,
% 5.45/5.60 ((~![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(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))))))),
% 5.45/5.60 inference(quant_inst,[status(thm)],[])).
% 5.45/5.60 tff(55,plain,
% 5.45/5.60 (~((~((~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[54, 45])).
% 5.45/5.60 tff(56,plain,
% 5.45/5.60 (((~((~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))))) | ((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(57,plain,
% 5.45/5.60 ((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[56, 55])).
% 5.45/5.60 tff(58,assumption,(~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))), introduced(assumption)).
% 5.45/5.60 tff(59,plain,
% 5.45/5.60 (intersection(C!2, intersection(B!3, B!3)) = intersection(C!2, B!3)),
% 5.45/5.60 inference(monotonicity,[status(thm)],[53])).
% 5.45/5.60 tff(60,plain,
% 5.45/5.60 (member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 5.45/5.60 inference(monotonicity,[status(thm)],[59])).
% 5.45/5.60 tff(61,plain,
% 5.45/5.60 (member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3)) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))),
% 5.45/5.60 inference(symmetry,[status(thm)],[60])).
% 5.45/5.60 tff(62,assumption,(~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))), introduced(assumption)).
% 5.45/5.60 tff(63,plain,
% 5.45/5.60 (((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(64,plain,
% 5.45/5.60 (member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[63, 62])).
% 5.45/5.60 tff(65,plain,
% 5.45/5.60 (member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[64, 61])).
% 5.45/5.60 tff(66,plain,
% 5.45/5.60 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))))),
% 5.45/5.60 inference(quant_inst,[status(thm)],[])).
% 5.45/5.60 tff(67,plain,
% 5.45/5.60 (~(((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[66, 11])).
% 5.45/5.60 tff(68,plain,
% 5.45/5.60 (((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(69,plain,
% 5.45/5.60 (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[68, 62])).
% 5.45/5.60 tff(70,plain,
% 5.45/5.60 (((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(71,plain,
% 5.45/5.60 ((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[70, 69])).
% 5.45/5.60 tff(72,plain,
% 5.45/5.60 ((((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))))) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3))))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(73,plain,
% 5.45/5.60 ((((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))) | (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[72, 71])).
% 5.45/5.60 tff(74,plain,
% 5.45/5.60 (~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, intersection(B!3, B!3)))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[73, 67])).
% 5.45/5.60 tff(75,plain,
% 5.45/5.60 ($false),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[74, 65])).
% 5.45/5.60 tff(76,plain,((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))), inference(lemma,lemma(discharge,[]))).
% 5.45/5.60 tff(77,plain,
% 5.45/5.60 (^[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))))))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(78,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(quant_intro,[status(thm)],[77])).
% 5.45/5.60 tff(79,plain,
% 5.45/5.60 (^[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))))))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(80,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(quant_intro,[status(thm)],[79])).
% 5.45/5.60 tff(81,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(transitivity,[status(thm)],[80, 78])).
% 5.45/5.60 tff(82,plain,
% 5.45/5.60 (^[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)))))))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(83,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(quant_intro,[status(thm)],[82])).
% 5.45/5.60 tff(84,plain,
% 5.45/5.60 (![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)))),
% 5.45/5.60 inference(rewrite,[status(thm)],[])).
% 5.45/5.60 tff(85,plain,
% 5.45/5.60 (^[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))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(86,plain,
% 5.45/5.60 (![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)))),
% 5.45/5.60 inference(quant_intro,[status(thm)],[85])).
% 5.45/5.60 tff(87,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')).
% 5.45/5.60 tff(88,plain,
% 5.45/5.60 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[87, 86])).
% 5.45/5.60 tff(89,plain,
% 5.45/5.60 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[88, 84])).
% 5.45/5.60 tff(90,plain,(
% 5.45/5.60 ![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)))))),
% 5.45/5.60 inference(skolemize,[status(sab)],[89])).
% 5.45/5.60 tff(91,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[90, 83])).
% 5.45/5.60 tff(92,plain,
% 5.45/5.60 (![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)))))))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[91, 81])).
% 5.45/5.60 tff(93,plain,
% 5.45/5.60 (((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))))))) <=> ((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))))))),
% 5.45/5.60 inference(rewrite,[status(thm)],[])).
% 5.45/5.60 tff(94,plain,
% 5.45/5.60 ((~((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~(subset(intersection(C!2, B!3), intersection(B!3, B!3)) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))))))) <=> (~((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))))))),
% 5.45/5.60 inference(rewrite,[status(thm)],[])).
% 5.45/5.60 tff(95,plain,
% 5.45/5.60 (((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~(subset(intersection(C!2, B!3), intersection(B!3, B!3)) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))))))))) <=> ((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))))))),
% 5.45/5.60 inference(monotonicity,[status(thm)],[94])).
% 5.45/5.60 tff(96,plain,
% 5.45/5.60 (((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~(subset(intersection(C!2, B!3), intersection(B!3, B!3)) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))))))))) <=> ((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))))))),
% 5.45/5.60 inference(transitivity,[status(thm)],[95, 93])).
% 5.45/5.60 tff(97,plain,
% 5.45/5.60 ((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~(subset(intersection(C!2, B!3), intersection(B!3, B!3)) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3))))))))),
% 5.45/5.60 inference(quant_inst,[status(thm)],[])).
% 5.45/5.60 tff(98,plain,
% 5.45/5.60 ((~![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(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))))))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[97, 96])).
% 5.45/5.60 tff(99,plain,
% 5.45/5.60 (~((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[98, 92])).
% 5.45/5.60 tff(100,plain,
% 5.45/5.60 (((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))))) | ((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(101,plain,
% 5.45/5.60 ((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[100, 99])).
% 5.45/5.60 tff(102,plain,
% 5.45/5.60 ((~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3)))) | (~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(103,plain,
% 5.45/5.60 ((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[102, 101])).
% 5.45/5.60 tff(104,plain,
% 5.45/5.60 (subset(intersection(C!2, B!3), intersection(B!3, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[103, 76])).
% 5.45/5.60 tff(105,plain,
% 5.45/5.60 (((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~((~((~member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_0(intersection(B!3, B!3), intersection(C!2, B!3)), intersection(B!3, B!3)))) | subset(intersection(C!2, B!3), intersection(B!3, B!3))))) | ((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(106,plain,
% 5.45/5.60 ((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[105, 99])).
% 5.45/5.60 tff(107,plain,
% 5.45/5.60 ((~((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3))))) | (~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))),
% 5.45/5.60 inference(tautology,[status(thm)],[])).
% 5.45/5.60 tff(108,plain,
% 5.45/5.60 ((~subset(intersection(C!2, B!3), intersection(B!3, B!3))) | ![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[107, 106])).
% 5.45/5.60 tff(109,plain,
% 5.45/5.60 (![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[108, 104])).
% 5.45/5.60 tff(110,plain,
% 5.45/5.60 (((~![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))) | ((~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))) <=> ((~![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))),
% 5.45/5.60 inference(rewrite,[status(thm)],[])).
% 5.45/5.60 tff(111,plain,
% 5.45/5.60 ((~![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))) | ((~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))),
% 5.45/5.60 inference(quant_inst,[status(thm)],[])).
% 5.45/5.60 tff(112,plain,
% 5.45/5.60 ((~![D: $i] : ((~member(D, intersection(C!2, B!3))) | member(D, intersection(B!3, B!3)))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))),
% 5.45/5.60 inference(modus_ponens,[status(thm)],[111, 110])).
% 5.45/5.60 tff(113,plain,
% 5.45/5.60 (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 5.45/5.60 inference(unit_resolution,[status(thm)],[112, 109, 58])).
% 5.45/5.60 tff(114,plain,
% 5.45/5.60 (^[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))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(115,plain,
% 5.45/5.60 (![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)))),
% 5.45/5.60 inference(quant_intro,[status(thm)],[114])).
% 5.45/5.60 tff(116,plain,
% 5.45/5.60 (![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)))),
% 5.45/5.60 inference(rewrite,[status(thm)],[])).
% 5.45/5.60 tff(117,plain,
% 5.45/5.60 (^[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))))),
% 5.45/5.60 inference(bind,[status(th)],[])).
% 5.45/5.60 tff(118,plain,
% 5.45/5.60 (![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)))),
% 5.45/5.61 inference(quant_intro,[status(thm)],[117])).
% 5.45/5.61 tff(119,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')).
% 5.45/5.61 tff(120,plain,
% 5.45/5.61 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[119, 118])).
% 5.45/5.61 tff(121,plain,
% 5.45/5.61 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[120, 116])).
% 5.45/5.61 tff(122,plain,(
% 5.45/5.61 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 5.45/5.61 inference(skolemize,[status(sab)],[121])).
% 5.45/5.61 tff(123,plain,
% 5.45/5.61 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[122, 115])).
% 5.45/5.61 tff(124,plain,
% 5.45/5.61 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 5.45/5.61 inference(quant_inst,[status(thm)],[])).
% 5.45/5.61 tff(125,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[124, 123])).
% 5.45/5.61 tff(126,plain,
% 5.45/5.61 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 5.45/5.61 inference(bind,[status(th)],[])).
% 5.45/5.61 tff(127,plain,
% 5.45/5.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 5.45/5.61 inference(quant_intro,[status(thm)],[126])).
% 5.45/5.61 tff(128,plain,
% 5.45/5.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 5.45/5.61 inference(rewrite,[status(thm)],[])).
% 5.45/5.61 tff(129,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 5.45/5.61 tff(130,plain,
% 5.45/5.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[129, 128])).
% 5.45/5.61 tff(131,plain,(
% 5.45/5.61 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 5.45/5.61 inference(skolemize,[status(sab)],[130])).
% 5.45/5.61 tff(132,plain,
% 5.45/5.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[131, 127])).
% 5.45/5.61 tff(133,plain,
% 5.45/5.61 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 5.45/5.61 inference(quant_inst,[status(thm)],[])).
% 5.45/5.61 tff(134,plain,
% 5.45/5.61 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[133, 132])).
% 5.45/5.61 tff(135,plain,
% 5.45/5.61 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 5.45/5.61 inference(symmetry,[status(thm)],[134])).
% 5.45/5.61 tff(136,plain,
% 5.45/5.61 (union(intersection(C!2, B!3), intersection(B!3, B!3)) = union(intersection(B!3, C!2), B!3)),
% 5.45/5.61 inference(monotonicity,[status(thm)],[135, 53])).
% 5.45/5.61 tff(137,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[136])).
% 5.45/5.61 tff(138,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3)))),
% 5.45/5.61 inference(symmetry,[status(thm)],[137])).
% 5.45/5.61 tff(139,plain,
% 5.45/5.61 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 5.45/5.61 inference(bind,[status(th)],[])).
% 5.45/5.61 tff(140,plain,
% 5.45/5.61 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 5.45/5.61 inference(quant_intro,[status(thm)],[139])).
% 5.45/5.61 tff(141,plain,
% 5.45/5.61 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 5.45/5.61 inference(rewrite,[status(thm)],[])).
% 5.45/5.61 tff(142,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 5.45/5.61 tff(143,plain,
% 5.45/5.61 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[142, 141])).
% 5.45/5.61 tff(144,plain,(
% 5.45/5.61 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 5.45/5.61 inference(skolemize,[status(sab)],[143])).
% 5.45/5.61 tff(145,plain,
% 5.45/5.61 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[144, 140])).
% 5.45/5.61 tff(146,plain,
% 5.45/5.61 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, intersection(B!3, C!2)) = union(intersection(B!3, C!2), B!3))),
% 5.45/5.61 inference(quant_inst,[status(thm)],[])).
% 5.45/5.61 tff(147,plain,
% 5.45/5.61 (union(B!3, intersection(B!3, C!2)) = union(intersection(B!3, C!2), B!3)),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[146, 145])).
% 5.45/5.61 tff(148,plain,
% 5.45/5.61 (union(intersection(B!3, B!3), intersection(C!2, B!3)) = union(B!3, intersection(B!3, C!2))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[53, 135])).
% 5.45/5.61 tff(149,plain,
% 5.45/5.61 (union(intersection(B!3, B!3), intersection(C!2, B!3)) = union(intersection(B!3, C!2), B!3)),
% 5.45/5.61 inference(transitivity,[status(thm)],[148, 147])).
% 5.45/5.61 tff(150,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[149])).
% 5.45/5.61 tff(151,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 5.45/5.61 inference(symmetry,[status(thm)],[150])).
% 5.45/5.61 tff(152,plain,
% 5.45/5.61 ((~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[151])).
% 5.45/5.61 tff(153,assumption,(~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))), introduced(assumption)).
% 5.45/5.61 tff(154,plain,
% 5.45/5.61 (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[153, 152])).
% 5.45/5.61 tff(155,plain,
% 5.45/5.61 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))))),
% 5.45/5.61 inference(rewrite,[status(thm)],[])).
% 5.45/5.61 tff(156,plain,
% 5.45/5.61 ((member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 5.45/5.61 inference(rewrite,[status(thm)],[])).
% 5.45/5.61 tff(157,plain,
% 5.45/5.61 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(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(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[156])).
% 5.45/5.61 tff(158,plain,
% 5.45/5.61 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(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(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))))),
% 5.45/5.61 inference(transitivity,[status(thm)],[157, 155])).
% 5.45/5.61 tff(159,plain,
% 5.45/5.61 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))),
% 5.45/5.61 inference(quant_inst,[status(thm)],[])).
% 5.45/5.61 tff(160,plain,
% 5.45/5.61 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[159, 158])).
% 5.45/5.61 tff(161,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[160, 123])).
% 5.45/5.61 tff(162,plain,
% 5.45/5.61 ((~![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(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))))))),
% 5.45/5.61 inference(quant_inst,[status(thm)],[])).
% 5.45/5.61 tff(163,plain,
% 5.45/5.61 (~((~((~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[162, 45])).
% 5.45/5.61 tff(164,plain,
% 5.45/5.61 (((~((~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))) | (member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_0(intersection(union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2)), tptp_fun_D_1(intersection(C!2, B!3), C!2)), union(intersection(C!2, B!3), tptp_fun_D_1(intersection(C!2, B!3), C!2))), intersection(B!3, B!3))))) | (~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))))) | ((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(165,plain,
% 5.45/5.61 ((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[164, 163])).
% 5.45/5.61 tff(166,plain,
% 5.45/5.61 (union(intersection(B!3, C!2), B!3) = union(B!3, intersection(B!3, C!2))),
% 5.45/5.61 inference(symmetry,[status(thm)],[147])).
% 5.45/5.61 tff(167,plain,
% 5.45/5.61 ((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) <=> (union(B!3, intersection(B!3, C!2)) = B!3)),
% 5.45/5.61 inference(monotonicity,[status(thm)],[166, 53])).
% 5.45/5.61 tff(168,plain,
% 5.45/5.61 ((union(B!3, intersection(B!3, C!2)) = B!3) <=> (union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))),
% 5.45/5.61 inference(symmetry,[status(thm)],[167])).
% 5.45/5.61 tff(169,plain,
% 5.45/5.61 ((~(union(B!3, intersection(B!3, C!2)) = B!3)) <=> (~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)))),
% 5.45/5.61 inference(monotonicity,[status(thm)],[168])).
% 5.45/5.61 tff(170,plain,
% 5.45/5.61 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) <=> (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B))),
% 5.45/5.61 inference(rewrite,[status(thm)],[])).
% 5.45/5.61 tff(171,axiom,(~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_absorbtion_for_union')).
% 5.45/5.61 tff(172,plain,
% 5.45/5.61 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[171, 170])).
% 5.45/5.61 tff(173,plain,
% 5.45/5.61 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[172, 170])).
% 5.45/5.61 tff(174,plain,
% 5.45/5.61 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[173, 170])).
% 5.45/5.61 tff(175,plain,
% 5.45/5.61 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[174, 170])).
% 5.45/5.61 tff(176,plain,(
% 5.45/5.61 ~(union(B!3, intersection(B!3, C!2)) = B!3)),
% 5.45/5.61 inference(skolemize,[status(sab)],[175])).
% 5.45/5.61 tff(177,plain,
% 5.45/5.61 (~(union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[176, 169])).
% 5.45/5.61 tff(178,plain,
% 5.45/5.61 ((~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))) | (union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(179,plain,
% 5.45/5.61 (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[178, 177, 165])).
% 5.45/5.61 tff(180,plain,
% 5.45/5.61 ((member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(181,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[180, 153, 179])).
% 5.45/5.61 tff(182,plain,
% 5.45/5.61 ((member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(183,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[182, 181])).
% 5.45/5.61 tff(184,plain,
% 5.45/5.61 ((~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3))) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(185,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[184, 183, 161])).
% 5.45/5.61 tff(186,plain,
% 5.45/5.61 ($false),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[185, 154])).
% 5.45/5.61 tff(187,plain,(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))), inference(lemma,lemma(discharge,[]))).
% 5.45/5.61 tff(188,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3)))),
% 5.45/5.61 inference(modus_ponens,[status(thm)],[187, 138])).
% 5.45/5.61 tff(189,plain,
% 5.45/5.61 ((~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3))) <=> (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), intersection(B!3, B!3)))) | (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(190,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[189, 188, 125])).
% 5.45/5.61 tff(191,plain,
% 5.45/5.61 ((~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(192,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)) | member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[191, 190])).
% 5.45/5.61 tff(193,plain,
% 5.45/5.61 ($false),
% 5.45/5.61 inference(unit_resolution,[status(thm)],[192, 113, 58])).
% 5.45/5.61 tff(194,plain,(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))), inference(lemma,lemma(discharge,[]))).
% 5.45/5.61 tff(195,plain,
% 5.45/5.61 ((member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) | (~member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))),
% 5.45/5.61 inference(tautology,[status(thm)],[])).
% 5.45/5.61 tff(196,plain,
% 5.45/5.61 (member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3))),
% 5.45/5.62 inference(unit_resolution,[status(thm)],[195, 187, 194])).
% 5.45/5.62 tff(197,plain,
% 5.45/5.62 ((~((union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)) | (~(member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(intersection(B!3, B!3), union(intersection(B!3, C!2), B!3)), intersection(B!3, B!3)))))) | (union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3))),
% 5.45/5.62 inference(unit_resolution,[status(thm)],[178, 196])).
% 5.45/5.62 tff(198,plain,
% 5.45/5.62 (union(intersection(B!3, C!2), B!3) = intersection(B!3, B!3)),
% 5.45/5.62 inference(unit_resolution,[status(thm)],[197, 57])).
% 5.45/5.62 tff(199,plain,
% 5.45/5.62 (union(B!3, intersection(B!3, C!2)) = B!3),
% 5.45/5.62 inference(transitivity,[status(thm)],[147, 198, 53])).
% 5.45/5.62 tff(200,plain,
% 5.45/5.62 ($false),
% 5.45/5.62 inference(unit_resolution,[status(thm)],[176, 199])).
% 5.45/5.62 % SZS output end Proof
% 5.45/5.62 % E exiting
%------------------------------------------------------------------------------