%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET146+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:25:21 AM UTC 2025
% Result : Theorem 0.23s 0.50s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET146+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n012.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 04:24:25 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.23/0.50 % SZS status Theorem
% 0.23/0.50 % SZS output start Proof
% 0.23/0.50 tff(member_type, type, (
% 0.23/0.50 member: ( $i * $i ) > $o)).
% 0.23/0.50 tff(intersection_type, type, (
% 0.23/0.50 intersection: ( $i * $i ) > $i)).
% 0.23/0.50 tff(tptp_fun_B_3_type, type, (
% 0.23/0.50 tptp_fun_B_3: $i)).
% 0.23/0.50 tff(empty_set_type, type, (
% 0.23/0.50 empty_set: $i)).
% 0.23/0.50 tff(tptp_fun_D_2_type, type, (
% 0.23/0.50 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.23/0.50 tff(tptp_fun_D_0_type, type, (
% 0.23/0.50 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.23/0.50 tff(1,assumption,(~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))), introduced(assumption)).
% 0.23/0.50 tff(2,plain,
% 0.23/0.50 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(3,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.50 tff(4,plain,
% 0.23/0.50 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(5,plain,
% 0.23/0.50 (![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, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[4])).
% 0.23/0.50 tff(6,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 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')).
% 0.23/0.50 tff(8,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.23/0.50 tff(9,plain,(
% 0.23/0.50 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[8])).
% 0.23/0.50 tff(10,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.23/0.50 tff(11,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.23/0.50 tff(12,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(13,plain,
% 0.23/0.50 ((~(~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(14,plain,
% 0.23/0.50 ((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(15,plain,
% 0.23/0.50 (((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(16,plain,
% 0.23/0.50 (((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(17,plain,
% 0.23/0.50 ((((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> ((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[16])).
% 0.23/0.50 tff(18,plain,
% 0.23/0.50 ((((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[17, 15])).
% 0.23/0.50 tff(19,plain,
% 0.23/0.50 ((((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[18, 14])).
% 0.23/0.50 tff(20,plain,
% 0.23/0.50 ((~(((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[19])).
% 0.23/0.50 tff(21,plain,
% 0.23/0.50 ((~(((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[20, 13])).
% 0.23/0.50 tff(22,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[21])).
% 0.23/0.50 tff(23,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[22, 12])).
% 0.23/0.50 tff(24,plain,
% 0.23/0.50 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(25,plain,
% 0.23/0.50 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.23/0.50 tff(26,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[25, 11, 1])).
% 0.23/0.50 tff(27,plain,(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(28,plain,
% 0.23/0.50 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(29,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.50 tff(30,plain,
% 0.23/0.50 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(pull_quant,[status(thm)],[])).
% 0.23/0.50 tff(31,plain,
% 0.23/0.50 (^[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_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(32,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[31])).
% 0.23/0.50 tff(33,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[32, 30])).
% 0.23/0.50 tff(34,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[33, 29])).
% 0.23/0.50 tff(35,plain,
% 0.23/0.50 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(36,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[35])).
% 0.23/0.50 tff(37,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[36, 34])).
% 0.23/0.50 tff(38,plain,
% 0.23/0.50 (^[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_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))) <=> (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(39,plain,
% 0.23/0.50 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.23/0.50 tff(40,plain,
% 0.23/0.50 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 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')).
% 0.23/0.50 tff(42,plain,
% 0.23/0.50 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.23/0.50 tff(43,plain,(
% 0.23/0.50 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.23/0.50 inference(skolemize,[status(sab)],[42])).
% 0.23/0.50 tff(44,plain,
% 0.23/0.50 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.23/0.50 tff(45,plain,
% 0.23/0.50 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.23/0.50 tff(46,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(47,plain,
% 0.23/0.50 ((~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))))) <=> (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(48,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[47])).
% 0.23/0.50 tff(49,plain,
% 0.23/0.50 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[48, 46])).
% 0.23/0.50 tff(50,plain,
% 0.23/0.50 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(51,plain,
% 0.23/0.50 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.23/0.50 tff(52,plain,
% 0.23/0.50 (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[51, 45])).
% 0.23/0.51 tff(53,plain,
% 0.23/0.51 (((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_2(B!3, empty_set), B!3) <=> member(tptp_fun_D_2(B!3, empty_set), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))) | ((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(54,plain,
% 0.23/0.51 ((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.23/0.51 tff(55,plain,
% 0.23/0.51 ((~((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))) | (~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(56,plain,
% 0.23/0.51 ((~(member(tptp_fun_D_2(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_2(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.23/0.51 tff(57,plain,
% 0.23/0.51 (B!3 = intersection(B!3, B!3)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[56, 27])).
% 0.23/0.51 tff(58,plain,
% 0.23/0.51 (intersection(B!3, B!3) = B!3),
% 0.23/0.51 inference(symmetry,[status(thm)],[57])).
% 0.23/0.51 tff(59,plain,
% 0.23/0.51 (intersection(empty_set, intersection(B!3, B!3)) = intersection(empty_set, B!3)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[58])).
% 0.23/0.51 tff(60,plain,
% 0.23/0.51 (member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[59])).
% 0.23/0.51 tff(61,plain,
% 0.23/0.51 (member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))),
% 0.23/0.51 inference(symmetry,[status(thm)],[60])).
% 0.23/0.51 tff(62,plain,
% 0.23/0.51 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(intersection(empty_set, B!3) = empty_set)) | (member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), empty_set)))) | (~((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)))))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(63,plain,
% 0.23/0.51 (~((~((~(intersection(empty_set, B!3) = empty_set)) | (member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), empty_set)))) | (~((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[62, 45])).
% 0.23/0.51 tff(64,plain,
% 0.23/0.51 (((~((~(intersection(empty_set, B!3) = empty_set)) | (member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(intersection(tptp_fun_D_0(B!3, empty_set), tptp_fun_D_0(B!3, empty_set)), intersection(B!3, B!3)), empty_set)))) | (~((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)))))) | ((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(65,plain,
% 0.23/0.51 ((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.23/0.51 tff(66,plain,
% 0.23/0.51 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(67,plain,
% 0.23/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[66])).
% 0.23/0.51 tff(68,plain,
% 0.23/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(69,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.23/0.51 tff(70,plain,
% 0.23/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.23/0.51 tff(71,plain,(
% 0.23/0.51 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.23/0.51 inference(skolemize,[status(sab)],[70])).
% 0.23/0.51 tff(72,plain,
% 0.23/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.23/0.51 tff(73,plain,
% 0.23/0.51 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, empty_set) = intersection(empty_set, B!3))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(74,plain,
% 0.23/0.51 (intersection(B!3, empty_set) = intersection(empty_set, B!3)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.23/0.51 tff(75,plain,
% 0.23/0.51 (intersection(empty_set, B!3) = intersection(B!3, empty_set)),
% 0.23/0.51 inference(symmetry,[status(thm)],[74])).
% 0.23/0.51 tff(76,plain,
% 0.23/0.51 ((intersection(empty_set, B!3) = empty_set) <=> (intersection(B!3, empty_set) = empty_set)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[75])).
% 0.23/0.51 tff(77,plain,
% 0.23/0.51 ((intersection(B!3, empty_set) = empty_set) <=> (intersection(empty_set, B!3) = empty_set)),
% 0.23/0.51 inference(symmetry,[status(thm)],[76])).
% 0.23/0.51 tff(78,plain,
% 0.23/0.51 ((~(intersection(B!3, empty_set) = empty_set)) <=> (~(intersection(empty_set, B!3) = empty_set))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[77])).
% 0.23/0.51 tff(79,plain,
% 0.23/0.51 ((~![B: $i] : (intersection(B, empty_set) = empty_set)) <=> (~![B: $i] : (intersection(B, empty_set) = empty_set))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(80,axiom,(~![B: $i] : (intersection(B, empty_set) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th61')).
% 0.23/0.51 tff(81,plain,
% 0.23/0.51 (~![B: $i] : (intersection(B, empty_set) = empty_set)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.23/0.51 tff(82,plain,
% 0.23/0.51 (~![B: $i] : (intersection(B, empty_set) = empty_set)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.23/0.51 tff(83,plain,
% 0.23/0.51 (~![B: $i] : (intersection(B, empty_set) = empty_set)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.23/0.51 tff(84,plain,
% 0.23/0.51 (~![B: $i] : (intersection(B, empty_set) = empty_set)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.23/0.51 tff(85,plain,(
% 0.23/0.51 ~(intersection(B!3, empty_set) = empty_set)),
% 0.23/0.51 inference(skolemize,[status(sab)],[84])).
% 0.23/0.51 tff(86,plain,
% 0.23/0.51 (~(intersection(empty_set, B!3) = empty_set)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.23/0.51 tff(87,plain,
% 0.23/0.51 ((~((intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))))) | (intersection(empty_set, B!3) = empty_set) | (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(88,plain,
% 0.23/0.51 (~(member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[87, 86, 65])).
% 0.23/0.51 tff(89,plain,
% 0.23/0.51 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(90,plain,
% 0.23/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.23/0.51 tff(91,plain,
% 0.23/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(92,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.23/0.51 tff(93,plain,
% 0.23/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.23/0.51 tff(94,plain,(
% 0.23/0.51 ![B: $i] : (~member(B, empty_set))),
% 0.23/0.51 inference(skolemize,[status(sab)],[93])).
% 0.23/0.51 tff(95,plain,
% 0.23/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.23/0.51 tff(96,plain,
% 0.23/0.51 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(97,plain,
% 0.23/0.51 (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.23/0.51 tff(98,plain,
% 0.23/0.51 ((member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3)) | member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(99,plain,
% 0.23/0.51 (member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, B!3))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[98, 97, 88])).
% 0.23/0.51 tff(100,plain,
% 0.23/0.51 (member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[99, 61])).
% 0.23/0.51 tff(101,plain,
% 0.23/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(102,plain,
% 0.23/0.51 ((~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))) <=> (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(103,plain,
% 0.23/0.51 ((((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))) <=> (((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(104,plain,
% 0.23/0.51 ((~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))) <=> (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[103])).
% 0.23/0.51 tff(105,plain,
% 0.23/0.51 ((~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))) <=> (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[104, 102])).
% 0.23/0.51 tff(106,plain,
% 0.23/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[105])).
% 0.23/0.51 tff(107,plain,
% 0.23/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[106, 101])).
% 0.23/0.51 tff(108,plain,
% 0.23/0.51 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(109,plain,
% 0.23/0.51 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.23/0.51 tff(110,plain,
% 0.23/0.51 (~(((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[109, 11])).
% 0.23/0.51 tff(111,plain,
% 0.23/0.51 (((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) | member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(112,plain,
% 0.23/0.51 ((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.23/0.51 tff(113,plain,
% 0.23/0.51 ((((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))) | (~((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3))))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(114,plain,
% 0.23/0.51 ((((~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(B!3, B!3)))) <=> member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))) | (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.23/0.51 tff(115,plain,
% 0.23/0.51 (~member(tptp_fun_D_2(empty_set, intersection(empty_set, B!3)), intersection(empty_set, intersection(B!3, B!3)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.23/0.51 tff(116,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[115, 100])).
% 0.23/0.51 % SZS output end Proof
% 0.23/0.51 % E exiting
%------------------------------------------------------------------------------