%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET011+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:24:45 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET011+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:01:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(member_type, type, (
% 0.20/0.48 member: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_B_3_type, type, (
% 0.20/0.48 tptp_fun_B_3: $i)).
% 0.20/0.48 tff(tptp_fun_D_1_type, type, (
% 0.20/0.48 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.20/0.48 tff(difference_type, type, (
% 0.20/0.48 difference: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_C_2_type, type, (
% 0.20/0.48 tptp_fun_C_2: $i)).
% 0.20/0.48 tff(intersection_type, type, (
% 0.20/0.48 intersection: ( $i * $i ) > $i)).
% 0.20/0.48 tff(1,assumption,((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(7,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.48 tff(9,plain,(
% 0.20/0.48 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[8])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))) | (~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(pull_quant,[status(thm)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[22, 18])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))) <=> (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(30,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.48 tff(32,plain,(
% 0.20/0.48 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[31])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 ((~![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)))))))) | (~((~((~(difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3))) | (member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), intersection(C!2, B!3))))) | (~((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (~((~((~(difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3))) | (member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), intersection(C!2, B!3))))) | (~((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((~((~(difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3))) | (member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(difference(B!3, difference(B!3, C!2)), intersection(C!2, B!3)), intersection(C!2, B!3))))) | (~((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))))))) | ((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.48 tff(44,plain,(
% 0.20/0.48 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.48 inference(skolemize,[status(sab)],[43])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.20/0.48 inference(symmetry,[status(thm)],[47])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 ((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) <=> (difference(B!3, difference(B!3, C!2)) = intersection(B!3, C!2))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 ((difference(B!3, difference(B!3, C!2)) = intersection(B!3, C!2)) <=> (difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3))),
% 0.20/0.48 inference(symmetry,[status(thm)],[49])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~(difference(B!3, difference(B!3, C!2)) = intersection(B!3, C!2))) <=> (~(difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))) <=> (~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(53,axiom,(~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_difference_difference_intersection')).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (~![B: $i, C: $i] : (difference(B, difference(B, C)) = intersection(B, C))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.49 tff(58,plain,(
% 0.20/0.49 ~(difference(B!3, difference(B!3, C!2)) = intersection(B!3, C!2))),
% 0.20/0.49 inference(skolemize,[status(sab)],[57])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (~(difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 ((~((difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))))) | (difference(B!3, difference(B!3, C!2)) = intersection(C!2, B!3)) | (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (~(member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[60, 59, 38])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 ((member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[63, 16])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(70,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.49 tff(72,plain,(
% 0.20/0.49 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[71])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))) | (~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[78, 64])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[82, 81, 1])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.20/0.49 tff(86,assumption,(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))), introduced(assumption)).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[87, 74, 86])).
% 0.20/0.49 tff(89,plain,(~(((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[91, 85])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[93, 92, 83, 81])).
% 0.20/0.49 tff(95,plain,(~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | (~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[102, 89])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[103, 101])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))) | ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[105, 13])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[106, 95])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), intersection(C!2, B!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 61])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[109, 107])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 ((((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) <=> member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))) | ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, difference(B!3, C!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[111, 76])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[112, 110])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~((~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2)))) | (~member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), B!3)) | member(tptp_fun_D_1(intersection(C!2, B!3), difference(B!3, difference(B!3, C!2))), difference(B!3, C!2))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[114, 113, 104, 97])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------