%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET626+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:02 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET626+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:31:48 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(member_type, type, (
% 0.18/0.37 member: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_C_3_type, type, (
% 0.18/0.37 tptp_fun_C_3: $i)).
% 0.18/0.37 tff(tptp_fun_D_0_type, type, (
% 0.18/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_B_4_type, type, (
% 0.18/0.37 tptp_fun_B_4: $i)).
% 0.18/0.37 tff(intersection_type, type, (
% 0.18/0.37 intersection: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_D_2_type, type, (
% 0.18/0.37 tptp_fun_D_2: $i)).
% 0.18/0.37 tff(intersect_type, type, (
% 0.18/0.37 intersect: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(9,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.37 tff(11,plain,(
% 0.18/0.37 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[10])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 ((~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))))) <=> (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))) | (intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C))) <=> (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : (intersect(B, intersection(C, D)) => intersect(B, C))) <=> (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,axiom,(~![B: $i, C: $i, D: $i] : (intersect(B, intersection(C, D)) => intersect(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th102')).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~intersect(B, intersection(C, D))) | intersect(B, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.18/0.38 tff(30,plain,(
% 0.18/0.38 ~((~intersect(B!4, intersection(C!3, D!2))) | intersect(B!4, C!3))),
% 0.18/0.38 inference(skolemize,[status(sab)],[29])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (~intersect(B!4, C!3)),
% 0.18/0.38 inference(or_elim,[status(thm)],[30])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ((~((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))))) <=> (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[37, 35])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2))))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (~((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[40, 13])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (((~(intersect(B!4, intersection(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, intersection(C!3, D!2)))))) | (~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))))) | ((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 ((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (intersect(B!4, intersection(C!3, D!2))),
% 0.18/0.38 inference(or_elim,[status(thm)],[30])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 ((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 ((~((~intersect(B!4, intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))) | member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)))) <=> ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | ((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[52, 49, 34])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(59,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')).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.39 tff(61,plain,(
% 0.18/0.39 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[60])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (~(((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))) | member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[66, 47])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2)))) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))) <=> member(tptp_fun_D_0(intersection(C!3, D!2), B!4), intersection(C!3, D!2))) | (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (~((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[69, 65])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, D!2), B!4), D!2))) | member(tptp_fun_D_0(intersection(C!3, D!2), B!4), C!3)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[71, 70, 53])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------