%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET574+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:53 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET574+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 05:28:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(member_type, type, (
% 0.13/0.37 member: ( $i * $i ) > $o)).
% 0.13/0.37 tff(tptp_fun_D_1_type, type, (
% 0.13/0.37 tptp_fun_D_1: $i)).
% 0.13/0.37 tff(tptp_fun_C_2_type, type, (
% 0.13/0.37 tptp_fun_C_2: $i)).
% 0.13/0.37 tff(intersect_type, type, (
% 0.13/0.37 intersect: ( $i * $i ) > $o)).
% 0.13/0.37 tff(tptp_fun_D_0_type, type, (
% 0.13/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.37 tff(tptp_fun_B_3_type, type, (
% 0.13/0.37 tptp_fun_B_3: $i)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (^[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))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (^[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))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (^[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)))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (![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)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 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')).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.37 tff(11,plain,(
% 0.13/0.37 ![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)))))),
% 0.13/0.37 inference(skolemize,[status(sab)],[10])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (((~![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(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1))))))))) <=> ((~![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(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 ((~((~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))) | (~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))))) <=> (~((~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1))))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (((~![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(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))) | (~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))))))) <=> ((~![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(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))))))),
% 0.13/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (((~![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(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))) | (~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))))))) <=> ((~![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(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((~![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(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))) | (~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~![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(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1))))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (~((~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1)))))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (((~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | (~((~intersect(C!2, D!1)) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | (~member(tptp_fun_D_0(D!1, C!2), D!1))))))) | (intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ((~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 ((~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => intersect(C, D))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(25,axiom,(~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => intersect(C, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th13')).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | intersect(C, D))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.13/0.38 tff(30,plain,(
% 0.13/0.38 ~((~(member(B!3, C!2) & member(B!3, D!1))) | intersect(C!2, D!1))),
% 0.13/0.38 inference(skolemize,[status(sab)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (~intersect(C!2, D!1)),
% 0.13/0.38 inference(or_elim,[status(thm)],[30])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 ((~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 ((~(intersect(C!2, D!1) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1))))) | ![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (member(B!3, C!2) & member(B!3, D!1)),
% 0.13/0.38 inference(or_elim,[status(thm)],[30])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (member(B!3, D!1)),
% 0.13/0.38 inference(and_elim,[status(thm)],[35])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (member(B!3, C!2)),
% 0.13/0.38 inference(and_elim,[status(thm)],[35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (((~![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))) | ((~member(B!3, C!2)) | (~member(B!3, D!1)))) <=> ((~![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))) | (~member(B!3, C!2)) | (~member(B!3, D!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 ((~![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))) | ((~member(B!3, C!2)) | (~member(B!3, D!1)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ((~![D: $i] : ((~member(D, C!2)) | (~member(D, D!1)))) | (~member(B!3, C!2)) | (~member(B!3, D!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[40, 37, 36, 34])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------