%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET014+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:24:47 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET014+3 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:01:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_D_2_type, type, (
% 0.12/0.38 tptp_fun_D_2: $i)).
% 0.12/0.38 tff(tptp_fun_D_0_type, type, (
% 0.12/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_C_3_type, type, (
% 0.12/0.38 tptp_fun_C_3: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, C!3)))) | (~(subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~((~subset(union(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, C!3)))) | (~(subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~((~subset(union(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, C!3)))) | (~(subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)))))) | (subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,axiom,(~![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_union_subset')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ~((~(subset(B!4, C!3) & subset(D!2, C!3))) | subset(union(B!4, D!2), C!3))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~subset(union(B!4, D!2), C!3)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~(subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))))) | subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~(subset(union(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))))) | (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))) | (~(subset(D!2, C!3) | (~((~member(tptp_fun_D_0(C!3, D!2), D!2)) | member(tptp_fun_D_0(C!3, D!2), C!3)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (~((~((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))) | (~(subset(D!2, C!3) | (~((~member(tptp_fun_D_0(C!3, D!2), D!2)) | member(tptp_fun_D_0(C!3, D!2), C!3))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 16])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))) | (~(subset(D!2, C!3) | (~((~member(tptp_fun_D_0(C!3, D!2), D!2)) | member(tptp_fun_D_0(C!3, D!2), C!3)))))) | ((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (subset(B!4, C!3) & subset(D!2, C!3)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (subset(D!2, C!3)),
% 0.12/0.38 inference(and_elim,[status(thm)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))) | (~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~((~subset(D!2, C!3)) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3)))) | ![D: $i] : ((~member(D, D!2)) | member(D, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![D: $i] : ((~member(D, D!2)) | member(D, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~![D: $i] : ((~member(D, D!2)) | member(D, C!3))) | ((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))) <=> ((~![D: $i] : ((~member(D, D!2)) | member(D, C!3))) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~![D: $i] : ((~member(D, D!2)) | member(D, C!3))) | ((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~![D: $i] : ((~member(D, D!2)) | member(D, C!3))) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 43, 34])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(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)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(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))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 16])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(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)))))) | ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (subset(B!4, C!3)),
% 0.20/0.39 inference(and_elim,[status(thm)],[39])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 55, 34])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~(member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (~(member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 59, 47])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (((~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), C!3)) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 32])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~(member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)))) | (~member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~(member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 63, 61])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.39 tff(71,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.39 tff(74,plain,(
% 0.20/0.39 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 ((member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4))) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[78, 76])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(C!3, union(B!4, D!2)), B!4) | member(tptp_fun_D_0(C!3, union(B!4, D!2)), D!2)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[81, 75, 65])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------