%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET194+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:26 AM UTC 2025
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET194+3 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 04:31:55 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(member_type, type, (
% 0.14/0.39 member: ( $i * $i ) > $o)).
% 0.14/0.39 tff(tptp_fun_C_2_type, type, (
% 0.14/0.39 tptp_fun_C_2: $i)).
% 0.14/0.39 tff(tptp_fun_D_0_type, type, (
% 0.14/0.39 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_B_3_type, type, (
% 0.14/0.39 tptp_fun_B_3: $i)).
% 0.14/0.39 tff(union_type, type, (
% 0.14/0.39 union: ( $i * $i ) > $i)).
% 0.14/0.39 tff(subset_type, type, (
% 0.14/0.39 subset: ( $i * $i ) > $o)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[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))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![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))))))) <=> ![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)))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (^[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))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (![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))))))) <=> ![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)))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![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))))))) <=> ![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)))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (^[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)))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![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))))) <=> ![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)))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (^[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))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.39 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')).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.14/0.39 tff(14,plain,(
% 0.14/0.39 ![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)))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[13])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (![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)))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![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)))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 ((~![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!3, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (~((~((~subset(B!3, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (((~((~subset(B!3, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))))) | (subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 ((~![B: $i, C: $i] : subset(B, union(B, C))) <=> (~![B: $i, C: $i] : subset(B, union(B, C)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(22,axiom,(~![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_subset_of_union')).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.14/0.40 tff(27,plain,(
% 0.14/0.40 ~subset(B!3, union(B!3, C!2))),
% 0.14/0.40 inference(skolemize,[status(sab)],[26])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 ((~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))) | subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 ((~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 ((member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)) | (~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))) | (~member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (~member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[35, 30])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~(member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) | (~(member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (~(member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[37, 36, 34])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.14/0.40 tff(44,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')).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.14/0.40 tff(47,plain,(
% 0.14/0.40 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[46])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 ((member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3))) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[54, 48, 38])).
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40 % E exiting
%------------------------------------------------------------------------------