%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET597+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 05:25:57 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET597+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:29:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_E_5_type, type, (
% 0.13/0.39 tptp_fun_E_5: $i)).
% 0.13/0.39 tff(tptp_fun_D_2_type, type, (
% 0.13/0.39 tptp_fun_D_2: $i)).
% 0.13/0.39 tff(tptp_fun_C_3_type, type, (
% 0.13/0.39 tptp_fun_C_3: $i)).
% 0.13/0.39 tff(tptp_fun_B_4_type, type, (
% 0.13/0.39 tptp_fun_B_4: $i)).
% 0.13/0.39 tff(union_type, type, (
% 0.13/0.39 union: ( $i * $i ) > $i)).
% 0.13/0.39 tff(member_type, type, (
% 0.13/0.39 member: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_D_0_type, type, (
% 0.13/0.39 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,assumption,(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[B: $i, C: $i] : trans(trans(monotonicity(rewrite((subset(B, C) & subset(C, B)) <=> (~((~subset(B, C)) | (~subset(C, B))))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))), rewrite(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))), rewrite((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(7,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))) <=> (B!4 = union(C!3, D!2))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~(((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))) <=> (B!4 = union(C!3, D!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.39 tff(14,assumption,(~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))), introduced(assumption)).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | subset(D!2, B!4)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (subset(D!2, B!4)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | subset(C!3, B!4)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (subset(C!3, B!4)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5))) <=> (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))))) <=> (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))) <=> (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> ((subset(C, B) & subset(D, B)) & ![E: $i] : ((subset(C, E) & subset(D, E)) => subset(B, E))))) <=> (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,axiom,(~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> ((subset(C, B) & subset(D, B)) & ![E: $i] : ((subset(C, E) & subset(D, E)) => subset(B, E))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th56')).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))),
% 0.13/0.40 inference(and_elim,[status(thm)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (~(B!4 = union(C!3, D!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[33, 18, 16, 1])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))) <=> (B!4 = union(C!3, D!2))) | ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))) | (B!4 = union(C!3, D!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))) <=> (B!4 = union(C!3, D!2))) | ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 13])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(41,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,(
% 0.13/0.40 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.13/0.40 inference(skolemize,[status(sab)],[42])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (union(D!2, C!3) = union(C!3, D!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (union(C!3, D!2) = union(D!2, C!3)),
% 0.13/0.40 inference(symmetry,[status(thm)],[46])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (subset(D!2, union(C!3, D!2)) <=> subset(D!2, union(D!2, C!3))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (subset(D!2, union(D!2, C!3)) <=> subset(D!2, union(C!3, D!2))),
% 0.13/0.40 inference(symmetry,[status(thm)],[48])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (^[B: $i, C: $i] : refl(subset(B, union(B, C)) <=> subset(B, union(B, C)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(53,axiom,(![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_of_union')).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.40 tff(55,plain,(
% 0.13/0.40 ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.13/0.40 inference(skolemize,[status(sab)],[54])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(D!2, union(D!2, C!3))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (subset(D!2, union(D!2, C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (subset(D!2, union(C!3, D!2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(C!3, union(C!3, D!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (subset(C!3, union(C!3, D!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 14])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))) <=> ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (subset(B!4, union(C!3, D!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[66, 63, 61, 59])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ((~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))) | (~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 ((~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))) | (~subset(union(C!3, D!2), B!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (~subset(union(C!3, D!2), B!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[69, 37])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (^[B: $i, C: $i, D: $i] : refl((subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(D, C)) <=> (~((~subset(B, C)) | (~subset(D, C))))), ((~(subset(B, C) & subset(D, C))) <=> (~(~((~subset(B, C)) | (~subset(D, C))))))), rewrite((~(~((~subset(B, C)) | (~subset(D, C))))) <=> ((~subset(B, C)) | (~subset(D, C)))), ((~(subset(B, C) & subset(D, C))) <=> ((~subset(B, C)) | (~subset(D, C))))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)))), rewrite((((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(D, C)) => subset(union(B, D), C)) <=> ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (![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))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.41 tff(78,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_subset')).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.13/0.41 tff(81,plain,(
% 0.13/0.41 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.13/0.41 inference(skolemize,[status(sab)],[80])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 ((subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4))) <=> ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.13/0.41 inference(transitivity,[status(thm)],[86, 84])).
% 0.13/0.41 tff(88,plain,
% 0.13/0.41 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[89, 83, 18, 16, 70])).
% 0.13/0.41 tff(91,plain,(((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[91, 1])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(95,plain,
% 0.13/0.41 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) <=> (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(96,plain,
% 0.13/0.41 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(C!3, E) & subset(D!2, E)) <=> (~((~subset(C!3, E)) | (~subset(D!2, E))))), ((~(subset(C!3, E) & subset(D!2, E))) <=> (~(~((~subset(C!3, E)) | (~subset(D!2, E))))))), rewrite((~(~((~subset(C!3, E)) | (~subset(D!2, E))))) <=> ((~subset(C!3, E)) | (~subset(D!2, E)))), ((~(subset(C!3, E) & subset(D!2, E))) <=> ((~subset(C!3, E)) | (~subset(D!2, E))))), (((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> (((~subset(C!3, E)) | (~subset(D!2, E))) | subset(B!4, E)))), rewrite((((~subset(C!3, E)) | (~subset(D!2, E))) | subset(B!4, E)) <=> (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))), (((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 (![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[96])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E))) <=> (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.13/0.41 tff(99,plain,
% 0.13/0.41 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E))) <=> (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[98, 95])).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[99])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[100, 94])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.41 ((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))),
% 0.13/0.41 inference(and_elim,[status(thm)],[31])).
% 0.13/0.41 tff(103,plain,
% 0.13/0.41 ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.13/0.41 tff(104,plain,
% 0.13/0.41 ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.13/0.41 tff(105,plain,
% 0.13/0.41 (B!4 = union(C!3, D!2)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[104, 92])).
% 0.13/0.41 tff(106,plain,
% 0.13/0.41 (union(C!3, D!2) = B!4),
% 0.13/0.41 inference(symmetry,[status(thm)],[105])).
% 0.13/0.41 tff(107,plain,
% 0.13/0.41 (union(D!2, C!3) = B!4),
% 0.13/0.41 inference(transitivity,[status(thm)],[46, 106])).
% 0.13/0.41 tff(108,plain,
% 0.13/0.41 (subset(D!2, union(D!2, C!3)) <=> subset(D!2, B!4)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.13/0.41 tff(109,plain,
% 0.13/0.41 (subset(D!2, B!4) <=> subset(D!2, union(D!2, C!3))),
% 0.13/0.41 inference(symmetry,[status(thm)],[108])).
% 0.13/0.41 tff(110,plain,
% 0.13/0.41 ((~subset(D!2, B!4)) <=> (~subset(D!2, union(D!2, C!3)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.13/0.41 tff(111,plain,
% 0.13/0.41 (subset(C!3, union(C!3, D!2)) <=> subset(C!3, B!4)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.13/0.41 tff(112,plain,
% 0.13/0.41 (subset(C!3, B!4)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[61, 111])).
% 0.13/0.41 tff(113,plain,
% 0.13/0.41 (~subset(D!2, B!4)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[33, 112, 105, 1])).
% 0.13/0.41 tff(114,plain,
% 0.13/0.41 (~subset(D!2, union(D!2, C!3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.13/0.41 tff(115,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[58, 114])).
% 0.13/0.41 tff(116,plain,(~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(117,plain,
% 0.13/0.41 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | subset(D!2, E!5)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(118,plain,
% 0.13/0.41 (subset(D!2, E!5)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.13/0.41 tff(119,plain,
% 0.13/0.41 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | subset(C!3, E!5)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(120,plain,
% 0.13/0.41 (subset(C!3, E!5)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.13/0.41 tff(121,plain,
% 0.13/0.41 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | (~subset(B!4, E!5))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(122,plain,
% 0.13/0.41 (~subset(B!4, E!5)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.13/0.41 tff(123,assumption,(B!4 = union(C!3, D!2)), introduced(assumption)).
% 0.13/0.41 tff(124,plain,
% 0.13/0.41 (union(C!3, D!2) = B!4),
% 0.13/0.41 inference(symmetry,[status(thm)],[123])).
% 0.13/0.41 tff(125,plain,
% 0.13/0.41 (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> member(tptp_fun_D_0(E!5, B!4), B!4)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[124])).
% 0.13/0.41 tff(126,plain,
% 0.13/0.41 (member(tptp_fun_D_0(E!5, B!4), B!4) <=> member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2))),
% 0.13/0.41 inference(symmetry,[status(thm)],[125])).
% 0.13/0.41 tff(127,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(128,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.13/0.41 tff(129,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(130,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.13/0.41 tff(131,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[130, 128])).
% 0.13/0.41 tff(132,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(133,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.13/0.41 tff(134,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(135,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(136,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[135])).
% 0.13/0.41 tff(137,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.13/0.41 tff(138,plain,
% 0.13/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.13/0.41 tff(139,plain,
% 0.13/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.13/0.41 tff(140,plain,(
% 0.13/0.41 ![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)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[139])).
% 0.13/0.41 tff(141,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.13/0.41 tff(142,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.13/0.41 tff(143,plain,
% 0.13/0.41 ((~![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, E!5)) | ![D: $i] : ((~member(D, B!4)) | member(D, E!5)))) | (~(subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(144,plain,
% 0.13/0.42 (~((~((~subset(B!4, E!5)) | ![D: $i] : ((~member(D, B!4)) | member(D, E!5)))) | (~(subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.13/0.42 tff(145,plain,
% 0.13/0.42 (((~((~subset(B!4, E!5)) | ![D: $i] : ((~member(D, B!4)) | member(D, E!5)))) | (~(subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)))))) | (subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(146,plain,
% 0.13/0.42 (subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.13/0.42 tff(147,plain,
% 0.13/0.42 ((~(subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5))))) | subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(148,plain,
% 0.13/0.42 ((~(subset(B!4, E!5) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5))))) | (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[147, 122])).
% 0.13/0.42 tff(149,plain,
% 0.13/0.42 (~((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[148, 146])).
% 0.13/0.42 tff(150,plain,
% 0.13/0.42 (((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)) | member(tptp_fun_D_0(E!5, B!4), B!4)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(151,plain,
% 0.13/0.42 (member(tptp_fun_D_0(E!5, B!4), B!4)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.13/0.42 tff(152,plain,
% 0.13/0.42 (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[151, 126])).
% 0.13/0.42 tff(153,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(154,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[153])).
% 0.13/0.42 tff(155,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(156,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(157,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[156])).
% 0.13/0.42 tff(158,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.13/0.42 tff(159,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.13/0.42 tff(160,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.13/0.42 tff(161,plain,(
% 0.13/0.42 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[160])).
% 0.13/0.42 tff(162,plain,
% 0.13/0.42 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.13/0.42 tff(163,plain,
% 0.13/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 ((member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), D!2) | member(tptp_fun_D_0(E!5, B!4), C!3))) <=> (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), D!2) | member(tptp_fun_D_0(E!5, B!4), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[164])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), D!2) | member(tptp_fun_D_0(E!5, B!4), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[165, 163])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), D!2) | member(tptp_fun_D_0(E!5, B!4), C!3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 (member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[168, 162])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ((~![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(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))) | (~(subset(C!3, E!5) | (~((~member(tptp_fun_D_0(E!5, C!3), C!3)) | member(tptp_fun_D_0(E!5, C!3), E!5)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 (~((~((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))) | (~(subset(C!3, E!5) | (~((~member(tptp_fun_D_0(E!5, C!3), C!3)) | member(tptp_fun_D_0(E!5, C!3), E!5))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[170, 142])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 (((~((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))) | (~(subset(C!3, E!5) | (~((~member(tptp_fun_D_0(E!5, C!3), C!3)) | member(tptp_fun_D_0(E!5, C!3), E!5)))))) | ((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 ((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 ((~((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))) | (~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 ((~((~subset(C!3, E!5)) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5)))) | ![D: $i] : ((~member(D, C!3)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[174, 120])).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 (![D: $i] : ((~member(D, C!3)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[175, 173])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 (((~member(tptp_fun_D_0(E!5, B!4), B!4)) | member(tptp_fun_D_0(E!5, B!4), E!5)) | (~member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(178,plain,
% 0.21/0.42 (~member(tptp_fun_D_0(E!5, B!4), E!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[177, 149])).
% 0.21/0.42 tff(179,plain,
% 0.21/0.42 (((~![D: $i] : ((~member(D, C!3)) | member(D, E!5))) | ((~member(tptp_fun_D_0(E!5, B!4), C!3)) | member(tptp_fun_D_0(E!5, B!4), E!5))) <=> ((~![D: $i] : ((~member(D, C!3)) | member(D, E!5))) | (~member(tptp_fun_D_0(E!5, B!4), C!3)) | member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(180,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, C!3)) | member(D, E!5))) | ((~member(tptp_fun_D_0(E!5, B!4), C!3)) | member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(181,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, C!3)) | member(D, E!5))) | (~member(tptp_fun_D_0(E!5, B!4), C!3)) | member(tptp_fun_D_0(E!5, B!4), E!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.42 tff(182,plain,
% 0.21/0.42 (~member(tptp_fun_D_0(E!5, B!4), C!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[181, 178, 176])).
% 0.21/0.42 tff(183,plain,
% 0.21/0.42 ((~![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, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))) | (~(subset(D!2, E!5) | (~((~member(tptp_fun_D_0(E!5, D!2), D!2)) | member(tptp_fun_D_0(E!5, D!2), E!5)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(184,plain,
% 0.21/0.42 (~((~((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))) | (~(subset(D!2, E!5) | (~((~member(tptp_fun_D_0(E!5, D!2), D!2)) | member(tptp_fun_D_0(E!5, D!2), E!5))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[183, 142])).
% 0.21/0.42 tff(185,plain,
% 0.21/0.42 (((~((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))) | (~(subset(D!2, E!5) | (~((~member(tptp_fun_D_0(E!5, D!2), D!2)) | member(tptp_fun_D_0(E!5, D!2), E!5)))))) | ((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(186,plain,
% 0.21/0.42 ((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.21/0.42 tff(187,plain,
% 0.21/0.42 ((~((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))) | (~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(188,plain,
% 0.21/0.42 ((~((~subset(D!2, E!5)) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5)))) | ![D: $i] : ((~member(D, D!2)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[187, 118])).
% 0.21/0.42 tff(189,plain,
% 0.21/0.42 (![D: $i] : ((~member(D, D!2)) | member(D, E!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[188, 186])).
% 0.21/0.42 tff(190,plain,
% 0.21/0.42 (((~![D: $i] : ((~member(D, D!2)) | member(D, E!5))) | ((~member(tptp_fun_D_0(E!5, B!4), D!2)) | member(tptp_fun_D_0(E!5, B!4), E!5))) <=> ((~![D: $i] : ((~member(D, D!2)) | member(D, E!5))) | (~member(tptp_fun_D_0(E!5, B!4), D!2)) | member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(191,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, D!2)) | member(D, E!5))) | ((~member(tptp_fun_D_0(E!5, B!4), D!2)) | member(tptp_fun_D_0(E!5, B!4), E!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(192,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, D!2)) | member(D, E!5))) | (~member(tptp_fun_D_0(E!5, B!4), D!2)) | member(tptp_fun_D_0(E!5, B!4), E!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.42 tff(193,plain,
% 0.21/0.42 (~member(tptp_fun_D_0(E!5, B!4), D!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[192, 178, 189])).
% 0.21/0.42 tff(194,plain,
% 0.21/0.42 ((~(member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))) | member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(195,plain,
% 0.21/0.43 (~(member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[194, 193, 182])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)))) | (~member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2))) | (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(E!5, B!4), C!3) | member(tptp_fun_D_0(E!5, B!4), D!2)))) | (~member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 (~member(tptp_fun_D_0(E!5, B!4), union(C!3, D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[197, 169])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[198, 152])).
% 0.21/0.43 tff(200,plain,(~(B!4 = union(C!3, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 200])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 (![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[62, 201])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 (((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))) <=> ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[205, 202, 122, 120, 118])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------