%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET598+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET598+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:31:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_2_type, type, (
% 0.12/0.37 tptp_fun_D_2: $i)).
% 0.12/0.37 tff(tptp_fun_E_5_type, type, (
% 0.12/0.37 tptp_fun_E_5: $i)).
% 0.12/0.37 tff(tptp_fun_C_3_type, type, (
% 0.12/0.37 tptp_fun_C_3: $i)).
% 0.12/0.37 tff(tptp_fun_B_4_type, type, (
% 0.12/0.37 tptp_fun_B_4: $i)).
% 0.12/0.37 tff(intersection_type, type, (
% 0.12/0.37 intersection: ( $i * $i ) > $i)).
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_0_type, type, (
% 0.12/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,assumption,(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))) <=> (B!4 = intersection(C!3, D!2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~(((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))) <=> (B!4 = intersection(C!3, D!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,assumption,(~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))), introduced(assumption)).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | subset(B!4, D!2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (subset(B!4, D!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | subset(B!4, C!3)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (subset(B!4, C!3)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4))) <=> (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[21, 19])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))))) <=> (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))) <=> (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> ((subset(B, C) & subset(B, D)) & ![E: $i] : ((subset(E, C) & subset(E, D)) => subset(E, B))))) <=> (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,axiom,(~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> ((subset(B, C) & subset(B, D)) & ![E: $i] : ((subset(E, C) & subset(E, D)) => subset(E, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th57')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~(B!4 = intersection(C!3, D!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 18, 16, 1])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))) <=> (B!4 = intersection(C!3, D!2))) | ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))) | (B!4 = intersection(C!3, D!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))) <=> (B!4 = intersection(C!3, D!2))) | ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 13])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[42])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(D!2, C!3) = intersection(C!3, D!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.12/0.38 inference(symmetry,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (subset(intersection(C!3, D!2), D!2) <=> subset(intersection(D!2, C!3), D!2)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (subset(intersection(D!2, C!3), D!2) <=> subset(intersection(C!3, D!2), D!2)),
% 0.12/0.38 inference(symmetry,[status(thm)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl(subset(intersection(B, C), B) <=> subset(intersection(B, C), B))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(53,axiom,(![B: $i, C: $i] : subset(intersection(B, C), B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_is_subset')).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.38 tff(55,plain,(
% 0.12/0.38 ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.38 inference(skolemize,[status(sab)],[54])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(D!2, C!3), D!2)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (subset(intersection(D!2, C!3), D!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (subset(intersection(C!3, D!2), D!2)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(C!3, D!2), C!3)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (subset(intersection(C!3, D!2), C!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[62, 14])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))) <=> ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (subset(intersection(C!3, D!2), B!4)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[66, 63, 61, 59])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 ((~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))) | (~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 ((~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))) | (~subset(B!4, intersection(C!3, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 (~subset(B!4, intersection(C!3, D!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[69, 37])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (^[B: $i, C: $i, D: $i] : refl((subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))) <=> ![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(B, D)) <=> (~((~subset(B, C)) | (~subset(B, D))))), ((~(subset(B, C) & subset(B, D))) <=> (~(~((~subset(B, C)) | (~subset(B, D))))))), rewrite((~(~((~subset(B, C)) | (~subset(B, D))))) <=> ((~subset(B, C)) | (~subset(B, D)))), ((~(subset(B, C) & subset(B, D))) <=> ((~subset(B, C)) | (~subset(B, D))))), (((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> (((~subset(B, C)) | (~subset(B, D))) | subset(B, intersection(C, D))))), rewrite((((~subset(B, C)) | (~subset(B, D))) | subset(B, intersection(C, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))), (((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D))) <=> ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.12/0.39 tff(78,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_subsets')).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.12/0.39 tff(81,plain,(
% 0.12/0.39 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[80])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2))) <=> ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 83, 18, 16, 70])).
% 0.20/0.39 tff(91,plain,(((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[91, 1])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) <=> (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(E, C!3) & subset(E, D!2)) <=> (~((~subset(E, C!3)) | (~subset(E, D!2))))), ((~(subset(E, C!3) & subset(E, D!2))) <=> (~(~((~subset(E, C!3)) | (~subset(E, D!2))))))), rewrite((~(~((~subset(E, C!3)) | (~subset(E, D!2))))) <=> ((~subset(E, C!3)) | (~subset(E, D!2)))), ((~(subset(E, C!3) & subset(E, D!2))) <=> ((~subset(E, C!3)) | (~subset(E, D!2))))), (((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> (((~subset(E, C!3)) | (~subset(E, D!2))) | subset(E, B!4)))), rewrite((((~subset(E, C!3)) | (~subset(E, D!2))) | subset(E, B!4)) <=> (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))), (((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4))) <=> (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4))) <=> (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[98, 95])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[100, 94])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 ((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[31])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (B!4 = intersection(C!3, D!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[104, 92])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (intersection(C!3, D!2) = B!4),
% 0.20/0.39 inference(symmetry,[status(thm)],[105])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (intersection(D!2, C!3) = B!4),
% 0.20/0.39 inference(transitivity,[status(thm)],[46, 106])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (subset(intersection(D!2, C!3), D!2) <=> subset(B!4, D!2)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 (subset(B!4, D!2) <=> subset(intersection(D!2, C!3), D!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[108])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 ((~subset(B!4, D!2)) <=> (~subset(intersection(D!2, C!3), D!2))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (subset(intersection(C!3, D!2), C!3) <=> subset(B!4, C!3)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (subset(B!4, C!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 111])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (~subset(B!4, D!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 112, 105, 1])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (~subset(intersection(D!2, C!3), D!2)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 114])).
% 0.20/0.39 tff(116,plain,(~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | subset(E!5, D!2)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (subset(E!5, D!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | subset(E!5, C!3)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(120,plain,
% 0.20/0.39 (subset(E!5, C!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | (~subset(E!5, B!4))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (~subset(E!5, B!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.20/0.39 tff(123,assumption,(B!4 = intersection(C!3, D!2)), introduced(assumption)).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 (intersection(C!3, D!2) = B!4),
% 0.20/0.39 inference(symmetry,[status(thm)],[123])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2)) <=> member(tptp_fun_D_0(B!4, E!5), B!4)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (member(tptp_fun_D_0(B!4, E!5), B!4) <=> member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))),
% 0.20/0.39 inference(symmetry,[status(thm)],[125])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 ((~member(tptp_fun_D_0(B!4, E!5), B!4)) <=> (~member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(129,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))))))) <=> ![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(131,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))))))) <=> ![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.39 tff(132,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))))))) <=> ![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)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.39 tff(133,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(134,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))))) <=> ![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.39 tff(135,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(136,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(137,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.39 tff(138,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')).
% 0.20/0.39 tff(139,plain,
% 0.20/0.39 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.40 tff(141,plain,(
% 0.20/0.40 ![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)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[140])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 ((~![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(E!5, B!4)) | ![D: $i] : ((~member(D, E!5)) | member(D, B!4)))) | (~(subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (~((~((~subset(E!5, B!4)) | ![D: $i] : ((~member(D, E!5)) | member(D, B!4)))) | (~(subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.20/0.40 tff(146,plain,
% 0.20/0.40 (((~((~subset(E!5, B!4)) | ![D: $i] : ((~member(D, E!5)) | member(D, B!4)))) | (~(subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)))))) | (subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 (subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 ((~(subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4))))) | subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 ((~(subset(E!5, B!4) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4))))) | (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[148, 122])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 (~((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[149, 147])).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 (((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)) | (~member(tptp_fun_D_0(B!4, E!5), B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 (~member(tptp_fun_D_0(B!4, E!5), B!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.40 tff(153,plain,
% 0.20/0.40 (~member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[152, 127])).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.40 tff(158,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(159,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.20/0.40 tff(160,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.40 tff(161,plain,(
% 0.20/0.40 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[160])).
% 0.20/0.40 tff(162,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.20/0.40 tff(163,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.20/0.40 tff(164,plain,
% 0.20/0.40 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))) <=> member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(165,plain,
% 0.20/0.40 (~(((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))) <=> member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.40 tff(166,plain,
% 0.20/0.40 ((~![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(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))) | (~(subset(E!5, C!3) | (~((~member(tptp_fun_D_0(C!3, E!5), E!5)) | member(tptp_fun_D_0(C!3, E!5), C!3)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(167,plain,
% 0.20/0.40 (~((~((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))) | (~(subset(E!5, C!3) | (~((~member(tptp_fun_D_0(C!3, E!5), E!5)) | member(tptp_fun_D_0(C!3, E!5), C!3))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[166, 143])).
% 0.20/0.40 tff(168,plain,
% 0.20/0.40 (((~((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))) | (~(subset(E!5, C!3) | (~((~member(tptp_fun_D_0(C!3, E!5), E!5)) | member(tptp_fun_D_0(C!3, E!5), C!3)))))) | ((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(169,plain,
% 0.20/0.40 ((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.40 tff(170,plain,
% 0.20/0.40 ((~((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))) | (~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(171,plain,
% 0.20/0.40 ((~((~subset(E!5, C!3)) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3)))) | ![D: $i] : ((~member(D, E!5)) | member(D, C!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[170, 120])).
% 0.20/0.40 tff(172,plain,
% 0.20/0.40 (![D: $i] : ((~member(D, E!5)) | member(D, C!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[171, 169])).
% 0.20/0.40 tff(173,plain,
% 0.20/0.40 (((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), B!4)) | member(tptp_fun_D_0(B!4, E!5), E!5)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(174,plain,
% 0.20/0.40 (member(tptp_fun_D_0(B!4, E!5), E!5)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[173, 150])).
% 0.20/0.40 tff(175,plain,
% 0.20/0.40 (((~![D: $i] : ((~member(D, E!5)) | member(D, C!3))) | ((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), C!3))) <=> ((~![D: $i] : ((~member(D, E!5)) | member(D, C!3))) | (~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), C!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(176,plain,
% 0.20/0.40 ((~![D: $i] : ((~member(D, E!5)) | member(D, C!3))) | ((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), C!3))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(177,plain,
% 0.20/0.40 ((~![D: $i] : ((~member(D, E!5)) | member(D, C!3))) | (~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), C!3)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.40 tff(178,plain,
% 0.20/0.40 (member(tptp_fun_D_0(B!4, E!5), C!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[177, 174, 172])).
% 0.20/0.40 tff(179,plain,
% 0.20/0.40 ((~![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(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))) | (~(subset(E!5, D!2) | (~((~member(tptp_fun_D_0(D!2, E!5), E!5)) | member(tptp_fun_D_0(D!2, E!5), D!2)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(180,plain,
% 0.20/0.40 (~((~((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))) | (~(subset(E!5, D!2) | (~((~member(tptp_fun_D_0(D!2, E!5), E!5)) | member(tptp_fun_D_0(D!2, E!5), D!2))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[179, 143])).
% 0.20/0.40 tff(181,plain,
% 0.20/0.40 (((~((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))) | (~(subset(E!5, D!2) | (~((~member(tptp_fun_D_0(D!2, E!5), E!5)) | member(tptp_fun_D_0(D!2, E!5), D!2)))))) | ((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(182,plain,
% 0.20/0.40 ((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.40 tff(183,plain,
% 0.20/0.40 ((~((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))) | (~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(184,plain,
% 0.20/0.40 ((~((~subset(E!5, D!2)) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2)))) | ![D: $i] : ((~member(D, E!5)) | member(D, D!2))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[183, 118])).
% 0.20/0.40 tff(185,plain,
% 0.20/0.40 (![D: $i] : ((~member(D, E!5)) | member(D, D!2))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[184, 182])).
% 0.20/0.40 tff(186,plain,
% 0.20/0.40 (((~![D: $i] : ((~member(D, E!5)) | member(D, D!2))) | ((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), D!2))) <=> ((~![D: $i] : ((~member(D, E!5)) | member(D, D!2))) | (~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), D!2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(187,plain,
% 0.20/0.40 ((~![D: $i] : ((~member(D, E!5)) | member(D, D!2))) | ((~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), D!2))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(188,plain,
% 0.20/0.40 ((~![D: $i] : ((~member(D, E!5)) | member(D, D!2))) | (~member(tptp_fun_D_0(B!4, E!5), E!5)) | member(tptp_fun_D_0(B!4, E!5), D!2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.40 tff(189,plain,
% 0.20/0.40 (member(tptp_fun_D_0(B!4, E!5), D!2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[188, 174, 185])).
% 0.20/0.41 tff(190,plain,
% 0.20/0.41 ((~((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2)))) | (~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(191,plain,
% 0.20/0.41 (~((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[190, 189, 178])).
% 0.20/0.41 tff(192,plain,
% 0.20/0.41 ((((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))) <=> member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))) | ((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))) | member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(193,plain,
% 0.20/0.41 ((((~member(tptp_fun_D_0(B!4, E!5), C!3)) | (~member(tptp_fun_D_0(B!4, E!5), D!2))) <=> member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))) | member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.41 tff(194,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!4, E!5), intersection(C!3, D!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[193, 165])).
% 0.20/0.41 tff(195,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[194, 153])).
% 0.20/0.41 tff(196,plain,(~(B!4 = intersection(C!3, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(197,plain,
% 0.20/0.41 (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[104, 196])).
% 0.20/0.41 tff(198,plain,
% 0.20/0.41 (![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[62, 197])).
% 0.20/0.41 tff(199,plain,
% 0.20/0.41 (((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))) <=> ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(200,plain,
% 0.20/0.41 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(201,plain,
% 0.20/0.41 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.41 tff(202,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[201, 198, 122, 120, 118])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------